Journal articles: 'Model of coupled harmonic oscillators'

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Wang, Shijiao, Xiao San Ma, and Mu-Tian Cheng. "Multipartite Entanglement Generation in a Structured Environment." Entropy 22, no. 2 (February 7, 2020): 191. http://dx.doi.org/10.3390/e22020191.

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In this paper, we investigate the entanglement generation of n-qubit states in a model consisting of n independent qubits, each coupled to a harmonic oscillator which is in turn coupled to a bath of N additional harmonic oscillators with nearest-neighbor coupling. With analysis, we can find that the steady multipartite entanglement with different values can be generated after a long-time evolution for different sizes of the quantum system. Under weak coupling between the system and the harmonic oscillator, multipartite entanglement can monotonically increase from zero to a stable value. Under strong coupling, multipartite entanglement generation shows a speed-up increase accompanied by some oscillations as non-Markovian behavior. Our results imply that the strong coupling between the harmonic oscillator and the N additional harmonic oscillators, and the large size of the additional oscillators will enhance non-Markovian dynamics and make it take a very long time for the entanglement to reach a stable value. Meanwhile, the couplings between the additional harmonic oscillators and the decay rate of additional harmonic oscillators have almost no effect on the multipartite entanglement generation. Finally, the entanglement generation of the additional harmonic oscillators is also discussed.

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Laszuk, Dawid, Jose O. Cadenas, and Slawomir J. Nasuto. "KurSL: Model of Anharmonic Coupled Oscillations Based on Kuramoto Coupling and Sturm–Liouville Problem." Advances in Data Science and Adaptive Analysis 10, no. 02 (April 2018): 1840002. http://dx.doi.org/10.1142/s2424922x18400028.

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Physiological signaling is often oscillatory and shows nonlinearity due to complex interactions of underlying processes or signal propagation delays. This is particularly evident in case of brain activity which is subject to various feedback loop interactions between different brain structures, that coordinate their activity to support normal function. In order to understand such signaling in health and disease, methods are needed that can deal with such complex oscillatory phenomena. In this paper, a data-driven method for analyzing anharmonic oscillations is introduced. The KurSL model incorporates two well-studied components, which in the past have been used separately to analyze oscillatory behavior. The Sturm–Liouville equations describe a form of a general oscillation, and the Kuramoto coupling model represents a set of oscillators interacting in the phase domain. Integration of these components provides a flexible framework for capturing complex interactions of oscillatory processes of more general form than the most commonly used harmonic oscillators. The paper introduces a mathematical framework of the KurSL model and analyzes its behavior for a variety of parameter ranges. The significance of the model follows from its ability to provide information about coupled oscillators’ phase dynamics directly from the time series. KurSL offers a novel framework for analyzing a wide range of complex oscillatory behaviors, such as the ones encountered in physiological signals.

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Velichko, Andrey, Maksim Belyaev, Vadim Putrolaynen, Alexander Pergament, and Valentin Perminov. "Switching dynamics of single and coupled VO2-based oscillators as elements of neural networks." International Journal of Modern Physics B 31, no. 02 (January 18, 2017): 1650261. http://dx.doi.org/10.1142/s0217979216502611.

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In the present paper, we report on the switching dynamics of both single and coupled VO2-based oscillators, with resistive and capacitive coupling, and explore the capability of their application in oscillatory neural networks. Based on these results, we further select an adequate SPICE model to describe the modes of operation of coupled oscillator circuits. Physical mechanisms influencing the time of forward and reverse electrical switching, that determine the applicability limits of the proposed model, are identified. For the resistive coupling, it is shown that synchronization takes place at a certain value of the coupling resistance, though it is unstable and a synchronization failure occurs periodically. For the capacitive coupling, two synchronization modes, with weak and strong coupling, are found. The transition between these modes is accompanied by chaotic oscillations. A decrease in the width of the spectrum harmonics in the weak-coupling mode, and its increase in the strong-coupling one, is detected. The dependences of frequencies and phase differences of the coupled oscillatory circuits on the coupling capacitance are found. Examples of operation of coupled VO2 oscillators as a central pattern generator are demonstrated.

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HAUPTMANN, C., F. KAISER, and C. EICHWALD. "SIGNAL TRANSFER AND STOCHASTIC RESONANCE IN COUPLED NONLINEAR SYSTEMS." International Journal of Bifurcation and Chaos 09, no. 06 (June 1999): 1159–67. http://dx.doi.org/10.1142/s0218127499000808.

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A model of coupled nonlinear oscillators is discussed, wherein Langevin-type bistable systems are combined with self-sustained oscillators. An external harmonic signal is coupled in a subthreshold manner into the bistable systems at the initial stage of the signal chain. Signal transfer through the oscillators is studied under the influence of noise. Different noise contributions, including spatially-incoherent and spatially-coherent noise sources are considered. Results reveal a stochastic resonance kind of behavior at different stages of the signal transfer, specifically the harmonic signal is transduced through the whole system of coupled oscillators. The combined action of spatially-incoherent and spatially-coherent noise exhibits constructive as well as destructive influences on signal amplification.

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Li, Wei, and Gen-Xiang Chen. "Classical coupled oscillators model of the rational harmonic mode locked laser." Journal of Applied Physics 100, no. 4 (August 15, 2006): 043115. http://dx.doi.org/10.1063/1.2335598.

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Gallo, James Mendoza, and Bienvenido Masirin Butanas Jr. "Quantum Propagator Derivation for the Ring of Four Harmonically Coupled Oscillators." Jurnal Penelitian Fisika dan Aplikasinya (JPFA) 9, no. 2 (December 31, 2019): 92. http://dx.doi.org/10.26740/jpfa.v9n2.p92-104.

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The ring model of the coupled oscillator has enormously studied from the perspective of quantum mechanics. The research efforts on this system contribute to fully grasp the concepts of energy transport, dissipation, among others, in mesoscopic and condensed matter systems. In this research, the dynamics of the quantum propagator for the ring of oscillators was analyzed anew. White noise analysis was applied to derive the quantum mechanical propagator for a ring of four harmonically coupled oscillators. The process was done after performing four successive coordinate transformations obtaining four separated Lagrangian of a one-dimensional harmonic oscillator. Then, the individual propagator was evaluated via white noise path integration where the full propagator is expressed as the product of the individual propagators. In particular, the frequencies of the first two propagators correspond to degenerate normal mode frequencies, while the other two correspond to non-degenerate normal mode frequencies. The full propagator was expressed in its symmetric form to extract the energy spectrum and the wave function.

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Komarov, M., and A. Pikovsky. "The Kuramoto model of coupled oscillators with a bi-harmonic coupling function." Physica D: Nonlinear Phenomena 289 (December 2014): 18–31. http://dx.doi.org/10.1016/j.physd.2014.09.002.

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Golovinski, P. A., A. V. Yakovets, and E. S. Khramov. "Application of the coupled classical oscillators model to the Fano resonance build-up in a plasmonic nanosystem." Computer Optics 43, no. 5 (October 2019): 747–55. http://dx.doi.org/10.18287/2412-6179-2019-43-5-747-755.

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We study the excitation dynamics of Fano resonance within the classical model framework of two linear coupled oscillators. An exact solution for the model with a damped harmonic force is obtained. Details of the growth of a Fano profile under the harmonic excitation are shown. For an incident ultra-wideband pulse, the reaction of the system becomes universal and coincides with the time-dependent response function. The results of numerical calculations clarify two alternative ways for the experimental measurement of complete characteristics of the system: via direct observation of the system response to a monochromatic force by frequency scanning or recording the time-dependent response to a d-pulse. As a specific example, the time-dependent excitation in a system consisting of a quantum dot and a metal nanoparticle is calculated. Then, we show the use of an extended model of damped oscillators with radiative correction to describe the plasmon Fano resonance build-up when a femtosecond laser pulse is scattered by a nanoantenna.

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ROMEO, FRANCESCO, and GIUSEPPE REGA. "PROPAGATION PROPERTIES OF BI-COUPLED NONLINEAR OSCILLATORY CHAINS: ANALYTICAL PREDICTION AND NUMERICAL VALIDATION." International Journal of Bifurcation and Chaos 18, no. 07 (July 2008): 1983–98. http://dx.doi.org/10.1142/s021812740802149x.

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Harmonic wave propagation in one-dimensional chains of nonlinear oscillators are investigated by means of nonlinear maps. The study extends previous results obtained for the mono-coupled oscillators to bi-coupled ones. The considered bi-coupled model refers to a chain of linearly coupled mechanical oscillators characterized by on-site cubic nonlinearities in both the longitudinal and rotational degrees of freedom. Pass, stop and complex regions are analytically determined for period-q orbits as they are governed by the eigenvalues of the linearized map arising from the relevant linear stability analysis. By varying the parameters governing both the coupling between the two d.o.f. and the nonlinearity, a variable scenario of propagation regions can be obtained, which includes the limit case of mono-coupled behavior. Theoretical predictions are validated through numerical results in terms of orbits, bifurcation diagrams and basins of attraction, obtained via nonlinear map iteration. They highlight a rich variety of regular and nonregular bounded solutions.

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Giraldi, F., and F. Petruccione. "Anomalies in Strongly Coupled Harmonic Quantum Brownian Motion II." Open Systems & Information Dynamics 20, no. 04 (November 25, 2013): 1350015. http://dx.doi.org/10.1142/s1230161213500157.

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The analysis of a strongly coupled harmonic quantum Brownian motion has been performed in [1] for a special class of spectral densities obtained as a generalization of the Drude model. In the present scenario, we extend the study of the strongly coupled harmonic quantum Brownian motion to regular spectral densities that are structured as sub-Ohmic at low frequencies and arbitrarily shaped at high frequencies. The bosonic environment is initially in the vacuum state unentangled from the coherent state of the main oscillator. As a generalization of the previous results, we obtain that the long time dynamics is determined uniquely by the initial condition and the low frequency structure of the spectral density. Also in the present framework, inverse power law regressions to the asymptotics appear. The position and the momentum tend to undamped oscillations. The number of excitations relaxes to its initial value with damped oscillations enveloped in inverse power law relaxations. For the momentum and the number of excitations the inverse power law decays become arbitrarily slow in critical configurations by approaching the upper bound of the sub-Ohmic regime. The critical frequencies of the main oscillator are determined by the first negative moment of the spectral densities. Differences with respect to the weak coupling regime arise.

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FAN, HONG-YI, and TONG-TONG WANG. "INVARIANT EIGEN-OPERATOR METHOD FOR SOLVING ENERGY GAP FOR SOME HAMILTONIANS IN MOLECULAR PHYSICS." International Journal of Modern Physics B 21, no. 12 (May 10, 2007): 1961–69. http://dx.doi.org/10.1142/s0217979207037156.

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We show that the recently proposed invariant eigen-operator method is particularly applicable to solving the energy levels for some Hamiltonians in molecular physics. These are tri-atom molecules, the identical d-dimensional coupled harmonic oscillators and the dissipative linear-chain molecular model etc. The calculation is more direct and simpler than the usual diagonalization method for dynamic Hamiltonians.

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Medjber, Salim, Salah Menouar, and Jeong Ryeol Choi. "Dynamical Invariant and Exact Mechanical Analyses for the Caldirola–Kanai Model of Dissipative Three Coupled Oscillators." Entropy 23, no. 7 (June 30, 2021): 837. http://dx.doi.org/10.3390/e23070837.

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We study the dynamical invariant for dissipative three coupled oscillators mainly from the quantum mechanical point of view. It is known that there are many advantages of the invariant quantity in elucidating mechanical properties of the system. We use such a property of the invariant operator in quantizing the system in this work. To this end, we first transform the invariant operator to a simple one by using a unitary operator in order that we can easily manage it. The invariant operator is further simplified through its diagonalization via three-dimensional rotations parameterized by three Euler angles. The coupling terms in the quantum invariant are eventually eliminated thanks to such a diagonalization. As a consequence, transformed quantum invariant is represented in terms of three independent simple harmonic oscillators which have unit masses. Starting from the wave functions in the transformed system, we have derived the full wave functions in the original system with the help of the unitary operators.

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Giraldi, F., and F. Petruccione. "Anomalies in Strongly Coupled Harmonic Quantum Brownian Motion." Open Systems & Information Dynamics 20, no. 01 (March 2013): 1350002. http://dx.doi.org/10.1142/s1230161213500029.

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The exact dynamics of a quantum damped harmonic oscillator coupled to a reservoir of boson modes has been formally described in terms of the coupling function, both in weak and strong coupling regime. In this scenario, we provide a further description of the exact dynamics through integral transforms. We focus on a special class of spectral densities, sub-ohmic at low frequencies, and including integrable divergencies referred to as photonic band gaps. The Drude form of the spectral densities is recovered as upper limit. Starting from special distributions of coherent states as external reservoir, the exact time evolution, described through Fox H-functions, shows long time inverse power law decays, departing from the exponential-like relaxations obtained for the Drude model. Different from the weak coupling regime, in the sub-ohmic condition, undamped oscillations plus inverse power law relaxations appear in the long time evolution of the observables position and momentum. Under the same condition, the number of excitations shows trapping of the population of the excited levels and oscillations enveloped in inverse power law relaxations. Similarly to the weak coupling regime, critical configurations give arbitrarily slow relaxations useful for the control of the dynamics. If compared to the value obtained in weak coupling condition, for strong couplings the critical frequency is enhanced by a factor 4.

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CUGLIANDOLO, L. F., G. S. LOZANO, and H. F. LOZZA. "ZERO-TEMPERATURE PHASE DIAGRAM OF DISSIPATIVE RANDOM ISING FERROMAGNETIC CHAINS." International Journal of Modern Physics B 20, no. 30n31 (December 20, 2006): 5219–23. http://dx.doi.org/10.1142/s0217979206036296.

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We study the zero-temperature critical behavior of dissipative quantum Ising spin chains of finite and infinite length. The spins interact with either constant or random nearest-neighbor ferro-magnetic couplings. They are also subject to a transverse field and coupled to an Ohmic bath of quantum harmonic oscillators. We analyze the coupled system performing Monte Carlo simulations on a classical two-dimensional counterpart model. We find that the coupling to the bath enhances the extent of the ordered phase, as it is known for mean-field spin-glass models. In the case of finite chains we show that a generalization of the Caldeira-Leggett localization transition exists.

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de Bettin, Federico, Alberto Cappellaro, and Luca Salasnich. "Action Functional for a Particle with Damping." Condensed Matter 4, no. 3 (September 10, 2019): 81. http://dx.doi.org/10.3390/condmat4030081.

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In this brief report we discuss the action functional of a particle with damping, showing that it can be obtained from the dissipative equation of motion through a modification which makes the new dissipative equation invariant for time reversal symmetry. This action functional is exactly the effective action of Caldeira-Leggett model but, in our approach, it is derived without the assumption that the particle is weakly coupled to a bath of infinite harmonic oscillators.

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Hab-Arrih, Radouan, Ahmed Jellal, and Abdeldjalil Merdaci. "Dynamics and redistribution of entanglement and coherence in three time-dependent coupled harmonic oscillators." International Journal of Geometric Methods in Modern Physics 18, no. 08 (May 8, 2021): 2150120. http://dx.doi.org/10.1142/s0219887821501206.

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We study the dynamics and redistribution of entanglement and coherence in three time-dependent coupled harmonic oscillators. We resolve the Schrödinger equation by using time-dependent Euler rotation together with a linear quench model to obtain the state of vacuum solution. Such state can be translated to the phase space picture to determine the Wigner distribution. We show that its Gaussian matrix [Formula: see text] can be used to directly cast the covariance matrix [Formula: see text]. To quantify the mixedness and entanglement of the state, one uses respectively linear and von Neumann entropies for three cases: fully symmetric, bi-symmetric and fully nonsymmetric. Then we determine the coherence, tripartite entanglement and local uncertainties and derive their dynamics. We show that the dynamics of all quantum information quantities are driven by the Ermakov modes. Finally, we use an homodyne detection to redistribute both resources of entanglement and coherence.

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Sasihithlu, Karthik. "Coupled harmonic oscillator model to describe surface-mode mediated heat transfer." Journal of Photonics for Energy 9, no. 03 (December 27, 2018): 1. http://dx.doi.org/10.1117/1.jpe.9.032709.

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Garcia Quijas, P. C., and L. M. Arevalo Aguilar. "A quantum coupler and the harmonic oscillator interacting with a reservoir: Defining the relative phase gate." Quantum Information and Computation 10, no. 3&4 (March 2010): 190–200. http://dx.doi.org/10.26421/qic10.3-4-2.

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In order to be able to study dissipation, the interaction between a single system and their environment was introduced in quantum mechanics. Master and quantum Langeving equations was derived. Moreover, decoherence has been studied using this approach. One of the most commonly used model in this research field is a single harmonic oscillator interacting with a reservoir. In this work we analytically solve this model, in the resonance case, using the evolution operator method. Then, we use this result to study a quantum coupler, which is a particular case where there are a finite number of harmonic oscillators interacting with the single one. After that, we focuses in the analisis of the conditional quantum dynamics of the quantum coupler (using the computational basis of two qubits) by choosing a proper interaction time. This conditional dynamics provides a realization of a new quantum phase gate, which we call the relative phase gate. To the best of our knowledge, this phase gate has not been previously defined or proposed.

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FAN, HONG-YI, HAO WU, and XUE-FEN XU. "VIBRATIONAL SPECTRUM FOR THE LINEAR LATTICE CHAIN GAINED BY VIRTUE OF THE "INVARIANT EIGEN-OPERATOR" METHOD." International Journal of Modern Physics B 19, no. 27 (October 30, 2005): 4073–80. http://dx.doi.org/10.1142/s0217979205032590.

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We propose an operator Hamiltonian (a ring of identically coupled harmonic oscillators) to describe the linear lattice chain with Born–von Karmann boundary condition. We apply the method of "invariant eigen-operator" to study this Hamiltonian and derive its invariant eigen-operator. The vibrational spectrum is thus obtained. This approach seems concise and direct and can be extended to tackle other Hamiltonian models.

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O'CONNELL, R. F. "BLACKBODY RADIATION: ROSETTA STONE OF HEAT BATH MODELS." Fluctuation and Noise Letters 07, no. 04 (December 2007): L483—L490. http://dx.doi.org/10.1142/s0219477507004124.

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The radiation field can be regarded as a collection of independent harmonic oscillators and, as such, constitutes a heat bath. Moreover, the known form of its interaction with charged particles provides a "rosetta stone" for deciding on and interpreting the correct interaction for the more general case of a quantum particle in an external potential and coupled to an arbitrary heat bath. In particular, combining QED with the machinery of stochastic physics, enables the usual scope of applications to be widened. We discuss blackbody radiation effects on: the equation of motion of a radiating electron (obtaining an equation of motion which is free from runaway solutions), anomalous diffusion, the spreading of a Gaussian wave packet, and decoherence effects due to zero-point oscillations. In addition, utilizing a formula we obtained for the free energy of an oscillator in a heat bath, enables us to determine all the quantum thermodynamic functions of interest (particularly in the areas of quantum information and nanophysics where small systems are involved) and from which we obtain temperature dependent Lamb shifts, quantum effects on the entropy at low temperature and implications for Nernst's law.

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Bell, Andrew, and Hero P. Wit. "The vibrating reed frequency meter: digital investigation of an early cochlear model." PeerJ 3 (October 13, 2015): e1333. http://dx.doi.org/10.7717/peerj.1333.

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The vibrating reed frequency meter, originally employed by Békésy and later by Wilson as a cochlear model, uses a set of tuned reeds to represent the cochlea’s graded bank of resonant elements and an elastic band threaded between them to provide nearest-neighbour coupling. Here the system, constructed of 21 reeds progressively tuned from 45 to 55 Hz, is simulated numerically as an elastically coupled bank of passive harmonic oscillators driven simultaneously by an external sinusoidal force. To uncover more detail, simulations were extended to 201 oscillators covering the range 1–2 kHz. Calculations mirror the results reported by Wilson and show expected characteristics such as traveling waves, phase plateaus, and a response with a broad peak at a forcing frequency just above the natural frequency. The system also displays additional fine-grain features that resemble those which have only recently been recognised in the cochlea. Thus, detailed analysis brings to light a secondary peak beyond the main peak, a set of closely spaced low-amplitude ripples, rapid rotation of phase as the driving frequency is swept, frequency plateaus, clustering, and waxing and waning of impulse responses. Further investigation shows that each reed’s vibrations are strongly localised, with small energy flow along the chain. The distinctive set of equally spaced ripples is an inherent feature which is found to be largely independent of boundary conditions. Although the vibrating reed model is functionally different to the standard transmission line, its cochlea-like properties make it an intriguing local oscillator model whose relevance to cochlear mechanics needs further investigation.

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Eberle, Henry, Slawomir J. Nasuto, and Yoshikatsu Hayashi. "Synchronization-based control for a collaborative robot." Royal Society Open Science 7, no. 12 (December 2020): 201267. http://dx.doi.org/10.1098/rsos.201267.

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This article introduces a new control scheme for controlling a robotic manipulator in a collaborative task, allowing it to respond proactively to its partner’s movements. Unlike conventional robotic systems, humans can operate in an unstructured, dynamic environment due to their ability to anticipate changes before they occur and react accordingly. Recreating this artificially by using a forward model would lead to the huge computational task of simulating a world full of complex nonlinear dynamics and autonomous human agents. In this study, a controller based on anticipating synchronization, where a ‘leader’ dynamical system is predicted by a coupled ‘follower’ with delayed self-feedback, is used to modify a robot’s dynamical behaviour to follow that of a series of leaky integrators and harmonic oscillators. This allows the robot (follower) to be coupled with a collaborative partner (leader) to anticipate its movements, without a complete model of its behaviour. This is tested by tasking a simulated Baxter robot with performing a collaborative manual coordination task with an autonomous partner under a range of feedback delay conditions, confirming its ability to anticipate using oscillators instead of a detailed forward model.

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Mendonça, Christovam, and Said R. Rabbani. "Anharmonic Lattice Vibrations and the Temperature Shift of Raman Spectral Lines." Zeitschrift für Naturforschung A 51, no. 5-6 (June 1, 1996): 716–20. http://dx.doi.org/10.1515/zna-1996-5-659.

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Abstract The temperature dependence of the average lattice mode frequency of a molecule undergoing librational motion in a quasi-harmonic potential has been calculated with the purpose of finding an explicit relationship between the observed shift of Raman spectral lines with temperature and the anharmonic term in the rotational potential. Calculations were carried out both for uncoupled and coupled oscillators. The equations obtained with this model provide good fittings for solid Cl2 and benzene data. This result can be applied to the analysis of the temperature dependence of NQR frequencies in molecular crystals.

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Galve, Fernando, and Roberta Zambrini. "Energy and information propagation in a finite coupled bosonic heat bath." International Journal of Quantum Information 12, no. 07n08 (November 2014): 1560022. http://dx.doi.org/10.1142/s0219749915600229.

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The finite coupled bosonic model of reservoir introduced by Vasile et al. [Phys. Rev. A 89 (2014) 022109] to characterize non-Markovianity, is used to study the different dissipative behaviors of a harmonic oscillator coupled to it when it is in resonance, close to resonance or far detuned. We show that information and energy exchange between system and heat bath go hand in hand because phonons are the carriers of both: in resonance free propagation of excitations is achieved, and therefore pure dissipation, while when far detuned the system can only correlate with the first oscillator in the bath's chain, leading to almost unitary evolution. In the intermediate situation, we show the penetration of correlations and the formation of oscillatory (dressed state) behavior, which lies at the root of non-Markovianity.

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Xiao-Ou, Wang, Li Chun-Fei, and Li Jun-Qing. "Surface second harmonic generation of chiral molecules using three-coupled-oscillator model." Chinese Physics 15, no. 11 (October 24, 2006): 2623–30. http://dx.doi.org/10.1088/1009-1963/15/11/028.

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Körner, Julia, Christopher F. Reiche, Bernd Büchner, Thomas Mühl, and Gerald Gerlach. "Employing electro-mechanical analogies for co-resonantly coupled cantilever sensors." Journal of Sensors and Sensor Systems 5, no. 2 (July 13, 2016): 245–59. http://dx.doi.org/10.5194/jsss-5-245-2016.

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Abstract. Understanding the behaviour of mechanical systems can be facilitated and improved by employing electro-mechanical analogies. These analogies enable the use of network analysis tools as well as purely analytical treatment of the mechanical system translated into an electric circuit. Recently, we developed a novel kind of sensor set-up based on two coupled cantilever beams with matched resonance frequencies (co-resonant coupling) and possible applications in magnetic force microscopy and cantilever magnetometry. In order to analyse the sensor's behaviour in detail, we describe it as an electric circuit model. Starting from a simplified coupled harmonic oscillator model with neglected damping, we gradually increase the complexity of the system by adding damping and interaction elements. For each stage, various features of the coupled system are discussed and compared to measured data obtained with a co-resonant sensor. Furthermore, we show that the circuit model can be used to derive sensor parameters which are essential for the evaluation of measured data. Finally, the much more complex circuit representation of a bending beam is discussed, revealing that the simplified circuit model of a coupled harmonic oscillator is a very good representation of the sensor system.

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PATEL, APOORVA. "OPTIMAL DATABASE SEARCH: WAVES AND CATALYSIS." International Journal of Quantum Information 04, no. 05 (October 2006): 815–25. http://dx.doi.org/10.1142/s0219749906002225.

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Grover's database search algorithm, although discovered in the context of quantum computation, can be implemented using any system that allows superposition of states. A physical realization of this algorithm is described using coupled simple harmonic oscillators, which can be exactly solved in both classical and quantum domains. Classical wave algorithms are far more stable against decoherence compared to their quantum counterparts. In addition to providing convenient demonstration models, they may have a role in practical situations, such as catalysis.

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Jiao, Xianfa, Wanyu Zhao, and Jinde Cao. "Phase Response Synchronization in Neuronal Population with Time-Varying Coupling Strength." Computational and Mathematical Methods in Medicine 2015 (2015): 1–6. http://dx.doi.org/10.1155/2015/816738.

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We present the dynamic model of global coupled neuronal population subject to external stimulus by the use of phase sensitivity function. We investigate the effect of time-varying coupling strength on the synchronized phase response of neural population subjected to external harmonic stimulus. For a time-periodic coupling strength, we found that the stimulus with increasing intensity or frequency can reinforce the phase response synchronization in neuronal population of the weakly coupled neural oscillators, and the neuronal population with stronger coupling strength has good adaptability to stimulus. When we consider the dynamics of coupling strength, we found that a strong stimulus can quickly cause the synchronization in the neuronal population, the degree of synchronization grows with the increasing stimulus intensity, and the period of synchronized oscillation induced by external stimulation is related to stimulus frequency.

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Nicu, Valentin Paul. "Revisiting an old concept: the coupled oscillator model for VCD. Part 1: the generalised coupled oscillator mechanism and its intrinsic connection to the strength of VCD signals." Physical Chemistry Chemical Physics 18, no. 31 (2016): 21202–12. http://dx.doi.org/10.1039/c6cp01282e.

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This work reports the development of a generalised coupled oscillator expression for VCD that is exact within the harmonic approximation and is applicable to all types of normal modes, regardless whether the considered molecule is symmetric or asymmetric.

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MARTINA, LUIGI, GIOVANNA RUGGERI, and GIULIO SOLIANI. "CORRELATION ENERGY AND ENTANGLEMENT GAP IN CONTINUOUS MODELS." International Journal of Quantum Information 09, no. 03 (April 2011): 843–62. http://dx.doi.org/10.1142/s0219749911007666.

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Our goal is to clarify the relation between entanglement and correlation energy in a bipartite system with infinite dimensional Hilbert space. To this aim, we consider the completely solvable Moshinsky's model of two linearly coupled harmonic oscillators. Also, for small values of the couplings, the entanglement of the ground state is nonlinearly related to the correlation energy, involving logarithmic or algebraic corrections. Then, looking for witness observables of the entanglement, we show how to give a physical interpretation of the correlation energy. In particular, we have proven that there exists a set of separable states, continuously connected with the Hartree–Fock state, which may have a larger overlap with the exact ground state, but also a larger energy expectation value. In this sense, the correlation energy provides an entanglement gap, i.e. an energy scale, under which measurements performed on the 1-particle harmonic sub-system can discriminate the ground state from any other separated state of the system. However, in order to verify the generality of the procedure, we have compared the energy distribution cumulants for the 1-particle harmonic sub-system of the Moshinsky's model with the case of a coupling with a damping Ohmic bath at 0 temperature.

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Laszuk, Dawid, Jose O. Cadenas, and Slawomir J. Nasuto. "On the Phase Coupling of Two Components Mixing in Empirical Mode Decomposition." Advances in Data Science and Adaptive Analysis 08, no. 01 (January 2016): 1650004. http://dx.doi.org/10.1142/s2424922x16500042.

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This paper investigates frequency mixing effect of empirical mode decomposition (EMD) and explores whether it can be explained by simple phase coupling between components of the input signal. The input is assumed to be a linear combination of harmonic oscillators. The hypothesis was tested assuming that phases of input signals’ components would couple according to Kuramoto’s model. Using a Kuramoto’s model with as many oscillators as the number of intrinsic mode functions (result of EMD), the model’s parameters were adjusted by a particle swarm optimization (PSO) method. The results show that our hypothesis is plausible, however, a different coupling mechanism than the simple sine-coupling Kuramoto’s model are likely to give better results.

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Кособукин, В. А. "Двумерные кулоновские плазмон-экситоны: релаксация возбуждений." Физика твердого тела 63, no. 8 (2021): 1157. http://dx.doi.org/10.21883/ftt.2021.08.51171.078.

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A theory is developed for the relaxation of two-dimensional non-radiative (Coulomb) plasmon-excitons in thin closely located layers of a metal and a semiconductor. In the framework of classical electrodynamics, the equations of motion are formulated for the polarization waves of non-radiative plasmons and excitons with taking into account the Coulomb coupling and the near-field of external polarization. In the model of coupled harmonic oscillators represented by the polarization fields of excitations, the problem of relaxation is solved for Coulomb plasmons, excitons and plasmon-excitons. It is shown that the two dispersion branches of normal plasmon-exciton modes undergo anticrossing (mutual repulsion) at the resonance between plasmon and exciton. With dissipative damping and power interchange between the excitations taken into account, the process of plasmon-exciton relaxation depending on time is investigated. The theory displays the principal analogies between dynamics of plasmon-excitons and of excitations in other objects of linear vibration theory, such as mechanical oscillators, resonant electric chains, etc.

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Komarov, M., and A. Pikovsky. "Erratum to “The Kuramoto model of coupled oscillators with a bi-harmonic coupling function” [Physica D 289 (2014) 18–31]." Physica D: Nonlinear Phenomena 313 (December 2015): 117. http://dx.doi.org/10.1016/j.physd.2015.11.001.

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Fring, Andreas, and Thomas Frith. "Time-dependent metric for the two-dimensional, non-Hermitian coupled oscillator." Modern Physics Letters A 35, no. 08 (November 29, 2019): 2050041. http://dx.doi.org/10.1142/s0217732320500418.

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We provide a time-dependent Dyson map and metric for the two-dimensional harmonic oscillator with a non-Hermitian ixy coupling term. This particular time-independent model exhibits spontaneously broken [Formula: see text]-symmetry and becomes unphysical in the broken regime, with the spectrum becoming partially complex. By introducing an explicit time dependence into the Dyson map, we provide a time-dependent metric that renders the model consistent across the unbroken and broken regimes.

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Layton, Anita T., Leon C. Moore, and Harold E. Layton. "Multistability in tubuloglomerular feedback and spectral complexity in spontaneously hypertensive rats." American Journal of Physiology-Renal Physiology 291, no. 1 (July 2006): F79—F97. http://dx.doi.org/10.1152/ajprenal.00048.2005.

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Single-nephron proximal tubule pressure in spontaneously hypertensive rats (SHR) can exhibit highly irregular oscillations similar to deterministic chaos. We used a mathematical model of tubuloglomerular feedback (TGF) to investigate potential sources of the irregular oscillations and the corresponding complex power spectra in SHR. A bifurcation analysis of the TGF model equations, for nonzero thick ascending limb (TAL) NaCl permeability, was performed by finding roots of the characteristic equation, and numerical simulations of model solutions were conducted to assist in the interpretation of the analysis. These techniques revealed four parameter regions, consistent with TGF gain and delays in SHR, where multiple stable model solutions are possible: 1) a region having one stable, time-independent steady-state solution; 2) a region having one stable oscillatory solution only, of frequency f1; 3) a region having one stable oscillatory solution only, of frequency f2, which is approximately equal to 2 f1; and 4) a region having two possible stable oscillatory solutions, of frequencies f1 and f2. In addition, we conducted simulations in which TAL volume was assumed to vary as a function of time and simulations in which two or three nephrons were assumed to have coupled TGF systems. Four potential sources of spectral complexity in SHR were identified: 1) bifurcations that permit switching between different stable oscillatory modes, leading to multiple spectral peaks and their respective harmonic peaks; 2) sustained lability in delay parameters, leading to broadening of peaks and of their harmonics; 3) episodic, but abrupt, lability in delay parameters, leading to multiple peaks and their harmonics; and 4) coupling of small numbers of nephrons, leading to multiple peaks and their harmonics. We conclude that the TGF system in SHR may exhibit multistability and that the complex power spectra of the irregular TGF fluctuations in this strain may be explained by switching between multiple dynamic modes, temporal variation in TGF parameters, and nephron coupling.

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Bougouffa, Smail, and Lazhar Bougoffa. "Solvability of the Caldeira–Leggett model." Canadian Journal of Physics 98, no. 7 (July 2020): 683–88. http://dx.doi.org/10.1139/cjp-2018-0538.

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In this paper, we illustrate the use of the method of the characteristics in various dissipative models of a single harmonic oscillator. The master equation governing the process can be transformed to a partial differential equation on the Wigner distribution, which in turn can be split to a system of coupled differential equations. We present a useful technique that can be used to separate the system without increasing the order and then the solutions can be obtained. The obtained solutions are used to calculate the average of energy observable of the system. This procedure can be extended to solve some other complex similar problems.

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Badveli, R., V. Jagadish, S. Akshaya, R. Srikanth, and F. Petruccione. "Dynamics of Quantum Correlations in a Qubit-Oscillator System Interacting via a Dissipative Bath." Open Systems & Information Dynamics 27, no. 01 (March 2020): 2050004. http://dx.doi.org/10.1142/s1230161220500043.

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The entanglement dynamics in a bipartite system consisting of a qubit and a harmonic oscillator interacting only through their coupling with the same bath is studied. The considered model assumes that the qubit is coupled to the bath via the Jaynes-Cummings interaction, whilst the position of the oscillator is coupled to the position of the bath via a dipole interaction. We give a microscopic derivation of the Gorini–Kossakowski–Sudarshan–Lindblad equation for the considered model. Based on the Kossakowski matrix, we show that non-classical correlations including entanglement can be generated by the considered dynamics. We then analytically identify specific initial states for which entanglement is generated. This result is also supported by our numerical simulations.

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Drexel, M. V., and J. H. Ginsberg. "Modal Overlap and Dissipation Effects of a Cantilever Beam with Multiple Attached Oscillators." Journal of Vibration and Acoustics 123, no. 2 (August 1, 2000): 181–87. http://dx.doi.org/10.1115/1.1340624.

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This work was prompted by a study performed by Strasberg [7] in which numerous small spring-mass-damper systems are attached to a large suspended mass representing the master structure. The isolated natural frequency of each attached system was selected to match in average the natural frequency of the isolated master structure. Strasberg found that the critical issue when an impulse excitation is applied to the master structure is the bandwidth of the isolated attached systems in comparison to the spacing between the natural frequencies of the system. Modal overlap, which corresponds to bandwidths that exceed the spacing of those frequencies, was shown to greatly influence the response of the master structure. Light damping, for which there is little or no modal overlap, corresponds to an impulse response that consists of a sequence of nearly periodic exponentially decaying pulses, and the transfer function for harmonic excitation of the master structure indicates that the substructure acts as a vibration absorber for the master structure. Increased damping leads to modal overlap, with the result that the impulse response consists of a single decaying pulse. The frequency domain transfer function indicates that the vibration absorber effect is enhanced. The present work explores these issues for continuous systems by replacing the one degree of freedom master structure with a cantilever beam. The system parameters are selected to match Strasberg’s model, with the suspended oscillators placed randomly along the beam. The beam displacement is represented as a Ritz series whose basis functions are the cantilever beam modes. The coupled equations are solved by a state-space eigenmode analysis that yields a closed form representation of the response in terms of the complex eigenmode properties. The continuous fuzzy structure is shown not to display the transfer of energy between the master structure and the substructure that was exhibited by the discrete fuzzy structure, apparently because of the asynchronous motion of the attachment points resulting from the spatial variability of the beam’s motion. The vibration absorber effect for harmonic excitation is only obtained for the heavy damping in the case of a beam.

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Dittrich, Thomas, and Santiago Peña Martínez. "Toppling Pencils—Macroscopic Randomness from Microscopic Fluctuations." Entropy 22, no. 9 (September 18, 2020): 1046. http://dx.doi.org/10.3390/e22091046.

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We construct a microscopic model to study discrete randomness in bistable systems coupled to an environment comprising many degrees of freedom. A quartic double well is bilinearly coupled to a finite number N of harmonic oscillators. Solving the time-reversal invariant Hamiltonian equations of motion numerically, we show that for N=1, the system exhibits a transition with increasing coupling strength from integrable to chaotic motion, following the Kolmogorov-Arnol’d-Moser (KAM) scenario. Raising N to values of the order of 10 and higher, the dynamics crosses over to a quasi-relaxation, approaching either one of the stable equilibria at the two minima of the potential. We corroborate the irreversibility of this relaxation on other characteristic timescales of the system by recording the time dependences of autocorrelation, partial entropy, and the frequency of jumps between the wells as functions of N and other parameters. Preparing the central system in the unstable equilibrium at the top of the barrier and the bath in a random initial state drawn from a Gaussian distribution, symmetric under spatial reflection, we demonstrate that the decision whether to relax into the left or the right well is determined reproducibly by residual asymmetries in the initial positions and momenta of the bath oscillators. This result reconciles the randomness and spontaneous symmetry breaking of the asymptotic state with the conservation of entropy under canonical transformations and the manifest symmetry of potential and initial condition of the bistable system.

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Кособукин, В. А. "Кулоновские плазмон-экситоны в планарных наноструктурах металл-полупроводник." Физика твердого тела 63, no. 4 (2021): 527. http://dx.doi.org/10.21883/ftt.2021.04.50720.248.

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A theory of Coulomb (non-radiative) plasmons-excitons in a semiconductor with adjacent quantum well and ultrathin metal film is presented. The equations of motion are formulated for the polarization waves of surface plasmons and quasi-two-dimensional excitons with taking account of Coulomb interaction between them. Within a model of coupled harmonic oscillators, solved are the problems of Coulomb plasmon, exciton and plasmon-exciton excitations in the presence of an external dipole force. The coupling contant is calculated for plasmon-excitons, their optical spectra are investigated, and the relative contributions of plasmons and excitons to the normal modes are found. It is concluded that near the resonance between plasmon and exciton the spectrum of plasmon-exciton excitations consists of two peaks whose behavior in passing through the resonance shows the signs of anti-crossing effect (repulsion of frequencies).

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Кособукин, В. А. "Кулоновские плазмон-экситоны в планарных наноструктурах металл-полупроводник." Физика твердого тела 63, no. 4 (2021): 527. http://dx.doi.org/10.21883/ftt.2021.04.50720.248.

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A theory of Coulomb (non-radiative) plasmons-excitons in a semiconductor with adjacent quantum well and ultrathin metal film is presented. The equations of motion are formulated for the polarization waves of surface plasmons and quasi-two-dimensional excitons with taking account of Coulomb interaction between them. Within a model of coupled harmonic oscillators, solved are the problems of Coulomb plasmon, exciton and plasmon-exciton excitations in the presence of an external dipole force. The coupling contant is calculated for plasmon-excitons, their optical spectra are investigated, and the relative contributions of plasmons and excitons to the normal modes are found. It is concluded that near the resonance between plasmon and exciton the spectrum of plasmon-exciton excitations consists of two peaks whose behavior in passing through the resonance shows the signs of anti-crossing effect (repulsion of frequencies).

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Caligiuri, Luigi Maxmilian. "A Novel Model of Interaction Between High Frequency Electromagnetic Non-Ionizing Fields and Microtubules Viewed as Coupled Two-Degrees of Freedom Harmonic Oscillators." Current Topics in Medicinal Chemistry 15, no. 6 (March 3, 2015): 549–58. http://dx.doi.org/10.2174/1568026615666150225101453.

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Nooijen, Marcel. "Explorations of many-body relativistic wave equations within a one-dimensional model." Canadian Journal of Chemistry 87, no. 10 (October 2009): 1499–511. http://dx.doi.org/10.1139/v09-119.

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A one-dimensional analog that reflects many of the features of the many-body Dirac equation is considered. The model can be solved numerically using a convenient finite basis discrete variable representation. Both an (unbound) harmonic oscillator potential and a (bound) inverse Gaussian one-particle potential are discussed for interacting particles. In a second thread in the paper, the mass term is neglected in the model many-body Dirac equation, and it is shown that the original equation, which has 2N coupled components for N particles can then be reduced to 2N decoupled one-component equations, which can be solved “analytically” for arbitrary many particles interacting through central two-body potentials.

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Davies, M. A., and F. C. Moon. "Transition From Soliton to Chaotic Motion Following Sudden Excitation of a Nonlinear Structure." Journal of Applied Mechanics 63, no. 2 (June 1, 1996): 445–49. http://dx.doi.org/10.1115/1.2788887.

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The existence of a transition from soliton-like motions to spatially and temporally disordered motions in a periodic structure with buckling nonlinearity is demonstrated. An experiment consisting of nine harmonic oscillators coupled with buckling sensitive elastica was constructed. This experiment is modeled using a modified Toda lattice. As has been shown in previous work, the experiment and the model show strong sensitivity to initial conditions. Here we show that this sensitivity may be related to a transition from relatively ordered solitary wave motion, immediately following the impact, to disordered motions at a later time. Some of the behavior of the observed wave structures is explained using Toda’s analytical results; however, the reasons for the break-up of the waves and their role in the generation of spatio-temporal disorder is not fully understood. We speculate that some type of transient chaotic motion is responsible for the observed behavior. These findings are relevant to aircraft, ship, and space structures that are subjected to large dynamic loads.

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BATISTA, A. B., J. C. FABRIS, S. V. B. GONCALVES, and J. TOSSA. "QUANTUM PERFECT FLUID COSMOLOGICAL MODEL AND ITS CLASSICAL ANALOGUE." International Journal of Modern Physics A 17, no. 20 (August 10, 2002): 2749. http://dx.doi.org/10.1142/s0217751x0201176x.

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The quantization of gravity coupled to a perfect fluid model leads to a Schrödinger-like equation, where the matter variable plays the role of time. The wave function can be determined, in the flat case, for an arbitrary barotropic equation of state p = α ρ; solutions can also be found for the radiative non-flat case. The wave packets are constructed, from which the expectation value for the scale factor is determined. The quantum scenarios reveal a bouncing Universe, free from singularity. Such quantum cosmological perfect fluid models admit a universal classical analogue, represented by the addition, to the ordinary classical model, of a repulsive stiff matter fluid1,2. The existence of this universal classical analogue may imply that this perfect fluid coupled to gravity model is not a real quantum system. The quantum cosmological perfect fluid model is, for a flat spatial section, formally equivalent to a free particle in ordinary quantum mechanics, for any value of α, while the radiative non-flat case is equivalent to the harmonic oscillator. The repulsive fluid needed to reproduce the quantum results is the same in both cases.

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Papachristou, P. K., E. Mavrommatis, V. Constantoudis, F. Κ. Diakonos, and J. Wambach. "Phase Space Analysis of Relaxation Dynamics of Isoscalar Giant Monopole Resonances." HNPS Proceedings 14 (December 5, 2019): 131. http://dx.doi.org/10.12681/hnps.2261.

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A classical model based on the independent particle approach to the nuclear dynamics is used to study the influence of the phase space structures on the onebody dissipation of isoscalar Giant Monopole Resonances. The model consists of a harmonic oscillator describing the collective excitation coupled with a nonlinear (Woods-Saxon) oscillator representing the motion of each nucléon. We are particulary interested in the dependence of relaxation on the energy of the system. We have found that in a rather broad region of parameter space, contrary to the common expectation, both Lyapunov exponent and relaxation time increase as a function of the total energy. We examine the conditions required for this effect to occur and demonstrate the key role of the dispersion relation of the nonlinear oscillator.

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Morozov, Nikita F., Dmitriy A. Indeitsev, Vasilisa S. Igumnova, Alexei V. Lukin, Ivan A. Popov, and Lev V. Shtukin. "Nonlinear dynamics of mode-localized MEMS accelerometer with two electrostatically coupled microbeam sensing elements." Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 8, no. 2 (2021): 233–46. http://dx.doi.org/10.21638/spbu01.2021.204.

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In the presented work, a model of a microelectromechanical accelerometer with two movable beam elements located between two fixed electrodes is proposed. The action of the transfer forces of inertia in the longitudinal direction leads to a change in the spectral properties of the system, which is a useful output signal of the sensor. The dynamics of the system in the presence of a weak electrostatic coupling between the sensitive elements is characterized by the phenomenon of modal localization - a significant change in the amplitude ratios for the forms of inphase and antiphase oscillations with small changes in the measured component of the acceleration vector of the moving object. Diagrams of equilibrium positions are plotted for varying the potential difference between a fixed electrode and a movable element and between two movable elements. The dependences of the frequencies and the ratio of the components of the eigenvectors on the magnitude of the inertial action are investigated. It is shown that the sensitivity of a sensor based on modal localization can be orders of magnitude higher than the sensitivity of known systems based on measuring the shift of natural frequencies. A nonlinear dynamic model of an accelerometer with external harmonic electrostatic excitation of oscillations is constructed. Resonance characteristics are obtained, a comparison is made between the model describing the modal characteristics of the system and the model describing the real dynamic mode of operation taking into account nonlinear factors.

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Meliga, P. "Harmonics generation and the mechanics of saturation in flow over an open cavity: a second-order self-consistent description." Journal of Fluid Mechanics 826 (August 4, 2017): 503–21. http://dx.doi.org/10.1017/jfm.2017.439.

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The flow over an open cavity is an example of supercritical Hopf bifurcation leading to periodic limit-cycle oscillations. One of its distinctive features is the existence of strong higher harmonics, which results in the time-averaged mean flow being strongly linearly unstable. For this class of flows, a simplified formalism capable of unravelling how exactly the instability grows and saturates is lacking. This study builds on previous work by Mantič-Lugo et al. (Phys. Rev. Lett., vol. 113, 2014, 084501) to fill in the gap using a parametrized approximation of an instantaneous, phase-averaged mean flow, coupled in a quasi-static manner to multiple linear harmonic disturbances interacting nonlinearly with one another and feeding back on the mean flow via their Reynolds stresses. This provides a self-consistent modelling of the mean flow–fluctuation interaction, in the sense that all perturbation structures are those whose Reynolds stresses force the mean flow in such a way that the mean flow generates exactly the aforementioned perturbations. The first harmonic is sought as the superposition of two components, a linear component generated by the instability and aligned along the leading eigenmode of the mean flow, and a nonlinear orthogonal component generated by the higher harmonics, which progressively distorts the linear growth rate and eigenfrequency of the eigenmode. Saturation occurs when the growth rate of the first harmonic is zero, at which point the stabilizing effect of the second harmonic balances exactly the linear instability of the eigenmode. The model does not require any input from numerical or experimental data, and accurately predicts the transient development and the saturation of the instability, as established from comparison to time and phase averages of direct numerical simulation data.

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Ringermacher, H. I., and L. R. Mead. "Reaffirmation of cosmological oscillations in the scale factor from the Pantheon compilation of 1048 Type Ia supernovae." Monthly Notices of the Royal Astronomical Society 494, no. 2 (April 10, 2020): 2158–65. http://dx.doi.org/10.1093/mnras/staa872.

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ABSTRACT We observe damped temporal oscillations in the scale factor at a dominant frequency of ∼7 cycles/Hubble-time in the Pantheon compilation of 1048 Type Ia supernovae (SNe Ia). The residual oscillations observed in the Pantheon data closely match and reaffirm our initial observation of oscillations from earlier SNe data (primarily SNLS3 data of Conley 2011) at 2σ confidence. The nearly identical shapes in amplitude, frequency, phase, and damping constant makes it highly likely that the signal is real. Furthermore, two-thirds of the Pantheon SNe cover different portions of the sky compared with SNLS3 strengthening this conclusion. Our model describing the oscillation, presented in an earlier paper, is a simple scalar field harmonic oscillator coupled to the Lambda cold dark matter (ΛCDM) Friedmann equation, but carried into the present epoch. The scalar field energy density plays the role of the dark matter energy density in ΛCDM cosmology, fits well as an average, and closely matches the present dark matter density parameter, suggesting the oscillation plays a role in the dark matter sector. Temporal oscillations in the scale factor and its derivative, as described in this work, would also induce temporal oscillations of the Hubble parameter.

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Sharma, R. P., Narender Kumar, R. Uma, Ram Kishor Singh, and P. K. Gupta. "Transient setting of relativistic ponderomotive non-linearity and filamentation of ultra-short laser pulses in collisionless plasmas." Laser and Particle Beams 37, no. 03 (July 11, 2019): 252–59. http://dx.doi.org/10.1017/s0263034619000454.

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AbstractWe study the setting up of relativistic ponderomotive non-linearity in an under-dense collisionless cold plasma. Using the fluid model, coupled system of equations of the laser beam and electron plasma oscillations has been derived. We present the numerical simulation for this coupled system of equations, when the coupling arises through relativistic ponderomotive non-linearity. The filamentation of the laser beam has been found to vary appreciably with perturbation wave number. The results show that with time, localized structures become more complex and the plasma oscillation frequency spectra have several harmonic peaks at terahertz frequencies when the electron plasma frequency is in terahertz range and laser frequency is around 2.35 × 1015 rad/s. We also present the semi-analytical model to capture the underlying physics.

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Journal articles on the topic 'Model of coupled harmonic oscillators'

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