Relevant bibliographies by topics / Coupled harmonic oscillator

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers
  5. Reports

Academic literature on the topic 'Coupled harmonic oscillator'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Coupled harmonic oscillator"

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Dattoli, G., A. Torre, S. Lorenzutta, and G. Maino. "Coupled harmonic oscillators, generalized harmonic-oscillator eigenstates and coherent states." Il Nuovo Cimento B Series 11 111, no. 7 (July 1996): 811–23. http://dx.doi.org/10.1007/bf02749013.

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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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Dudinetc, I. V., and V. I. Man’ko. "Quantum correlations for two coupled oscillators interacting with two heat baths." Canadian Journal of Physics 98, no. 4 (April 2020): 327–31. http://dx.doi.org/10.1139/cjp-2019-0067.

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We study a system of two coupled oscillators (A oscillators), each of which linearly interact with their own heat bath consisting of a set of independent harmonic oscillators (B oscillators). The initial state of the A oscillator is taken to be coherent while the B oscillator is in a thermal state. We analyze the time-dependent state of the A oscillator, which is a two-mode Gaussian state. By making use of Simon’s separability criterion, we show that this state is separable for all times. We consider the equilibrium state of the A oscillator in detail and calculate its Wigner function.
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LAWANDE, S. V., and Q. V. LAWANDE. "PATH INTEGRAL DERIVATION OF AN EXACT MASTER EQUATION." Modern Physics Letters B 09, no. 02 (January 20, 1995): 87–94. http://dx.doi.org/10.1142/s0217984995000097.

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The Feynman propagator in coherent states representation is obtained for a system of a single harmonic oscillator coupled to a reservoir of N oscillators. Using this propagator, an exact master equation is obtained for the evolution of the reduced density matrix for the open system of the oscillator.
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Chakrabarti, Barnali, and Bambi Hu. "Level correlation in coupled harmonic oscillator systems." Physics Letters A 315, no. 1-2 (August 2003): 93–100. http://dx.doi.org/10.1016/s0375-9601(03)01001-6.

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Merdaci, Abdeldjalil, Ahmed Jellal, Ayman Al Sawalha, and Abdelhadi Bahaoui. "Purity temperature dependency for coupled harmonic oscillator." Journal of Statistical Mechanics: Theory and Experiment 2018, no. 9 (September 6, 2018): 093101. http://dx.doi.org/10.1088/1742-5468/aad19b.

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Maidanik, G., and K. J. Becker. "Noise control of a master harmonic oscillator coupled to a set of satellite harmonic oscillators." Journal of the Acoustical Society of America 104, no. 5 (November 1998): 2628–37. http://dx.doi.org/10.1121/1.423846.

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Tung, Mingwhei, Elia Eschenazi, and Jian-Min Yuan. "Dynamics of a morse oscillator coupled to a bath of harmonic oscillators." Chemical Physics Letters 115, no. 4-5 (April 1985): 405–10. http://dx.doi.org/10.1016/0009-2614(85)85158-7.

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Burrows, B. L., M. Cohen, and Tova Feldmann. "Coupled harmonic oscillator systems: Improved algebraic decoupling approach." International Journal of Quantum Chemistry 92, no. 4 (2003): 345–54. http://dx.doi.org/10.1002/qua.10521.

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Maidanik, G., and K. J. Becker. "Various loss factors of a master harmonic oscillator coupled to a number of satellite harmonic oscillators." Journal of the Acoustical Society of America 103, no. 6 (June 1998): 3184–95. http://dx.doi.org/10.1121/1.423035.

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Dissertations / Theses on the topic "Coupled harmonic oscillator"

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Monteiro, João Frederico Haas Leandro. "O estudo do emaranhamento na emissão espontânea no espaço livre e em uma cadeia de osciladores harmônicos acoplados." UNIVERSIDADE ESTADUAL DE PONTA GROSSA, 2010. http://tede2.uepg.br/jspui/handle/prefix/879.

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Made available in DSpace on 2017-07-21T19:25:58Z (GMT). No. of bitstreams: 1 Joao Frederico.pdf: 2218397 bytes, checksum: 781c58d12bce3113c45da4e65bd0e36d (MD5) Previous issue date: 2010-03-11
Conselho Nacional de Desenvolvimento Científico e Tecnológico
In this dissertation, we studied entanglement in some fundamental systems of physics, such as an excited atom in free-space spontaneously decaying and coupled harmonic oscillators. In order to study entanglement in spontaneous emission in free-space, we employed theWeisskopf-Wigner theory which allowed us to obtain the time evolution of both the atom and field states. In the case of bipartite entanglement among field modes after spontaneous emission, we showed that the modes can become highly entangled and that the features of this entanglement strongly depend on the way the partitions are made. For the entanglement between atom and field during spontaneous emission, we were able to relate entanglement to a well known physical quantity namely the lifetime of an atom in a excited state. Keeping in mind the intention to study simple but relevant physical systems, we used in the second work a chain of coupled harmonic oscillators. It was well-known among researchers in the field of quantum information that a linear chain of coupled oscillators in the rotating wave approximation and prepared in classical states would never create entanglement. Then, we used two reference oscillators prepared in squeezed states to make creation of entanglement possible. We found results concerning the relationship between the phases in the reference oscillators’ state and dynamics of entanglement in the chain for some coupling configurations. We showed that it is not always true that squeezing can favor entanglement creation and that with the configuration used by us it is possible to localize entanglement. We proposed a possible implementation of our results in coupled microelectromechanical systems.
Nesta dissertação estudamos o emaranhamento em alguns sistemas fundamentais da Física, como um átomo no espaço livre realizando emissão espontânea e em osciladores harmônicos acoplados. Para o estudo do emaranhamento na emissão espontânea no espaço livre, utilizamos a teoria de Weisskopf-Wigner que nos permitiu obter a evolução temporal, tanto do estado do átomo, quanto do estado do campo. Para o caso de emaranhamento bipartido entre os modos do campo após a emissão espontânea, mostramos que os modos podem ficar altamente emaranhados e que as características desse emaranhamento dependem fortemente de como são realizadas as partições. Para o emaranhamento entre o átomo e o campo durante a emissão espontânea, pudemos relacionar o emaranhamento com uma quantidade Física bastante conhecida, o tempo de vida do átomo no seu estado excitado. Ainda com o intuito de estudar sistemas físicos simples, mas de relevância na Física, utilizamos, em um segundo trabalho, uma cadeia de osciladores harmônicos acoplados. Já era bem conhecido dos pesquisadores na área de informação quântica que uma cadeia linear de osciladores acoplados, na aproximação de onda girante e preparados em estados clássicos, não cria emaranhamento. Assim, utilizamos dois osciladores de referência em estados comprimidos para permitir a criação de emaranhamento. Encontramos resultados a respeito da relação das fases dos osciladores de referência e a dinâmica do emaranhamento na cadeia para algumas configurações de acoplamentos. Mostramos que nem sempre a compressão dos estados comprimidos favorece a criação de emaranhamento e que na configuração utilizada por nós é possível localizar o emaranhamento. Nós propusemos uma possível implementação de nossos estudos em sistemas microeletromecânicos acoplados.
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Penbegul, Ali Yetkin. "Synchronization Of Linearly And Nonlinearly Coupled Harmonic Oscillators." Master's thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613258/index.pdf.

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In this thesis, the synchronization in the arrays of identical and non-identical coupled harmonic oscillators is studied. Both linear and nonlinear coupling is considered. The study consists of two main parts. The first part concentrates on theoretical analysis and the second part contains the simulation results. The first part begins with introducing the harmonic oscillators and the basics of synchronization. Then some theoretical aspects of synchronization of linearly and nonlinearly coupled harmonic oscillators are presented. The theoretical results say that linearly coupled identical harmonic oscillators synchronize for any frequency of oscillation. For nonlinearly coupled identical harmonic oscillators, synchronization is shown to occur at large enough frequency values. In the second part, the simulator and simulation results are presented. A GUI is designed in MATLAB to run the simulations. In the simulations, synchronization of coupled harmonic oscillators are studied according to different coupling strength values, different frequency values, different coupling graph types (e.g. all-to-all, ring, tree) and different coupling function types (e.g. linear, saturation, cubic). The simulation results do not only support the theoretical part of the thesis but also give some idea about the part of the synchronization of coupled harmonic oscillators uncovered by theory.
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Venkataraman, Vignesh. "Understanding open quantum systems with coupled harmonic oscillators." Thesis, Imperial College London, 2015. http://hdl.handle.net/10044/1/30715.

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When a quantum system interacts with many other quantum mechanical objects, the behaviour of the system is strongly affected; this is referred to as an open quantum system (OQS). Since the inception of quantum theory the development of OQSs has been synonymous with realistic descriptions of quantum mechanical models. With recent activity in the advancement of quantum technologies, there has been vested interest in manipulating OQSs. Therefore understanding and controlling environmental effects, by structuring environments, has become an important field. The method of choice for tackling OQSs is the master equation approach, which requires approximations and doesn't allow direct assessment of the environment. This thesis tackles the issues of OQSs with an unorthodox method; we employ a series of coupled quantum harmonic oscillators to simulate an OQS. This permits the use of the covariance matrix technique which allows us to avoid approximations and analyse the environment modes. We investigate the Markov approximation and Rotating-Wave approximation (RWA), which are commonly used in the field. By considering four OQS models, we study an entanglement-based non-Markovian behaviour (NMB) quantifier (ENMBQ). The relevance of detuning, coupling strength and bath structures in determining the amount of NMB is noted. A brief study of the factors that affect a fidelity-based NMB quantifier is also conducted. We also analyse the effect on the ENMBQ if the terms excluded by the RWA are included in the models. Finally, an examination of the applicability of the RWA in the presence of strong coupling is undertaken in a three oscillator model. The fidelity-based analysis utilised could allow one to ascertain when and if the RWA can be applied to a model of interest, including OQSs. The knowledge within, and the methodology used throughout this thesis, could arm researchers with insights to control the flow of quantum information in their systems.
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Gryga, Michal. "Silná vazba v plazmonických strukturách." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2018. http://www.nusl.cz/ntk/nusl-382251.

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This diploma thesis deals with numerical simulations of the optical response of plasmonic infrared antennas placed on silicon substrates with thin film of silicon dioxide and subsequently with fitting of scattering spectra by model of coupled harmonic oscillators. In this work, we study an influence of length of antennas on the strength of coupling of localized surface plasmons in the antennas with phonons in silicon dioxide film. Also, the influence of silicon dioxide film thickness on this coupling is investigated.
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Shih-YiYang and 楊士毅. "Study of quantum coherence and entanglement dynamics in coupled harmonic oscillator systems." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/02490690414690043777.

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碩士
國立成功大學
物理學系
102
Quantum Entanglement has been wildly discuss and studied in recent years. To verify whether a system is separable or not, A. Peres introduced a criterion called Positive Partial Transpose criterion, it can only be functional when it fulfill some sufficient and necessary condition which is it must be used in 2×2 and 2×3 low dimension states . However, R. Simon extended Peres-Horodecki criterion to continuous variable system. He found that it only fulfill sufficient and necessary condition in Gaussian state. In this thesis, we will study some interaction effect between some Coupled Simple Harmonic Oscillators system. By using the criterion mentioned above, we will closely observe two simple harmonic oscillator system and four simple harmonic oscillator system in time evolution dynamics of Entanglement. On the other hand, we will discuss under what kind of condition, Simon’s Gaussian states of PPT criterion can be simplified. Through these models analyze, we hope they can help us understand better in the entanglement phenomenon of few particles.
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Abdul-Latif, Mohammed. "Frequency Synthesizers and Oscillator Architectures Based on Multi-Order Harmonic Generation." Thesis, 2011. http://hdl.handle.net/1969.1/ETD-TAMU-2011-12-10281.

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Frequency synthesizers are essential components for modern wireless and wireline communication systems as they provide the local oscillator signal required to transmit and receive data at very high rates. They are also vital for computing devices and microcontrollers as they generate the clocks required to run all the digital circuitry responsible for the high speed computations. Data rates and clocking speeds are continuously increasing to accommodate for the ever growing demand on data and computational power. This places stringent requirements on the performance metrics of frequency synthesizers. They are required to run at higher speeds, cover a wide range of frequencies, provide a low jitter/phase noise output and consume minimum power and area. In this work, we present new techniques and architectures for implementing high speed frequency synthesizers which fulfill the aforementioned requirements. We propose a new architecture and design approach for the realization of wideband millimeter-wave frequency synthesizers. This architecture uses two-step multi-order harmonic generation of a low frequency phase-locked signal to generate wideband mm-wave frequencies. A prototype of the proposed system is designed and fabricated in 90nm Complementary Metal Oxide Semiconductor (CMOS) technology. Measurement results demonstrated that a very wide tuning range of 5 to 32 GHz can be achieved, which is costly to implement using conventional techniques. Moreover the power consumption per octave resembles that of state-of-the art reports. Next, we propose the N-Push cyclic coupled ring oscillator (CCRO) architecture to implement two high performance oscillators: (1) a wideband N-Push/M-Push CCRO operating from 3.16-12.8GHz implemented by two harmonic generation operations using the availability of different phases from the CCRO, and (2) a 13-25GHz millimeter-wave N-Push CCRO with a low phase noise performance of -118dBc/Hz at 10MHz. The proposed oscillators achieve low phase noise with higher FOM than state of the art work. Finally, we present some improvement techniques applied to the performance of phase locked loops (PLLs). We present an adaptive low pass filtering technique which can reduce the reference spur of integer-N charge-pump based PLLs by around 20dB while maintaining the settling time of the original PLL. Another PLL is presented, which features very low power consumption targeting the Medical Implantable Communication Standard. It operates at 402-405 MHz while consuming 600microW from a 1V supply.
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Jhih-YuanGao and 高至遠. "A Study of Coupled Harmonic Oscillator Models toward Quantum Entanglement Dynamics in Macroscopic Quantum Phenomena." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/96826573450199014221.

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碩士
國立成功大學
物理學系
102
Peres-Horodecki-Simon criterion and logarithmic negativity are very powerful tools to determine the separability and to measure the entanglement of Gaussian states. In this thesis, we set up several models, all of which comprise a number of coupled oscillators, and by facilitating the separability criterion and measure we're able to calculate the entanglement between each pair of oscillators at any time analytically, which reveals several interesting phenomena, including entanglement sudden death and revival of entanglement. Also, we compare the entanglement between center of mass coordinates and that of their member oscillators, and thereby understand the role of it in a composite system. Lastly, we'll make an attempt at appreciating the effects of particle numbers on entanglement. We hope these analytically solvable models can help us understand more about the entanglement of interacting systems and of large systems.
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Tay, Buang Ann Petrosky Tomio Y. Sudarshan E. C. G. "Coherence and decoherence processes of a harmonic oscillator coupled with finite temperature field exact eigenbasis solution of Kossakowski-Linblad's equation /." 2004. http://repositories.lib.utexas.edu/bitstream/handle/2152/2218/tayba042.pdf.

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Tay, Buang Ann. "Coherence and decoherence processes of a harmonic oscillator coupled with finite temperature field: exact eigenbasis solution of Kossakowski-Linblad's equation." Thesis, 2004. http://hdl.handle.net/2152/2218.

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(9759650), Conor S. Pyles. "The Dynamics of Coupled Resonant Systems and Their Applications in Sensing." Thesis, 2020.

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The field of coupled resonant systems is a rich research area with enumerable real-world applications, including the fields of neural computing and pattern recognition, energy harvesting, and even modeling the behavior of certain types of biological systems. This work is primarily focused on the study of the behaviors of two subsets of this field: large networks of globally coupled resonators (which, in this work, refers to passive, damped resonant elements which require external stimulus) and smaller networks of oscillators (referring to active devices capable of self-sustained motion), which are coupled through a network of light-sensitive resistive elements. In the case of the former, we begin by developing an analytical and experimental framework to examine the behaviors of this system under various conditions, such as different coupling modalities and element-level parametric mistunings. Once a proper understanding of the dynamics of these systems has been established, we go on to develop the system into a single-input, single-output, multi-analyte volatile organic compound sensor. For the study of oscillator networks, we begin by building a device which utilizes a network of Colpitts oscillators, coupled through a series of color-filtered CdSe photocells. We then establish that through the analysis of particular emergent behaviors (most notably, frequency locking within the network), this type of system may show promise as a threshold color sensor. By exploiting these behaviors, this type of system may find applications in neuromorphic computing (particularly in optical pattern recognition).
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Book chapters on the topic "Coupled harmonic oscillator"

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Garrett, Steven L. "The Simple Harmonic Oscillator." In Understanding Acoustics, 59–131. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-44787-8_2.

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Abstract This chapter will introduce a system that is fundamental to our understanding of more physical phenomena than any other. Although the “simple” harmonic oscillator seems to be only the combination of the most mundane components, the formalism developed to explain the behavior of a mass, spring, and damper is used to describe systems that range in size from atoms to oceans. Our investigation goes beyond the “traditional” treatments found in the elementary physics textbooks. For example, the introduction of damping will open a two-way street: a damping element (i.e., a mechanical resistance, Rm) will dissipate the oscillator’s energy, reducing the amplitudes of successive oscillations, but it will also connect the oscillator to the surrounding environment that will return thermal energy to the oscillator. The excitation of a harmonic oscillator by an externally applied force, displacement, or combination of the two will result in a response that is critically dependent upon the relationship between the frequency of excitation and the natural frequency of the oscillator and will introduce the critical concepts of mechanical impedance, resonance, and quality factor. Finally, the harmonic oscillator model will be extended to coupled oscillators that are represented by combinations of several masses and several springs.
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Song, Qiang, Fang Liu, Guanghui Wen, Jinde Cao, and Yang Tang. "Synchronization in Coupled Harmonic Oscillator Systems Based on Sampled Position Data." In Handbook of Real-Time Computing, 1–23. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-4585-87-3_21-1.

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Quintana, C., P. Jiménez-Macías, and O. Rosas-Ortiz. "Quantum Master Equation for the Time-Periodic Density Operator of a Single Qubit Coupled to a Harmonic Oscillator." In Trends in Mathematics, 271–81. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-53305-2_17.

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Brandt, Siegmund, and Hans Dieter Dahmen. "Coupled Harmonic Oscillators: Distinguishable Particles." In The Picture Book of Quantum Mechanics, 129–41. New York, NY: Springer US, 1995. http://dx.doi.org/10.1007/978-1-4684-0233-9_7.

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Brandt, Siegmund, and Hans Dieter Dahmen. "Coupled Harmonic Oscillators: Indistinguishable Particles." In The Picture Book of Quantum Mechanics, 142–56. New York, NY: Springer US, 1995. http://dx.doi.org/10.1007/978-1-4684-0233-9_8.

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Brandt, Siegmund, and Hans Dieter Dahmen. "Coupled Harmonic Oscillators: Distinguishable Particles." In The Picture Book of Quantum Mechanics, 145–57. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4613-0167-7_8.

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Brandt, Siegmund, and Hans Dieter Dahmen. "Coupled Harmonic Oscillators: Indistinguishable Particles." In The Picture Book of Quantum Mechanics, 158–72. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4613-0167-7_9.

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Brandt, Siegmund, and Hans Dieter Dahmen. "Coupled Harmonic Oscillators: Distinguishable Particles." In The Picture Book of Quantum Mechanics, 157–69. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-3951-6_8.

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Brandt, Siegmund, and Hans Dieter Dahmen. "Coupled Harmonic Oscillators: Indistinguishable Particles." In The Picture Book of Quantum Mechanics, 170–84. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-3951-6_9.

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Brandt, Siegmund, Hans Dieter Dahmen, and Tilo Stroh. "A Two-Particle System: Coupled Harmonic Oscillators." In Interactive Quantum Mechanics, 122–37. New York, NY: Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-7424-2_5.

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Conference papers on the topic "Coupled harmonic oscillator"

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Yu, Bo, James S. Freudenberg, R. Brent Gillespie, and Richard H. Middleton. "String instability in coupled harmonic oscillator systems." In 2011 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC 2011). IEEE, 2011. http://dx.doi.org/10.1109/cdc.2011.6161385.

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Suarez, Almudena, Franco Ramirez, and Sergio Sancho. "Coupled-oscillator systems: Efficient simulation with harmonic-balance based oscillator models." In 2014 International Conference on Numerical Electromagnetic Modeling and Optimization for RF, Microwave, and Terahertz Applications (NEMO). IEEE, 2014. http://dx.doi.org/10.1109/nemo.2014.6995676.

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Georgiadis, Apostolos. "Design of Coupled Oscillator Arrays for Second Harmonic Radiation." In 2007 IEEE/MTT-S International Microwave Symposium. IEEE, 2007. http://dx.doi.org/10.1109/mwsym.2007.380061.

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Georgiou, Ioannis T., and Ira B. Schwartz. "Decoupling the Free Axial-Transverse Motions of a Nonlinear Plate: An Invariant Manifold Approach." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0320.

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Abstract We approximate the nonlinearly coupled transverse-axial motions of an isotropic elastic plate with three nonlinearly coupled fundamental oscillators, and show that transverse motions can be decoupled from in-plane motions. We demonstrate this decoupling by showing analytically and numerically the existence of a global two-dimensional nonlinear invariant manifold. The invariant manifold carries a continuum of slow, periodic motions. In particular, for any motion on the slow invariant manifold, the transverse oscillator executes a periodic motion and it slaves the in-plane oscillators into periodic motions of half its period. The spectrum of the in-plane slaved motions consists of two distinct harmonics with frequencies twice and quadruple than that of the dominant harmonic of the transverse motion. Furthermore, as the energy level of motion on the slow manifold increases the frequency of the largest harmonic of the in-plane motions approaches the in-plane natural frequencies. This causes the in-plane oscillators to oscillate in pure compression.
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Kawasaki, Kengo, Takayuki Tanaka, and Masayoshi Aikawa. "Ku band second harmonic N-coupled push-push oscillator array using microstrip resonator." In 2010 IEEE/MTT-S International Microwave Symposium - MTT 2010. IEEE, 2010. http://dx.doi.org/10.1109/mwsym.2010.5517980.

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Kaw, K., T. Tanaka, and M. Aikawa. "Ku band second harmonic N-coupled push-push oscillator array using microstrip resonator." In 2010 IEEE/MTT-S International Microwave Symposium - MTT 2010. IEEE, 2010. http://dx.doi.org/10.1109/mwsym.2010.5518317.

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Gourc, Etienne, Guilhem Michon, Se´bastien Seguy, and Alain Berlioz. "Experimental Investigation and Theoretical Analysis of a Nonlinear Energy Sink Under Harmonic Forcing." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-48090.

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In the present works, we examine experimentally and theoretically the dynamic behavior of linear oscillator strongly coupled to a nonlinear energy sink under external periodic forcing. The nonlinear oscillator has a nonlinear restoring force realized geometrically with two linear springs that extend axially and are free to rotate. Hence, the force-displacement relationship is cubic. The linear oscillator is directly excited via an electrodynamic shaker. Experiments realized on the test bench consist of measuring the displacement of the oscillators while increasing and decreasing frequencies around the fundamental resonance of the linear oscillator. Many nonlinear dynamical phenomena are observed on the experimental setup such as jumps, bifurcation, and quasiperiodic regimes. The retained nonlinear model is a two degree of freedom system. The behavior of the system is then explained analytically and numerically. The complexification averaging technique is used to derive a set of modulation equation governing the evolution of the complex amplitude at the frequency of excitation, and a stability analysis is performed.
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Muraki, Yasushi. "Application of a Coupled Harmonic Oscillator Model to Solar Activity and El Niño Phenomena." In 35th International Cosmic Ray Conference. Trieste, Italy: Sissa Medialab, 2017. http://dx.doi.org/10.22323/1.301.0084.

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Prados, A., L. L. Bonilla, and A. Carpio. "Statics and dynamics of a harmonic oscillator coupled to a one-dimensional Ising system." In NONEQUILIBRIUM STATISTICAL PHYSICS TODAY: Proceedings of the 11th Granada Seminar on Computational and Statistical Physics. AIP, 2011. http://dx.doi.org/10.1063/1.3569511.

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10

Haaker, T. I. "Analysis of a Class of Coupled Nonlinear Oscillators With an Application to Flow Induced Vibrations." In ASME 2001 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/detc2001/vib-21416.

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Abstract:
Abstract We consider in this paper the following system of coupled nonlinear oscillatorsx..+x-k(y-x)=εf(x,x.),y..+(1+δ)y-k(x-y)=εf(y,y.). In this system we assume ε to be a small parameter, i.e. 0 < ε ≪ 1. A coupling between the two oscillators is established through the terms involving the positive parameter k. The coupling may be interpreted as a mutual force depending on the relative positions of the two oscillators. For both ε and k equal to zero the two oscillators are decoupled and behave as harmonic oscillators with frequencies 1 and 1+δ, respectively. The parameter δ may therefore be viewed as a detuning parameter. Finally, the term ε f represents a small force acting upon each oscillator. Note that this force depends only on the position and velocity of the oscillator upon which the force is acting. To analyse the system’s dynamic behaviour we use the method of averaging. When k and δ are choosen such that no internal resonance occurs, one typically observes the following behaviour. If the trivial solution is unstable, solutions asymptotically tend to one of the two normal modes or to a mixed mode solution. For the special case with δ = 0 a system of two identical oscillators is found. If in addition k is O(ε) we obtain a 1 : 1 internal resonant system. The averaged equations may then be reduced to a system of three coupled equations — two for the amplitudes and one for the phase difference. Due to the fact that we consider identical oscillators there is a symmetry in the averaged equations. The normal mode solutions, as found for the non-resonant case, are still present. New mixed mode solutions appear. Moreover, Hopf bifurcations in the averaged system lead to limit cycles that correspond to oscillations in the original system with periodically modulated amplitudes and phases. We also consider the case with δ = O(ε), i.e. the case with nearly identical oscillators. If k = O(ε) again a 1 : 1 internal resonant system is found. Contrary to the previous cases the normal mode solutions no longer exist. Moreover, different bifurcations are observed due to the disappearance of the symmetry present in the system for s = 0. We apply some of the results obtained to a model describing aeroelastic oscillations of a structure with two-degrees-of-freedom.
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Reports on the topic "Coupled harmonic oscillator"

1

Yeon, Kyu-Hwang, Chung-In Um, Woo-Hyung Kahng, and Thomas F. George. Propagators for Driven Coupled Harmonic Oscillators. Fort Belvoir, VA: Defense Technical Information Center, September 1988. http://dx.doi.org/10.21236/ada199418.

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2

Maidanik, G. Loss Factors of a Complex Composed of a Number of Coupled Harmonic Oscillators. Fort Belvoir, VA: Defense Technical Information Center, February 1997. http://dx.doi.org/10.21236/ada325092.

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