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Journal articles on the topic 'Quantum-mechanical oscillator'

Author: Grafiati

Published: 4 June 2021

Last updated: 4 February 2022

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1

Burd, S. C., R. Srinivas, J. J. Bollinger, et al. "Quantum amplification of mechanical oscillator motion." Science 364, no. 6446 (2019): 1163–65. http://dx.doi.org/10.1126/science.aaw2884.

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Detection of the weakest forces in nature is aided by increasingly sensitive measurements of the motion of mechanical oscillators. However, the attainable knowledge of an oscillator’s motion is limited by quantum fluctuations that exist even if the oscillator is in its lowest possible energy state. We demonstrate a technique for amplifying coherent displacements of a mechanical oscillator with initial magnitudes well below these zero-point fluctuations. When applying two orthogonal squeezing interactions, one before and one after a small displacement, the displacement is amplified, ideally with no added quantum noise. We implemented this protocol with a trapped-ion mechanical oscillator and determined an increase by a factor of up to 7.3 (±0.3) in sensitivity to small displacements.

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2

Mercier de Lépinay, Laure, Caspar F. Ockeloen-Korppi, Matthew J. Woolley, and Mika A. Sillanpää. "Quantum mechanics–free subsystem with mechanical oscillators." Science 372, no. 6542 (2021): 625–29. http://dx.doi.org/10.1126/science.abf5389.

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Quantum mechanics sets a limit for the precision of continuous measurement of the position of an oscillator. We show how it is possible to measure an oscillator without quantum back-action of the measurement by constructing one effective oscillator from two physical oscillators. We realize such a quantum mechanics–free subsystem using two micromechanical oscillators, and show the measurements of two collective quadratures while evading the quantum back-action by 8 decibels on both of them, obtaining a total noise within a factor of 2 of the full quantum limit. This facilitates the detection of weak forces and the generation and measurement of nonclassical motional states of the oscillators. Moreover, we directly verify the quantum entanglement of the two oscillators by measuring the Duan quantity 1.4 decibels below the separability bound.

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3

Ikot, Akpan N., Louis E. Akpabio, Ita O. Akpan, Michael I. Umo, and Eno E. Ituen. "Quantum Damped Mechanical Oscillator." International Journal of Optics 2010 (2010): 1–6. http://dx.doi.org/10.1155/2010/275910.

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The exact solutions of the Schrödinger equation for quantum damped oscillator with modified Caldirola-Kanai Hamiltonian are evaluated. We also investigate the cases of under-, over-, and critical damping.

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4

Sergeev, S. "Quantum curve inq-oscillator model." International Journal of Mathematics and Mathematical Sciences 2006 (2006): 1–31. http://dx.doi.org/10.1155/ijmms/2006/92064.

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A lattice model of interactingq-oscillators, proposed by V. Bazhanov and S. Sergeev in 2005 is the quantum-mechanical integrable model in2+1dimensional space-time. Its layer-to-layer transfer matrix is a polynomial of two spectral parameters, it may be regarded in terms of quantum groups both as a sum ofsl(N)transfer matrices of a chain of lengthMand as a sum ofsl(M)transfer matrices of a chain of lengthNfor reducible representations. The aim of this paper is to derive the Bethe ansatz equations for theq-oscillator model entirely in the framework of2+1integrability providing the evident rank-size duality.

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5

BLASONE, MASSIMO, GIUSEPPE VITIELLO, PETR JIZBA, and FABIO SCARDIGLI. "DETERMINISM BENEATH COMPOSITE QUANTUM SYSTEMS." International Journal of Modern Physics A 24, no. 18n19 (2009): 3652–59. http://dx.doi.org/10.1142/s0217751x09047314.

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This paper aims at the development of 't Hooft's quantization proposal to describe composite quantum mechanical systems. In particular, we show how 't Hooft's method can be utilized to obtain from two classical Bateman oscillators a composite quantum system corresponding to a quantum isotonic oscillator. For a suitable range of parameters, the composite system can be also interpreted as a particle in an effective magnetic field interacting through a spin-orbital interaction term. In the limit of a large separation from the interaction region we can identify the irreducible subsystems with two independent quantum oscillators.

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6

Rath, Biswanath, Pravanjan Mallick, Prachiprava Mohapatra, Jihad Asad, Hussein Shanak, and Rabab Jarrar. "Position-dependent finite symmetric mass harmonic like oscillator: Classical and quantum mechanical study." Open Physics 19, no. 1 (2021): 266–76. http://dx.doi.org/10.1515/phys-2021-0024.

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Abstract We formulated the oscillators with position-dependent finite symmetric decreasing and increasing mass. The classical phase portraits of the systems were studied by analytical approach (He’s frequency formalism). We also study the quantum mechanical behaviour of the system and plot the quantum mechanical phase space for necessary comparison with the same obtained classically. The phase portrait in all the cases exhibited closed loop reflecting the stable system but the quantum phase portrait exhibited the inherent signature (cusp or kink) near origin associated with the mass. Although the systems possess periodic motion, the discrete eigenvalues do not possess any similarity with that of the simple harmonic oscillator having m = 1.

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7

SISTO, RENATA, and ARTURO MOLETI. "ON THE SENSITIVITY OF GRAVITATIONAL WAVE RESONANT BAR DETECTORS." International Journal of Modern Physics D 13, no. 04 (2004): 625–39. http://dx.doi.org/10.1142/s021827180400475x.

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Different theoretical estimates of the sensitivity of gravitational wave resonant bar detectors, which have been published in the last decades, are reviewed and discussed. The "classical" cross-section estimate is obtained considering the bar as a classical or quantum oscillator, whose initial thermal state is that of a single oscillator driven by a single external stochastic force. Other theoretical studies computed a much larger cross-section, using a variety of quantum-mechanical arguments. The review of the existing literature shows that there is no well established model for the response of a resonant detector to gravitational waves. The resonant, yet random, nature of the Brownian thermal motion may justify considering the bar response at the fundamental longitudinal eigenfrequency as that of a large number of effective quantum mechanical oscillators. Assuming this hypothesis, quantum coherence effects, as first suggested by Weber, lead to a much larger cross-section than that "classically" predicted. The reduction of this amplification due to thermal noise itself is also computed.

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8

Trifonov, E. D. "Quantum-mechanical oscillator in a uniform force field." Russian Journal of Physical Chemistry B 6, no. 2 (2012): 205–9. http://dx.doi.org/10.1134/s1990793112020248.

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9

Hardy, L., D. Home, E. J. Squires, and M. A. B. Whitaker. "Realism and the quantum-mechanical two-state oscillator." Physical Review A 45, no. 7 (1992): 4267–70. http://dx.doi.org/10.1103/physreva.45.4267.

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10

Floratos, E. G., and T. N. Tomaras. "A quantum mechanical analogue for the q-oscillator." Physics Letters B 251, no. 1 (1990): 163–66. http://dx.doi.org/10.1016/0370-2693(90)90247-4.

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11

Floratos, E. G. "A quantum mechanical analogue for the q-oscillator." Nuclear Physics B - Proceedings Supplements 22, no. 1 (1991): 144–47. http://dx.doi.org/10.1016/0920-5632(91)90361-h.

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12

McKean, H. P., and E. Trubowitz. "The spectral class of the quantum-mechanical oscillator." Communications in Mathematical Physics 99, no. 4 (1985): 626. http://dx.doi.org/10.1007/bf01215913.

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13

Shababi, Homa, Pouria Pedram, and Won Sang Chung. "On the quantum mechanical solutions with minimal length uncertainty." International Journal of Modern Physics A 31, no. 18 (2016): 1650101. http://dx.doi.org/10.1142/s0217751x16501013.

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In this paper, we study two generalized uncertainty principles (GUPs) including [Formula: see text] and [Formula: see text] which imply minimal measurable lengths. Using two momentum representations, for the former GUP, we find eigenvalues and eigenfunctions of the free particle and the harmonic oscillator in terms of generalized trigonometric functions. Also, for the latter GUP, we obtain quantum mechanical solutions of a particle in a box and harmonic oscillator. Finally we investigate the statistical properties of the harmonic oscillator including partition function, internal energy, and heat capacity in the context of the first GUP.

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14

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 (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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15

ISAR, A., A. SANDULESCU, H. SCUTARU, E. STEFANESCU, and W. SCHEID. "OPEN QUANTUM SYSTEMS." International Journal of Modern Physics E 03, no. 02 (1994): 635–714. http://dx.doi.org/10.1142/s0218301394000164.

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The damping of the harmonic oscillator is studied in the framework of the Lindblad theory for open quantum systems. A generalization of the fundamental constraints on quantum mechanical diffusion coefficients which appear in the master equation for the damped quantum oscillator is presented; the Schrödinger, Heisenberg and Weyl-Wigner-Moyal representations of the Lindblad equation are given explicitly. On the basis of these representations it is shown that various master equations for the damped quantum oscillator used in the literature are particular cases of the Lindblad equation and that not all of these equations are satisfying the constraints on quantum mechanical diffusion coefficients. Analytical expressions for the first two moments of coordinate and momentum are obtained by using the characteristic function of the Lindblad master equation. The master equation is transformed into Fokker-Planck equations for quasiprobability distributions and a comparative study is made for the Glauber P representation, the antinormal ordering Q representation, and the Wigner W representation. The density matrix is represented via a generating function, which is obtained by solving a timedependent linear partial differential equation derived from the master equation. Illustrative examples for specific initial conditions of the density matrix are provided. The solution of the master equation in the Weyl-Wigner-Moyal representation is of Gaussian type if the initial form of the Wigner function is taken to be a Gaussian corresponding (for example) to a coherent wavefunction. The damped harmonic oscillator is applied for the description of the charge equilibration mode observed in deep inelastic reactions. For a system consisting of two harmonic oscillators the time dependence of expectation values, Wigner function and Weyl operator, are obtained and discussed. In addition models for the damping of the angular momentum are studied. Using this theory to the quantum tunneling through the nuclear barrier, besides Gamow’s transitions with energy conservation, additional transitions with energy loss are found. The tunneling spectrum is obtained as a function of the barrier characteristics. When this theory is used to the resonant atom-field interaction, new optical equations describing the coupling through the environment of the atomic observables are obtained. With these equations, some characteristics of the laser radiation absorption spectrum and optical bistability are described.

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16

Ganesan, L. R., and M. Balaji. "The Harmonic Oscillator–A Simplified Approach." E-Journal of Chemistry 5, no. 3 (2008): 663–65. http://dx.doi.org/10.1155/2008/931317.

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Among the early problems in quantum chemistry, the one dimensional harmonic oscillator problem is an important one, providing a valuable exercise in the study of quantum mechanical methods. There are several approaches to this problem, the time honoured infinite series method, the ladder operator methodetc. A method which is much shorter, mathematically simpler is presented here.

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17

NOZARI, KOUROSH, and TAHEREH AZIZI. "QUANTUM MECHANICAL COHERENT STATES OF THE HARMONIC OSCILLATOR AND THE GENERALIZED UNCERTAINTY PRINCIPLE." International Journal of Quantum Information 03, no. 04 (2005): 623–32. http://dx.doi.org/10.1142/s0219749905001468.

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In this paper, dynamics and quantum mechanical coherent states of a simple harmonic oscillator are considered in the framework of the Generalized Uncertainty Principle (GUP). Equations of motion for the simple harmonic oscillator are derived and some of their new implications are discussed. Then, coherent states of the harmonic oscillator in the case of the GUP are compared with the relative situation in ordinary quantum mechanics. It is shown that in the framework of GUP there is no considerable difference in definition of coherent states relative to ordinary quantum mechanics. But, considering expectation values and variances of some operators, based on quantum gravitational arguments, one concludes that although it is possible to have complete coherency and vanishing broadening in usual quantum mechanics, gravitational induced uncertainty destroys complete coherency in quantum gravity and it is not possible to have a monochromatic ray in principle.

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18

Riseborough, Peter S., Peter Hanggi, and Ulrich Weiss. "Exact results for a damped quantum-mechanical harmonic oscillator." Physical Review A 31, no. 1 (1985): 471–78. http://dx.doi.org/10.1103/physreva.31.471.

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19

McCormick, Katherine C., Jonas Keller, Shaun C. Burd, David J. Wineland, Andrew C. Wilson, and Dietrich Leibfried. "Quantum-enhanced sensing of a single-ion mechanical oscillator." Nature 572, no. 7767 (2019): 86–90. http://dx.doi.org/10.1038/s41586-019-1421-y.

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20

Bussell, M., and P. Strange. "Evolution of superoscillations in the quantum mechanical harmonic oscillator." European Journal of Physics 36, no. 6 (2015): 065028. http://dx.doi.org/10.1088/0143-0807/36/6/065028.

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21

Truong, T. T. "The quantum mechanical Schrodinger picture of a q-oscillator." Journal of Physics A: Mathematical and General 27, no. 11 (1994): 3829–46. http://dx.doi.org/10.1088/0305-4470/27/11/032.

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22

Giri, Pulak Ranjan. "Generalized solutions for quantum mechanical oscillator on Kähler conifold." Journal of Physics A: Mathematical and General 39, no. 24 (2006): 7719–26. http://dx.doi.org/10.1088/0305-4470/39/24/008.

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23

Raghavan, S., and V. M. Kenkre. "Quantum mechanical bound rotator as a generalized harmonic oscillator." Journal of Physics: Condensed Matter 6, no. 47 (1994): 10297–306. http://dx.doi.org/10.1088/0953-8984/6/47/013.

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24

Inyang, E. P., B. I. Ita, and E. P. Inyang. "Relativistic Treatment of Quantum Mechanical Gravitational-Harmonic Oscillator Potential." European Journal of Applied Physics 3, no. 3 (2021): 42–47. http://dx.doi.org/10.24018/ejphysics.2021.3.3.83.

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The solutions of the Klein- Gordon equation for the quantum mechanical gravitational plus harmonic oscillator potential with equal scalar and vector potential have been presented using the parametric Nikiforov-Uvarov method. The energy eigenvalues were obtained in relativistic and non-relativistic regime and the corresponding un-normalized eigenfunctions in terms of Laguerre polynomials. The numerical values for the S – wave bound state were obtained.

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25

Le Coq, Yann, Klaus Mølmer, and Signe Seidelin. "Position- and momentum-squeezed quantum states in micro-scale mechanical resonators." Modern Physics Letters B 34, no. 17 (2020): 2050193. http://dx.doi.org/10.1142/s0217984920501936.

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A challenge of modern physics is to investigate the quantum behavior of a bulk material object, for instance a mechanical oscillator. We have earlier demonstrated that by coupling a mechanical oscillator to the energy levels of embedded rare-earth ion dopants, it is possible to prepare such a resonator in a low phonon number state. Here, we describe how to extend this protocol in order to prepare momentum- and position-squeezed states, and we analyze how the obtainable degree of squeezing depends on the initial conditions and on the coupling of the oscillator to its thermal environment.

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26

Kienzler, D., H. Y. Lo, B. Keitch, et al. "Quantum harmonic oscillator state synthesis by reservoir engineering." Science 347, no. 6217 (2014): 53–56. http://dx.doi.org/10.1126/science.1261033.

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The robust generation of quantum states in the presence of decoherence is a primary challenge for explorations of quantum mechanics at larger scales. Using the mechanical motion of a single trapped ion, we utilize reservoir engineering to generate squeezed, coherent, and displaced-squeezed states as steady states in the presence of noise. We verify the created state by generating two-state correlated spin-motion Rabi oscillations, resulting in high-contrast measurements. For both cooling and measurement, we use spin-oscillator couplings that provide transitions between oscillator states in an engineered Fock state basis. Our approach should facilitate studies of entanglement, quantum computation, and open-system quantum simulations in a wide range of physical systems.

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27

Shababi, Homa, and Won Sang Chung. "Some quantum mechanical solutions in nonrelativistic anti-Snyder framework." International Journal of Modern Physics A 32, no. 27 (2017): 1750170. http://dx.doi.org/10.1142/s0217751x17501706.

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In this paper, we investigate nonrelativistic anti-Snyder model in momentum representation and obtain quantum mechanical eigenvalues and eigenfunctions. Using this framework, first, in one dimension, we study a particle in a box and the harmonic oscillator problems. Then, for more investigations, in three dimensions, the quantum mechanical eigenvalues and eigenfunctions of a free particle problem and the radius of the neutron star are obtained.

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28

Wu, E., FengZhi Li, XueFeng Zhang, and YongHong Ma. "Optomechanical entanglement of a macroscopic oscillator by quantum feedback." International Journal of Quantum Information 14, no. 05 (2016): 1650022. http://dx.doi.org/10.1142/s0219749916500222.

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We propose a scheme to generate the case of macroscopic entanglement in the optomechanical system, which consist of Fabry–Perot cavity and a mechanical oscillator by applying a homodyne-mediated quantum feedback. We explore the effect of feedback on the entanglement in vacuum and coherent state, respectively. The results show that the introduction of quantum feedback can increase the entanglement effectively between the cavity mode and the oscillator mode.

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29

Hsueh, Ya-Wei, Che-Hsiu Hsueh, and Wen-Chin Wu. "Thermalization in a Quantum Harmonic Oscillator with Random Disorder." Entropy 22, no. 8 (2020): 855. http://dx.doi.org/10.3390/e22080855.

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We propose a possible scheme to study the thermalization in a quantum harmonic oscillator with random disorder. Our numerical simulation shows that through the effect of random disorder, the system can undergo a transition from an initial nonequilibrium state to a equilibrium state. Unlike the classical damped harmonic oscillator where total energy is dissipated, total energy of the disordered quantum harmonic oscillator is conserved. In particular, at equilibrium the initial mechanical energy is transformed to the thermodynamic energy in which kinetic and potential energies are evenly distributed. Shannon entropy in different bases are shown to yield consistent results during the thermalization.

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30

Fradkin, David M. "Novel solution of the one‐dimensional quantum‐mechanical harmonic oscillator." Journal of Mathematical Physics 33, no. 5 (1992): 1705–9. http://dx.doi.org/10.1063/1.529648.

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31

Yuan, Xueyong, Michael Schwendtner, Rinaldo Trotta, et al. "A frequency-tunable nanomembrane mechanical oscillator with embedded quantum dots." Applied Physics Letters 115, no. 18 (2019): 181902. http://dx.doi.org/10.1063/1.5126670.

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32

Blood, F. A. "A relativistic quantum mechanical harmonic oscillator without space‐time variables." Journal of Mathematical Physics 29, no. 6 (1988): 1389–95. http://dx.doi.org/10.1063/1.527931.

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33

Dutta, A. K., and R. S. Willey. "Exact analytic solutions for the quantum mechanical sextic anharmonic oscillator." Journal of Mathematical Physics 29, no. 4 (1988): 892–900. http://dx.doi.org/10.1063/1.527986.

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34

Kime, K. "Control of transition probabilities of the quantum-mechanical harmonic oscillator." Applied Mathematics Letters 6, no. 3 (1993): 11–15. http://dx.doi.org/10.1016/0893-9659(93)90024-h.

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35

Amore, Paolo, and Francisco M. Fernández. "A quantum-mechanical anharmonic oscillator with a most interesting spectrum." Annals of Physics 385 (October 2017): 1–9. http://dx.doi.org/10.1016/j.aop.2017.07.007.

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36

Eckhardt, W. "The quantum-mechanical harmonic oscillator: Markovian limit and commutation relations." Physics Letters A 114, no. 2 (1986): 75–76. http://dx.doi.org/10.1016/0375-9601(86)90482-2.

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37

Schmitt, H. A., and A. Mufti. "Noncompact orthosympletic supersymmetry: an example from N = 1, d = 1 supersymmetric quantum mechanics." Canadian Journal of Physics 68, no. 12 (1990): 1454–55. http://dx.doi.org/10.1139/p90-208.

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The supersymmetric quantum mechanical harmonic oscillator, a particular example of an N = 1, d = 1 supersymmetric quantum mechanical model, is used to construct a Hamiltonian exhibiting a noncompact orthosymplectic supersymmetry. This Hamiltonian is the strong-coupling limit of the Jaynes–Cummings model.

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38

Babenko, V. A., and N. M. Petrov. "On the quantum anharmonic oscillator and Padé approximations." Nuclear Physics and Atomic Energy 22, no. 2 (2021): 127–42. http://dx.doi.org/10.15407/jnpae2021.02.127.

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For the quantum quartic anharmonic oscillator with the Hamiltonian H = (p2+x2)/2+λx4, which is one of the traditional quantum-mechanical and quantum-field-theory models, we study summation of its factorially divergent perturbation series by the proposed method of averaging of the corresponding Padé approximants. Thus, for the first time, we are able to construct the Padé-type approximations that possess correct asymptotic behaviour at infinity with a rise of the coupling constant λ. The approach gives very essential theoretical and applicatory-computational advantages in applications of the given method. We also study convergence of the applied approximations and calculate by the proposed method the ground state energy E0(λ) of the anharmonic oscillator for a wide range of variation of the coupling constant λ.

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39

HÜFFEL, H., and H. NAKAZATO. "TRANSITION AMPLITUDES WITHIN THE STOCHASTIC QUANTIZATION SCHEME." Modern Physics Letters A 09, no. 32 (1994): 2953–66. http://dx.doi.org/10.1142/s0217732394002793.

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Quantum mechanical transition amplitudes are calculated within the stochastic quantization scheme for the free nonrelativistic particle, the Harmonic oscillator and the nonrelativistic particle in a constant magnetic field; we conclude with free Grassmann quantum mechanics.

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40

SAMSONOV, BORIS F. "NEW FEATURES IN SUPERSYMMETRY BREAKDOWN IN QUANTUM MECHANICS." Modern Physics Letters A 11, no. 19 (1996): 1563–67. http://dx.doi.org/10.1142/s0217732396001557.

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The supersymmetric quantum mechanical model based on higher-derivative supercharge operators possessing unbroken supersymmetry and discrete energies below the vacuum state energy is described. As an example harmonic oscillator potential is considered.

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41

Doherty, Andrew C., A. Szorkovszky, G. I. Harris, and W. P. Bowen. "The quantum trajectory approach to quantum feedback control of an oscillator revisited." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 370, no. 1979 (2012): 5338–53. http://dx.doi.org/10.1098/rsta.2011.0531.

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We revisit the stochastic master equation approach to feedback cooling of a quantum mechanical oscillator undergoing position measurement. By introducing a rotating wave approximation for the measurement and bath coupling, we can provide a more intuitive analysis of the achievable cooling in various regimes of measurement sensitivity and temperature. We also discuss explicitly the effect of backaction noise on the characteristics of the optimal feedback. The resulting rotating wave master equation has found application in our recent work on squeezing the oscillator motion using parametric driving and may have wider interest.

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42

Tóth, L. D., N. R. Bernier, A. Nunnenkamp, A. K. Feofanov, and T. J. Kippenberg. "A dissipative quantum reservoir for microwave light using a mechanical oscillator." Nature Physics 13, no. 8 (2017): 787–93. http://dx.doi.org/10.1038/nphys4121.

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43

Youn, Sun-Hyun, Jai-Hyung Lee, and Joon-Sung Chang. "Quantum-mechanical noise characteristics in a doubly resonant optical parametric oscillator." Journal of the Optical Society of America B 11, no. 11 (1994): 2282. http://dx.doi.org/10.1364/josab.11.002282.

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44

Yeo, I., P.-L. de Assis, A. Gloppe, et al. "Strain-mediated coupling in a quantum dot–mechanical oscillator hybrid system." Nature Nanotechnology 9, no. 2 (2013): 106–10. http://dx.doi.org/10.1038/nnano.2013.274.

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45

Sakakura, T., and K. Tanaka. "Atomic displacement parameters based on quantum mechanical treatment of anharmonic oscillator." Acta Crystallographica Section A Foundations of Crystallography 64, a1 (2008): C436. http://dx.doi.org/10.1107/s0108767308086017.

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46

Mohazzabi, P. "On classical and quantum harmonic potentials." Canadian Journal of Physics 78, no. 10 (2000): 937–46. http://dx.doi.org/10.1139/p00-071.

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To date, the only potential energy function that has been demonstrated to be classical harmonic but not quantum harmonic is that of the asymmetrically matched harmonic oscillator. By investigating the accurate quantum mechanical energy levels of the potential V = V0 [Formula: see text], we demonstrate that this is the second member of the class. PACS No.: 03.65Ge

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47

Szasz A., Vincze Gy. "Rosen-Chambers Variation Theory of Linearly-Damped Classic and Quantum Oscillator." JOURNAL OF ADVANCES IN PHYSICS 4, no. 1 (2014): 404–26. http://dx.doi.org/10.24297/jap.v4i1.6966.

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Phenomena of damped harmonic oscillator is important in the description of the elementary dissipative processes of linear responses in our physical world. Its classical description is clear and understood, however it is not so in the quantum physics, where it also has a basic role. Starting from the Rosen-Chambers restricted variation principle a Hamilton like variation approach to the damped harmonic oscillator will be given. The usual formalisms of classical mechanics, as Lagrangian, Hamiltonian, Poisson brackets, will be covered too. We shall introduce two Poisson brackets. The first one has only mathematical meaning and for the second, the so-called constitutive Poisson brackets, a physical interpretation will be presented. We shall show that only the fundamental constitutive Poisson brackets are not invariant throughout the motion of the damped oscillator, but these show a kind of universal time dependence in the universal time scale of the damped oscillator. The quantum mechanical Poisson brackets and commutation relations belonging to these fundamental time dependent classical brackets will be described. Our objective in this work is giving clearer view to the challenge of the dissipative quantum oscillator.

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48

Bräuer, Kurt. "Nonlinear Analysis of Individual Quantum Events in a Model with Bohm Trajectories." Zeitschrift für Naturforschung A 54, no. 12 (1999): 663–74. http://dx.doi.org/10.1515/zna-1999-1201.

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Abstract The quantum mechanical model under consideration describes a particle beam under the influence of an oscillator. Bohm’s causal interpretation of quantum mechanics is used to calculate trajectories of the particles. Individual quantum events are defined by the intersection of the beam particle trajectories and the particle detector. The time sequence of individual quantum events is interpreted as a time series and is analyzed by linear and nonlinear methods, which involves reconstruction and investigation of the system in an embedding space. The Fourier amplitudes and the fill factors show white noise, however the Karhunen-Loeve components indicate the influence of the oscillator on the beam particles. In this model individual quantum events carry information which can be detected by the Karhunen-Loeve ex-pansion.

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Blasone, Massimo, and Giuseppe Vitiello. "Dissipation, coherence and entanglement." International Journal of Geometric Methods in Modern Physics 17, supp01 (2020): 2040005. http://dx.doi.org/10.1142/s0219887820400058.

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The study of the damped harmonic oscillator shows that dissipation could be seen at the origin of the zero point energy, which is the signature of quantum behavior. This is in accord with ’t Hooft proposal that loss of information in a completely deterministic dynamics would play a rôle in the quantum mechanical nature of our world. We show the equivalence, within quite general conditions, between the pair of a damped oscillator and its time-reversed image and electrodynamics. The ground state of the damped-amplified oscillator pair appears to be a finite temperature coherent two-mode squeezed state with fractal self-similarity properties and the modes are maximally entangled. Temperature is strictly related to the zero point energy.

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Aounallah, H., B. C. Lütfüoğlu, and J. Kříž. "Thermal properties of a two-dimensional Duffin–Kemmer–Petiau oscillator under an external magnetic field in the presence of a minimal length." Modern Physics Letters A 35, no. 33 (2020): 2050278. http://dx.doi.org/10.1142/s0217732320502788.

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Generalized uncertainty principle puts forward the existence of the shortest distances and/or maximum momentum at the Planck scale for consideration. In this article, we investigate the solutions of a two-dimensional Duffin–Kemmer–Petiau (DKP) oscillator within an external magnetic field in a minimal length (ML) scale. First, we obtain the eigensolutions in ordinary quantum mechanics. Then, we examine the DKP oscillator in the presence of an ML for the spin-zero and spin-one sectors. We determine an energy eigenvalue equation in both cases with the corresponding eigenfunctions in the non-relativistic limit. We show that in the ordinary quantum mechanic limit, where the ML correction vanishes, the energy eigenvalue equations become identical with the habitual quantum mechanical ones. Finally, we employ the Euler–Mclaurin summation formula and obtain the thermodynamic functions of the DKP oscillator in the high-temperature scale.

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