Quantum dynamics of the damped harmonic oscillator

Philbin, T. G.

doi:10.1088/1367-2630/14/8/083043

Cited by 33 publications

(70 citation statements)

References 37 publications

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“…This is usually known as microscopic causality, and for instance, it is fulfilled for the free Maxwell electromagnetic field [40]. As a consequence, we show in Appendix C that the self-energy satisfies a generalized Kramers-Kronig identity [23,39], i.e.…”

Section: A Generalized Lanvegin Equationmentioning

confidence: 61%

“…the system particles mainly interact with the field low-energy modes in comparison with the oscillator bare frequencies). Substituting these results (19) and (23) in (10), we obtain a quadratic Hamiltonian which constitutes a firstorder approximation to the low-lying dissipative dynamics (10). At this point, the latter Hamiltonian can be brought into a suitable form by performing the Goeppert-Mayer transformation [43],…”

Section: Quantum Dissipationmentioning

confidence: 99%

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Quantum dissipation of planar harmonic systems: Maxwell-Chern-Simons theory

Valido¹

2019

Phys. Rev. D

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Conventional Brownian motion in harmonic systems has provided a deep understanding of a great diversity of dissipative phenomena. We address a rather fundamental microscopic description for the (linear) dissipative dynamics of two-dimensional harmonic oscillators that contains the conventional Brownian motion as a particular instance. This description is derived from first principles in the framework of the so-called Maxwell-Chern-Simons electrodynamics, or also known, Abelian topological massive gauge theory. Disregarding backreaction effects and endowing the system Hamiltonian with a suitable renormalized potential interaction, the conceived description is equivalent to a minimal-coupling theory with a gauge field giving rise to a fluctuating force that mimics the Lorentz force induced by a particle-attached magnetic flux. We show that the underlying symmetry structure of the theory (i.e. time-reverse asymmetry and parity violation) yields an interacting vortex-like Brownian dynamics for the system particles. An explicit comparison to the conventional Brownian motion in the quantum Markovian limit reveals that the proposed description represents a second-order correction to the well-known damped harmonic oscillator, which manifests that there may be dissipative phenomena intrinsic to the dimensionality of the interesting system.

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Section: A Generalized Lanvegin Equationmentioning

confidence: 61%

Section: Quantum Dissipationmentioning

confidence: 99%

Quantum dissipation of planar harmonic systems: Maxwell-Chern-Simons theory

Valido¹

2019

Phys. Rev. D

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“…Therefore, this treatment is formally correct from a classical point of review but a complete investigation on a quantum dissipative system should resort to the open quantum theory by including a continuum reservoir which can be modeled by an ensemble of harmonic oscillators with infinite degree of freedom [12]. However, the open quantum theory is somehow cumbersome and heavily depends on the statistical properties of the reservoirs that we should know in advance.…”

Section: A a Brief Note On Dissipative Quantum Systemmentioning

confidence: 99%

“…The mass m 0 and the frequency ω 0 used in Eq. (12) are the intrinsic or characteristic parameters which can be properly chosen according to the initial conditions for a controlled system. Then the six generators of su(2) and h(4) algebras arê…”

Section: The General Quadratic Hamiltonian and Its Lie Algebramentioning

confidence: 99%

Lie transformation method on quantum state evolution of a general time-dependent driven and damped parametric oscillator

Zhang

2016

Annals of Physics

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A variety of dynamics in nature and society can be approximately treated as a driven and damped parametric oscillator. An intensive investigation of this time-dependent model from an algebraic point of view provides a consistent method to resolve the classical dynamics and the quantum evolution in order to understand the time-dependent phenomena that occur not only in the macroscopic classical scale for the synchronized behaviors but also in the microscopic quantum scale for a coherent state evolution. By using a Floquet U-transformation on a general time-dependent quadratic Hamiltonian, we exactly solve the dynamic behaviors of a driven and damped parametric oscillator to obtain the optimal solutions by means of invariant parameters of Ks to combine with Lewis-Riesenfeld invariant method. This approach can discriminate the external dynamics from the internal evolution of a wave packet by producing independent parametric equations that dramatically facilitate the parametric control on the quantum state evolution in a dissipative system. In order to show the advantages of this method, several time-dependent models proposed in the quantum control field are analyzed in details.

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“…This has been a persistent challenge for a long time since dissipation causes difficulties in the quantization of the damped oscillator [1,2,3]. This problem has remained under intensive investigation [4,5]. There are some widely accepted Hamilton-like variation theories about the treatment of a linearly damped classic or quantum-damped oscillator.…”

Section: Introductionmentioning

confidence: 99%