Independent-oscillator model and the quantum Langevin equation for an oscillator: A review
- URL: http://arxiv.org/abs/2306.02665v2
- Date: Tue, 9 Jul 2024 07:48:08 GMT
- Title: Independent-oscillator model and the quantum Langevin equation for an oscillator: A review
- Authors: Aritra Ghosh, Malay Bandyopadhyay, Sushanta Dattagupta, Shamik Gupta,
- Abstract summary: A derivation of the quantum Langevin equation is outlined based on the microscopic model of the heat bath.
In the steady state, we analyze the quantum counterpart of energy equipartition theorem.
The free energy, entropy, specific heat, and third law of thermodynamics are discussed for one-dimensional quantum Brownian motion.
- Score: 19.372542786476803
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: This review provides a brief and quick introduction to the quantum Langevin equation for an oscillator, while focusing on the steady-state thermodynamic aspects. A derivation of the quantum Langevin equation is carefully outlined based on the microscopic model of the heat bath as a collection of a large number of independent quantum oscillators, the so-called independent-oscillator model. This is followed by a discussion on the relevant `weak-coupling' limit. In the steady state, we analyze the quantum counterpart of energy equipartition theorem which has generated a considerable amount of interest in recent literature. The free energy, entropy, specific heat, and third law of thermodynamics are discussed for one-dimensional quantum Brownian motion in a harmonic well. Following this, we explore some aspects of dissipative diamagnetism in the context of quantum Brownian oscillators, emphasizing upon the role of confining potentials and also upon the environment-induced classical-quantum crossover. We discuss situations where the system-bath coupling is via the momentum variables by focusing on a gauge-invariant model of momentum-momentum coupling in the presence of a vector potential; for this problem, we derive the quantum Langevin equation and discuss quantum thermodynamic functions. Finally, the topic of fluctuation theorems is discussed (albeit, briefly) in the context of classical and quantum cyclotron motion of a particle coupled to a heat bath.
Related papers
- Quantum Effects on the Synchronization Dynamics of the Kuramoto Model [62.997667081978825]
We show that quantum fluctuations hinder the emergence of synchronization, albeit not entirely suppressing it.
We derive an analytical expression for the critical coupling, highlighting its dependence on the model parameters.
arXiv Detail & Related papers (2023-06-16T16:41:16Z) - Partition of kinetic energy and magnetic moment in dissipative
diamagnetism [20.218184785285132]
We analyze dissipative diamagnetism, arising due to dissipative cyclotron motion in two dimensions, in the light of the quantum counterpart of energy equipartition theorem.
The expressions for kinetic energy and magnetic moment are reformulated in the context of superstatistics.
arXiv Detail & Related papers (2022-07-30T08:07:28Z) - Correspondence Between the Energy Equipartition Theorem in Classical
Mechanics and its Phase-Space Formulation in Quantum Mechanics [62.997667081978825]
In quantum mechanics, the energy per degree of freedom is not equally distributed.
We show that in the high-temperature regime, the classical result is recovered.
arXiv Detail & Related papers (2022-05-24T20:51:03Z) - Energy fluctuation relations and repeated quantum measurements [4.724825031148412]
We discuss the statistical description in non-equilibrium regimes of energy fluctuations originated by the interaction between a quantum system and a measurement apparatus.
To properly quantify the information about energy fluctuations, both the exchanged heat probability density function and the corresponding characteristic function are derived and interpreted.
arXiv Detail & Related papers (2022-02-05T16:20:13Z) - Dynamics of entropy and information of time-dependent quantum systems:
exact results [0.0]
Dynamical aspects of information-theoretic and entropic measures of quantum systems are studied.
We show that for the time-dependent harmonic oscillator, as well as for the charged particle in certain time-varying electromagnetic fields, the increase of the entropy and dynamics of the Fisher information can be directly described and related.
We detail the behavior of quantum quenches for the case of mutually non-interacting non-relativistic fermions in a harmonic trap.
arXiv Detail & Related papers (2021-08-02T15:22:32Z) - From geometry to coherent dissipative dynamics in quantum mechanics [68.8204255655161]
We work out the case of finite-level systems, for which it is shown by means of the corresponding contact master equation.
We describe quantum decays in a 2-level system as coherent and continuous processes.
arXiv Detail & Related papers (2021-07-29T18:27:38Z) - Quantum simulation of non-equilibrium dynamics and thermalization in the
Schwinger model [0.0]
We present simulations of non-equilibrium dynamics of quantum field theories on digital quantum computers.
We consider the Schwinger model, a 1+1 dimensional U(1) gauge theory, coupled through a Yukawa-type interaction to a thermal environment.
arXiv Detail & Related papers (2021-06-15T19:48:05Z) - Evolution of a Non-Hermitian Quantum Single-Molecule Junction at
Constant Temperature [62.997667081978825]
We present a theory for describing non-Hermitian quantum systems embedded in constant-temperature environments.
We find that the combined action of probability losses and thermal fluctuations assists quantum transport through the molecular junction.
arXiv Detail & Related papers (2021-01-21T14:33:34Z) - Probing eigenstate thermalization in quantum simulators via
fluctuation-dissipation relations [77.34726150561087]
The eigenstate thermalization hypothesis (ETH) offers a universal mechanism for the approach to equilibrium of closed quantum many-body systems.
Here, we propose a theory-independent route to probe the full ETH in quantum simulators by observing the emergence of fluctuation-dissipation relations.
Our work presents a theory-independent way to characterize thermalization in quantum simulators and paves the way to quantum simulate condensed matter pump-probe experiments.
arXiv Detail & Related papers (2020-07-20T18:00:02Z) - Zitterbewegung and Klein-tunneling phenomena for transient quantum waves [77.34726150561087]
We show that the Zitterbewegung effect manifests itself as a series of quantum beats of the particle density in the long-time limit.
We also find a time-domain where the particle density of the point source is governed by the propagation of a main wavefront.
The relative positions of these wavefronts are used to investigate the time-delay of quantum waves in the Klein-tunneling regime.
arXiv Detail & Related papers (2020-03-09T21:27:02Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.