Independent-oscillator model and the quantum Langevin equation for an oscillator: A review
arXiv:2306.02665 · doi:10.1088/1742-5468/ad5711
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.
arXiv commentv2: accepted for publication in J Stat Mech: Theory Exp (2024)
References in corpus (38)
- A nonequilibrium equality for free energy differences
- Dynamical Ensembles in Nonequilibrium Statistical Mechanics
- Decoherence, the measurement problem, and interpretations of quantum mechanics
- Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems
- Colloquium. Quantum Fluctuation Relations: Foundations and Applications
- Fluctuation theorem for stochastic dynamics
- Quantum Decoherence
- A Brief History of the GKLS Equation
- Finite quantum dissipation: the challenge of obtaining specific heat
- Specific heat anomalies of open quantum systems
- Symmetries in Fluctuations Far from Equilibrium
- Two refreshing views of Fluctuation Theorems through Kinematics Elements and Exponential Martingale
- Symmetry properties of the large-deviation function of the velocity of a self-propelled polar particle
- Diffusion coefficient of a Brownian particle in equilibrium and nonequilibrium: Einstein model and beyond
- Heisenberg-Langevin vs. quantum master equation
- Low temperature Thermodynamics in the Context of Dissipative Diamagnetism
- Quantum thermodynamics of systems with anomalous dissipative coupling
- Quantum analogue of energy equipartition theorem
- Entropy of a Quantum Oscillator coupled to a Heat Bath and implications for Quantum Thermodynamics
- Anisotropic Isometric Fluctuation Relations in experiment and theory on a self-propelled rod
- Quantum partition of energy for a free Brownian particle: Impact of dissipation
- Dissipative Quantum Systems and the Heat Capacity Enigma
- Quantum Langevin equation of a charged oscillator in a magnetic field and coupled to a heat bath through momentum variables
- Quantum Counterpart of Classical Equipartition of Energy
- Quantum Brownian motion and the Third Law of thermodynamics
- Quantum thermodynamics of a charged magneto-oscillator coupled to a heat bath
- Does the Third Law of Thermodynamics hold in the Quantum Regime?
- Quantum counterpart of energy equipartition theorem for a dissipative charged magneto-oscillator: Effect of dissipation, memory, and magnetic field
- Quantum Brownian Motion: Drude and Ohmic Baths as Continuum Limits of the Rubin Model
- Partition of kinetic energy and magnetic moment in dissipative diamagnetism
- Generalised energy equipartition in electrical circuits
- Quantum dissipation and the virial theorem
- Multimode Brownian oscillators: Exact solutions to heat transport
- Landau diamagnetism revisited
- Free energy of a charged oscillator in a magnetic field and coupled to a heat bath through the momentum variables
- Weak-coupling limits of the quantum Langevin equation for an oscillator
- Generalized fluctuation theorems for classical systems
- Quantum fluctuation theorem for dissipative cyclotron motion
Cited by in corpus (5)
- Brownian-motion approach to statistical mechanics: Langevin equations, fluctuations, and timescales
- Explicit noise and dissipation operators for quantum stochastic thermodynamics
- Spin-orbit coupled spin-boson model : A variational analysis
- Detecting zero-point fluctuations with stochastic Brownian oscillators
- Quantum Counterpart of Equipartition Theorem: A Möbius Inversion Approach