Quantum dissipation and the virial theorem

Ghosh, Aritra; Bandyopadhyay, Malay

doi:10.1016/j.physa.2023.128999

Cited by 5 publications

(3 citation statements)

References 33 publications

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“…It may be verified from the above expressions that both the average kinetic and potential energies of the system are non-decreasing functions of parameters γ, ω cut , and ω 0 [37,42]. One should also note that unlike in the weak-coupling limit, the average kinetic energy is not equal to the average potential energy [80].…”

Section: J Stat Mech (2024) 074002mentioning

confidence: 88%

“…We now briefly discuss the weak-coupling limit in the context of the quantum Langevin equation [69,[76][77][78][79][80][81], in the sense of the Born-Markov approximation. For a generic open system which is described by a total Hamiltonian H, the full density operator ρ undergoes a unitary evolution as described by the Liouville-von Neumann equation:…”

Section: Weak-coupling Limitmentioning

confidence: 99%

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Independent-oscillator model and the quantum Langevin equation for an oscillator: a review

Ghosh,

Bandyopadhyay,

Dattagupta

et al. 2024

J. Stat. Mech.

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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.

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Section: J Stat Mech (2024) 074002mentioning

confidence: 88%

Section: Weak-coupling Limitmentioning

confidence: 99%

Independent-oscillator model and the quantum Langevin equation for an oscillator: a review

Ghosh,

Bandyopadhyay,

Dattagupta

et al. 2024

J. Stat. Mech.

View full text Add to dashboard Cite

show abstract

“…The time evolution of a chain of coupled harmonic oscillators is deterministic and can be analytically expressed. However, it exhibits complicated behaviours such as Brownian motion [11][12][13][14][15]. These pseudo-random motions originate from the superposition of harmonic oscillations with irrational frequencies.…”

Section: Introductionmentioning

confidence: 99%

Statistical analysis of coupled oscillations with a single fixed endpoint and its application to carbon nanomaterials

Inui

2024

Phys. Scr.

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Squared deviations from the equilibrium positions of one-dimensional coupled harmonic oscillators with fixed and free endpoints are calculated, and the time averages are expressed as a function of the initial displacements and velocities. Furthermore, we consider the averages of squared deviations over an ensemble of initial displacements and velocities, which distribute based on a product of the same distribution functions with variances of the initial coordinates σx 2 and velocities σv 2, respectively. We demonstrate that the mean squared deviation linearly increases as the oscillator separates further from the fixed endpoint because of the asymmetrical boundary conditions, and that the increase rate depends only on σv 2 and not on σx 2. This simple statistical property of harmonic oscillation is similarly observed in the oscillations of a graphene sheet and carbon nanotube in molecular dynamics simulations, in which the interacting forces are nonlinear.

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Weak-coupling limits of the quantum Langevin equation for an oscillator

Ghosh,

Dattagupta

2024

Physica A: Statistical Mechanics and its Applications

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Quantum dissipation and the virial theorem

Cited by 5 publications

References 33 publications

Independent-oscillator model and the quantum Langevin equation for an oscillator: a review

Independent-oscillator model and the quantum Langevin equation for an oscillator: a review

Statistical analysis of coupled oscillations with a single fixed endpoint and its application to carbon nanomaterials

Weak-coupling limits of the quantum Langevin equation for an oscillator

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