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Equilibration of a dissipative quantum oscillator

Vinay Ambegaokar

Abstract An explicit demonstration is given of a harmonic oscillator in equilibrium approaching the equilibrium of a corresponding interacting system by coupling it to a thermal bath consisting of a continuum of harmonic oscillators.

Annalen der PhysikJan 19, 20070 citations

Irreversible behavior of a quantum harmonic oscillator coupled to a heat bath

Ernest Braun

Physica A Statistical Mechanics and its ApplicationsJan 1, 198522 citations

Quantum Brownian motion: Drude and Ohmic baths as continuum limits of the Rubin model

Avijit Das, Abhishek Dhar, Ion Santra +2 more

The motion of a free quantum particle in a thermal environment is usually described by the quantum Langevin equation, where the effect of the bath is encoded through a dissipative and a noise term, related to each other via the fluctuation dissipation theorem. The quantum Langevin equation can be derived starting from a microscopic model of the thermal bath as an infinite collection of harmonic oscillators prepared in an initial equilibrium state. The spectral properties of the bath oscillators and their coupling to the particle determine the specific form of the dissipation and noise. Here we investigate in detail the well-known Rubin bath model, which consists of a one-dimensional harmonic chain with the boundary bath particle coupled to the Brownian particle. We show how in the limit of infinite bath bandwidth, we get the Drude model, and a second limit of infinite system-bath coupling gives the Ohmic model. A detailed analysis of relevant equilibrium correlation functions, such as the mean squared displacement, velocity autocorrelation functions, and response function are presented, with the aim of understanding the various temporal regimes. In particular, we discuss the quantum-to-classical crossover time scales where the mean square displacement changes from a ∼lnt to a ∼t dependence. We relate our study to recent work using linear response theory to understand quantum Brownian motion.The motion of a free quantum particle in a thermal environment is usually described by the quantum Langevin equation, where the effect of the bath is encoded through a dissipative and a noise term, related to each other via the fluctuation dissipation theorem. The quantum Langevin equation can be derived starting from a microscopic model of the thermal bath as an infinite collection of harmonic oscillators prepared in an initial equilibrium state. The spectral properties of the bath oscillators and their coupling to the particle determine the specific form of the dissipation and noise. Here we investigate in detail the well-known Rubin bath model, which consists of a one-dimensional harmonic chain with the boundary bath particle coupled to the Brownian particle. We show how in the limit of infinite bath bandwidth, we get the Drude model, and a second limit of infinite system-bath coupling gives the Ohmic model. A detailed analysis of relevant equilibrium correlation functions, such as the mean squared displacement, velocity autocorrelation functions, and response function are presented, with the aim of understanding the various temporal regimes. In particular, we discuss the quantum-to-classical crossover time scales where the mean square displacement changes from a ∼lnt to a ∼t dependence. We relate our study to recent work using linear response theory to understand quantum Brownian motion.

arXiv:2006.14637Physical review. EDec 14, 202013 citations

Equilibration and thermalization of the dissipative quantum harmonic oscillator in a nonthermal environment

D. Pagel, Andreas Alvermann, Holger Fehske

We study the dissipative quantum harmonic oscillator with general nonthermal preparations of the harmonic oscillator bath. The focus is on equilibration of the oscillator in the long-time limit and the additional requirements for thermalization. Our study is based on the exact solution of the microscopic model obtained by means of operator equations of motion, which provides us with the time evolution of the central oscillator density matrix in terms of the propagating function. We find a hierarchy of conditions for thermalization, together with the relation of the asymptotic temperature to the energy distribution in the initial bath state. We discuss the presence and absence of equilibration for the example of an inhomogeneous chain of harmonic oscillators, and we illustrate the general findings about thermalization for the nonthermal environment that results from a quench.We study the dissipative quantum harmonic oscillator with general nonthermal preparations of the harmonic oscillator bath. The focus is on equilibration of the oscillator in the long-time limit and the additional requirements for thermalization. Our study is based on the exact solution of the microscopic model obtained by means of operator equations of motion, which provides us with the time evolution of the central oscillator density matrix in terms of the propagating function. We find a hierarchy of conditions for thermalization, together with the relation of the asymptotic temperature to the energy distribution in the initial bath state. We discuss the presence and absence of equilibration for the example of an inhomogeneous chain of harmonic oscillators, and we illustrate the general findings about thermalization for the nonthermal environment that results from a quench.

arXiv:1205.2068Physical Review EJan 22, 201317 citations

Quantum thermodynamics of a driven damped quantum harmonic oscillator

Jan 1, 20210 citations

Quantum gates based on two strongly coupled harmonic oscillators in thermal non-equilibrium conditions

Behzad Lari, Won Sang Chung, HASSAN HASSANABADI

Physica A Statistical Mechanics and its ApplicationsJan 27, 20242 citations

Equilibration of a dissipative quantum oscillator

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Equilibration of a dissipative quantum oscillator

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