Quantum thermodynamic functions for an oscillator coupled to a heat bath

Ford, G. W.; O’Connell, R. F.

doi:10.1103/physrevb.75.134301

Cited by 42 publications

(65 citation statements)

References 13 publications

(22 reference statements)

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“…In this work, we want to give up this assumption and formulate generalized nonequilibrium fluctuation relations for nonthermal initial states. To do so, we consider the dissipative quantum mechanical harmonic oscillator [29][30][31][32][33][34][35][36][37]. Building on our previous work in [38] we study a central oscillator coupled to an arbitrary number of harmonic baths each of which can be prepared in its own individual initial state.…”

Section: Introductionmentioning

confidence: 99%

Nonequilibrium quantum fluctuation relations for harmonic systems in nonthermal environments

Pagel¹,

Nalbach²,

Alvermann³

et al. 2013

New J. Phys.

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We formulate exact generalized nonequilibrium fluctuation relations for the quantum mechanical harmonic oscillator coupled to multiple harmonic baths. Each of the different baths is prepared in its own individual (in general nonthermal) state. Starting from the exact solution for the oscillator dynamics we study fluctuations of the oscillator position as well as of the energy current through the oscillator under general nonequilibrium conditions. In particular, we formulate a fluctuation-dissipation relation for the oscillator position autocorrelation function that generalizes the standard result for the case of a single bath at thermal equilibrium. Moreover, we show that the generating function for the position operator fulfils a generalized Gallavotti-Cohen-like relation. For the energy transfer through the oscillator, we determine the average energy current together with the current fluctuations. Finally, we discuss the generalization of the cumulant generating function for the energy transfer to nonthermal bath preparations.

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Section: Introductionmentioning

confidence: 99%

Nonequilibrium quantum fluctuation relations for harmonic systems in nonthermal environments

Pagel¹,

Nalbach²,

Alvermann³

et al. 2013

New J. Phys.

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“…where 1,2 ), The part of action (12) cl S corresponding to an interaction of two oscillators in Eq. (37) is determined as follows …”

Section: Appendix B Coefficients In Eqs(38)(39)mentioning

confidence: 99%

“…The hamiltonian system composed by a selected particle plus a thermal reservoir followed by reduction with respect to reservoir's variables allow investigating the origin of irreversibility in the dynamics of a quantum system interacting with a heat bat; see for instance [1][2][3][4][5][6][7][8][9][10]. In this connection, thermodynamic characteristics of a quantum oscillator coupled to a heat bath, various definitions of the characteristics, some subtleties due to possible approximations were studied in [11][12][13][14][15]. In parallel, another set of adjoint studies were performed from the point of view of the relaxation of open systems to the steady state and description of the nonequilibrium transport phenomena.…”

Section: Introductionmentioning

confidence: 99%

Relaxation of two coupled quantum oscillators to quasi-equilibrium states based on path integrals

DorofeyevIllarion

2014

Can. J. Phys.

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The paper addresses the problem of relaxation of open quantum systems. Using the path integral methods we found an analytical expression for time-dependent density matrix of two coupled quantum oscillators interacting with different baths of oscillators. The expression for density matrix was found in the linear regime with respect to the coupling constant between selected oscillators.Time-dependent spatial variances and covariance were investigated analytically and numerically. It was shown that asymptotic variances in the long-time limit are always in accordance with the fluctuation dissipation theorem despite on their initial values. In the weak coupling approach there is good reason to believe that subsystems asymptotically in equilibrium at their own temperatures even despite of the arbitrary difference in temperatures within the whole system.

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“…The reduced partition function is defined in terms of the partition functions of the coupled system and the uncoupled bath [2,4,23,45,25,26,27,28,29,30,31,32], which is defined as…”

Section: Equilibrium Momentum Dispersion Of the Free Particlementioning

confidence: 99%

Quantum dynamics of a dissipative and confined cyclotron motion

Kumar¹

2014

Physica A: Statistical Mechanics and its Applications

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We study the dissipative dynamics of a charged oscillator in a magnetic field by coupling (a la Caldeira and Leggett) it to a heat bath consisting of non-interacting harmonic oscillators. We derive here the autocorrelation functions of the position and momentum and study its behavior at various limiting situations. The equilibrium (steady state) dispersions of position and momentum are obtained from their respective autocorrelation functions. We analyse the equilibrium position and momentum dispersions at low and high temperatures for both low and high magnetic field strengths. We obtain the classical diffusive behavior (at long times) as well as the equilibrium momentum dispersion of the free quantum charged particle in a magnetic field, in the limit of vanishing oscillator potential ω 0 . We establish the relations between the reduced partition function and the equilibrium dispersions of the dissipative and confined cyclotron problem.

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Quantum thermodynamic functions for an oscillator coupled to a heat bath

Cited by 42 publications

References 13 publications

Nonequilibrium quantum fluctuation relations for harmonic systems in nonthermal environments

Nonequilibrium quantum fluctuation relations for harmonic systems in nonthermal environments

Relaxation of two coupled quantum oscillators to quasi-equilibrium states based on path integrals

Quantum dynamics of a dissipative and confined cyclotron motion

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