Dissipative quantum systems and the heat capacity

Dattagupta, Sushanta; Kumar, Jishad; Sinha, Subhasis; Sreeram, P. A.

doi:10.1103/physreve.81.031136

Cited by 31 publications

(41 citation statements)

References 31 publications

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“…This proves that the issue of this "equality" seem to be just esoteric to the strict ohmic damping case. In our previous work [35], we have seen that in the strict ohmic limit (ω D → ∞), the specific heat calculated from the two different approaches matches each other exactly. This rather puzzling equality of the two approaches in the strict ohmic limit was pointed out earlier by Hänggi and Ingold [25] and Hänggi et al, [45], for a damped harmonic oscillator and a damped quantum free particle respectively.…”

Section: Equilibrium Momentum Dispersion Of the Free Particlementioning

confidence: 83%

“…For t ′ = t, we have seen that the time dependence disappeared completely from the position autocorrelation function and, we obtain, after a contour integration, the equilibrium value of the position autocorrelation as [35] …”

Section: Equilibrium Position Dispersionmentioning

confidence: 99%

“…(2)) is modified by the bath. We therefore rewrite the subsystem Hamiltonian as an effective stochastic Hamiltonian given by [35] …”

Section: Stochastic Modeling Position and Momentum Dispersionsmentioning

confidence: 99%

“…With all these spectacular phenomena in the frontier, one may interest to choose a charged oscillator in a magnetic field (actually a non-interacting electron gas confined in two dimensions) as the relevant quantum system of interest. This model of a dissipative charged oscillator in a magnetic field has been studied by many authors [15,16,17,18,19,21,22,33,34,35,36,37]. In particular, this model was used to study the dissipative Landau diamagnetism [19,21,33] as well as to verify the validity of the third law of thermodynamics [33,35,36].…”

Section: Introductionmentioning

confidence: 99%

“…In a previous paper [35] we have worked out the steady state equilibrium values of the position and momentum dispersions in order to compute the internal energy as the aim was to basically study the behavior of the specific heat at low and high temperatures under different limiting sequences within the framework of two different and distinct approaches to statistical mechanics, viz., the Gibbsian and the Einsteinian approaches. Some of the details about the model and the basic mathematical framework we use here can be found in our previous paper [35]. But for the sake of continuity and completeness we describe here the model and the required mathematical details from our previous work.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Equilibrium Momentum Dispersion Of the Free Particlementioning

confidence: 83%

Section: Equilibrium Position Dispersionmentioning

confidence: 99%

“…(2)) is modified by the bath. We therefore rewrite the subsystem Hamiltonian as an effective stochastic Hamiltonian given by [35] …”

Section: Stochastic Modeling Position and Momentum Dispersionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quantum dynamics of a dissipative and confined cyclotron motion

Kumar¹

2014

Physica A: Statistical Mechanics and its Applications

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Thermodynamics of a quantum dissipative charged magneto‐oscillator

Kumar

2014

Annalen der Physik

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Quantum dissipative effect on the thermodynamics of an electron in the combined presence of a parabolic potential and a uniform (and homogeneous) magnetic field, is investigated here. Starting from the microscopic system plus bath model, we explicitly derive the thermodynamic properties using the reduced partition function of the system which is calculated using the imaginary time path integral method. The quantum heat bath we consider here is a structured heat bath whose spectral density corresponds to a structured thermal harmonic noise. All the statistical thermodynamic functions calculated do reconcile with the requirements of the fundamental axioms of physics. In particular, the specific heat and the entropy vanishes as the temperature approaches its absolute zero value, a necessity of the third law of thermodynamics. Moreover the specific heat satisfies classical equipartition theorem at high temperatures. The coefficients of the leading temperature dependent terms of the thermodynamic quantities depend only on the damping constant but not on other parameters of the bath spectral density, which is similar to the analysis based on the Drude bath spectral density. Our study facilitates the physics of small quantum systems, which are always in contact with some environments, at very low temperatures.

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Classical and quantum Brownian motion in an electromagnetic field

Patriarca

Sodano

2016

Fortschritte der Physik

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The dynamics of a Brownian particle in a constant magnetic field and time‐dependent electric field is studied in the limit of white noise, using a Langevin approach for the classical problem and the path‐integral Feynman‐Vernon and Caldeira‐Leggett framework for the quantum problem. A first goal of this study is to use the two‐dimensional problem of a Brownian particle in a magnetic field to show that a proper re‐formulation of the oscillator model of quantum Brownian motion allows one to recover the classical limit of the dynamics correctly. Furthermore, the probability distribution in configuration space of an initial pure state represented by an asymmetrical Gaussian wave function is worked out and its general time evolution is decomposed in the superposition of basic processes: (a) the classical motion of the center of mass, (b) a rotation around the mean position, and (c) spreading processes along the principal axes.

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Dissipative quantum systems and the heat capacity

Cited by 31 publications

References 31 publications

Quantum dynamics of a dissipative and confined cyclotron motion

Quantum dynamics of a dissipative and confined cyclotron motion

Thermodynamics of a quantum dissipative charged magneto‐oscillator

Classical and quantum Brownian motion in an electromagnetic field

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