Role of the on-site pinning potential in establishing quasi-steady-state conditions of heat transport in finite quantum systems

Cuansing, Eduardo C.; Li, Huanan; Wang, Jian‐Sheng

doi:10.1103/physreve.86.031132

Cited by 18 publications

(25 citation statements)

References 27 publications

(21 reference statements)

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“…The first step in such a calculation is to determine the surface Green's functions. The eigenvalues and eigenvectors of the uniform tridiagonal matrix can be obtained analytically [63,64], given…”

Section: Landauer Formulamentioning

confidence: 99%

Nonequilibrium Green’s function method for quantum thermal transport

et al. 2013

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This review deals with the nonequilibrium Green's function (NEGF) method applied to the problems of energy transport due to atomic vibrations (phonons), primarily for small junction systems. We present a pedagogical introduction to the subject, deriving some of the well-known results such as the Laudauer-like formula for heat current in ballistic systems. The main aim of the review is to build the machinery of the method so that it can be applied to other situations, which are not directly treated here. In addition to the above, we consider a number of applications of NEGF, not in routine model system calculations, but in a few new aspects showing the power and usefulness of the formalism. In particular, we discuss the problems of multiple leads, coupled left-right-lead system, and system without a center. We also apply the method to the problem of full counting statistics. In the case of nonlinear systems, we make general comments on the thermal expansion effect, phonon relaxation time, and a certain class of mean-field approximations. Lastly, we examine the relationship between NEGF, reduced density matrix, and master equation approaches to thermal transport.

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Section: Landauer Formulamentioning

confidence: 99%

Nonequilibrium Green’s function method for quantum thermal transport

et al. 2013

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“…8 shows the time dependence of the dimensionless heat current 10 5 J th (t)/ ω 2 0 , where J th (t) is determined by (44). The shown time dependences are generic for the considered model.…”

Section: Temperature Relaxation and Fourier's Lawmentioning

confidence: 99%

“…8), when ∆/ω 0 0.001 approximate expression (69) for the G factor gives essentially the same result for J th (t) as when the corresponding accurate expression (65) is used. Thus, the short-scale oscillations from accurate G(ν k , t) around its approximate value (69) average out due to summation in (44) and smooth resulting J th (t) is determined by (69). It must be mentioned that even when ∆t is large, the heat current still can be non-zero if one recovers the contributions to J th (t) containing explicitly g(t) orġ(t) (see the text just before Eq.…”

Section: Temperature Relaxation and Fourier's Lawmentioning

confidence: 99%

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Size effects in long-term quasistatic heat transport

Panasyuk

Yerkes

2013

Phys. Rev. E

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We consider finite size effects on heat transfer between thermal reservoirs mediated by a quantum system, where the number of modes in each reservoir is finite. Our approach is based on the generalized quantum Langevin equation and the thermal reservoirs are described as ensembles of oscillators within the DrudeUllersma model. A general expression for the heat current between the thermal reservoirs in the long-time quasi-static regime, when an observation time is of the order of ∆ −1 and ∆ is the mode spacing constant of a thermal reservoir, is obtained. The resulting equations that govern the long-time relaxation for the mode temperatures and the average temperatures of the reservoirs are derived and approximate analytical solutions are found. The obtained time dependences of the temperatures and the resulting heat current reveal peculiarities at t = 2πm/∆ with nonnegative integers m and the heat current vanishes non-monotonically when t → ∞. The validity of Fourier's law for a chain of finite-size macroscopic subsystems is considered. As is shown, for characteristic times of the order of ∆ −1 the temperatures of subsystems' modes deviate from each other and the validity of Fourier's law cannot be established. In a case when deviations of initial temperatures of the subsystems from their average value are small, t → ∞ asymptotic values for the mode temperatures do not depend on a mode's number and are the same as if Fourier's law were valid for all times.

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“…The nonequilibrium Green's function approach offers a natural framework to study transient effects both in electronic [41][42][43] and phononic systems [44][45][46]. Also in the case of phonon transport, it would be extremely useful to have a time-dependent Landauer-Büttiker formula for interpreting the transient oscillations and relaxation times in an intuitive fashion.…”

Section: Introductionmentioning

confidence: 99%

Phononic heat transport in the transient regime: An analytic solution

et al. 2016

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We investigate the time-resolved quantum transport properties of phonons in arbitrary harmonic systems connected to phonon baths at different temperatures. We obtain a closed analytic expression of the time-dependent one-particle reduced density matrix by explicitly solving the equations of motion for the nonequilibrium Green's function. This is achieved through a well-controlled approximation of the frequency-dependent bath self-energy. Our result allows for exploring transient oscillations and relaxation times of local heat currents, and correctly reduces to an earlier known result in the steady-state limit. We apply the formalism to atomic chains, and benchmark the validity of the approximation against full numerical solutions of the bosonic Kadanoff-Baym equations for the Green's function. We find good agreement between the analytic and numerical solutions for weak contacts and baths with a wide energy dispersion. We further analyze relaxation times from low to high temperature gradients.

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Role of the on-site pinning potential in establishing quasi-steady-state conditions of heat transport in finite quantum systems

Cited by 18 publications

References 27 publications

Nonequilibrium Green’s function method for quantum thermal transport

Nonequilibrium Green’s function method for quantum thermal transport

Size effects in long-term quasistatic heat transport

Phononic heat transport in the transient regime: An analytic solution

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