Fourier’s law: Insight from a simple derivation

Ventra, Massimiliano Di

doi:10.1103/physreve.79.042101

Cited by 57 publications

(85 citation statements)

References 44 publications

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“…This growth is partially due to the fact that the understanding of how energy flow can be controlled and efficiently distributed has been identified as one of the crucial fields of study for the development of modern societies [1,2]. One of the conceptual pillars in energy transport, the validity of Fourier's law of heat conduction, has become an active area of investigation and has been investigated in classical [3,4] and quantum systems [5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Quantum transport efficiency and Fourier's law

et al. 2012

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We analyze the steady-state energy transfer in a chain of coupled two-level systems connecting two thermal reservoirs. Through an analytic treatment we find that the energy current is independent of the system size, hence violating Fourier's law of heat conduction. The classical diffusive behavior in Fourier's law of heat conduction can be recovered by introducing decoherence to the quantum systems constituting the chain. We relate these results to recent discussions of energy transport in biological light-harvesting systems, and discuss the role of quantum coherence and entanglement.

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Section: Introductionmentioning

confidence: 99%

Quantum transport efficiency and Fourier's law

et al. 2012

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“…We have previously [40] studied the asymmetric forces in this system neglecting the coupling to electrode phonons. Figure 1 shows the average excess kinetic energy [ΔE n ¼ E n ðeVÞ − E n ð0Þ] [41][42][43][44][45][46] of atoms along the chain for three different Fermi levels E F . The structure is almost mirror symmetric.…”

Section: H Y S I C a L R E V I E W L E T T E R S Week Ending 6 March mentioning

confidence: 99%

Current-Induced Forces and Hot Spots in Biased Nanojunctions

et al. 2015

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We investigate theoretically the interplay of current-induced forces (CIFs), Joule heating, and heat transport inside a current-carrying nanoconductor. We find that the CIFs, due to the electron-phonon coherence, can control the spatial heat dissipation in the conductor. This yields a significant asymmetric concentration of excess heating (hot spot) even for a symmetric conductor. When coupled to the electrode phonons, CIFs drive different phonon heat flux into the two electrodes. First-principles calculations on realistic biased nanojunctions illustrate the importance of the effect.

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“…(55) is accurate (no need for any additional linearizing to produce (53) and (55) from (51)). One can also define average temperatures T 1,2 (t) of each bath from the condition that T 1,2 (t) provide the same total energies of the baths:…”

Section: Quasi-static Heat Balancementioning

confidence: 99%

“…The chain system discussed above is similar to some extend to chain systems considered in Refs. [52,53]. In Ref.…”

Section: A Fourier's Lawmentioning

confidence: 99%

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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Fourier’s law: Insight from a simple derivation

Cited by 57 publications

References 44 publications

Quantum transport efficiency and Fourier's law

Quantum transport efficiency and Fourier's law

Current-Induced Forces and Hot Spots in Biased Nanojunctions

Size effects in long-term quasistatic heat transport

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