Heat transport in oscillator chains with long-range interactions coupled to thermal reservoirs

Iubini, Stefano; Cintio, Pierfrancesco Di; Lepri, Stefano; Livi, Roberto; Casetti, Lapo

doi:10.1103/physreve.97.032102

Cited by 36 publications

(48 citation statements)

References 42 publications

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“…3 changes geometry. We show in the inset of cous heat equations predict a steeper-than-Fourier's law or non-linear temperature gradient that is reminiscent of that obtained in molecular dynamics simulations [88][89][90][91][92][93][94][95][96][97] and in explicit solutions of the LBTE [34].…”

Section: Case Studysupporting

confidence: 59%

Generalization of Fourier’s Law into Viscous Heat Equations

2020

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Heat conduction in dielectric crystals originates from the propagation of atomic vibrational waves, whose microscopic dynamics is well described by linearized or generalized phonon Boltzmann transport. Recently, it was shown that the thermal conductivity can be resolved exactly and in a closed form as a sum over relaxons, i.e. the collective phonon excitations that are eigenvectors of Boltzmann equation's scattering matrix [Cepellotti and Marzari, Phys. Rev. X 6, 041013 (2016)]. Relaxons have a well-defined parity and only odd relaxons contribute to the thermal conductivity. Here, we show that the complementary set of even relaxons determines another quantity -the thermal viscosity -that enters into the description of heat transport in the hydrodynamic regime, where dissipation of crystal momentum by Umklapp scattering phases out. We also show how the thermal viscosity and conductivity parametrize two novel viscous heat equations -two coupled equations for the local temperature and drift velocity fields -which represent the thermal counterpart of the Navier-Stokes equations of hydrodynamics in the linear, laminar regime. These viscous heat equations are derived from a coarse-graining of the linearized Boltzmann transport equation for phonons, and encompass both limits of Fourier's law or second sound for strong or weak Umklapp dissipation, respectively. Last, we introduce the Fourier deviation number, a dimensionless parameter that quantifies the steady-state deviations from Fourier's law due to hydrodynamic effects. We showcase these findings in a test case of a complex-shaped device made of silicon or diamond. This formulation generalizes rigorously Fourier's heat equation, and extends the reach of microscopic computational techniques to characterize the fundamental parameters governing heat conduction. * michele.simoncelli@epfl.ch ics. Sussmann and Thellung [12], starting from the linearized BTE (LBTE) in absence of momentumdissipating (Umklapp) phonon-phonon scattering events, derived mesoscopic equations in terms of temperature and phonon drift velocity, the thermal counterpart of pressure and fluid velocity in liquids. Further advances came from Gurzhi [13,14] and Guyer & Krumhansl [15,16] who, including the effect of weak crystal momentum dissipation, obtained equations for damped second sound and Poiseuille heat flow. Among early works, we also mention the discussions on phonon hydrodynamics using approaches different from the LBTE of Refs. [17,18]. While correctly capturing the qualitative features of phonon hydrodynamics, all the theoretical investigations mentioned above are heuristic, e.g. they assume simplified phonon dispersion relations (either power-law [13,14] or linear isotropic [12,15,16]), or neglect momentum dissipation. A more rigorous and general formulation -albeit valid only in the hydrodynamic regime of weak Umklapp scattering -was introduced by Hardy, who extended the discussion of second sound [19] and, together with Albers, of Poiseuille flow in terms of mesoscopic transport equations...

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Section: Case Studysupporting

confidence: 59%

Generalization of Fourier’s Law into Viscous Heat Equations

2020

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“…These include dipolar BECs [50], where the recent formation of quantum droplets and their bound states [51] suggests that interesting types of long-range interactions can also arise in the study of BECs in optical lattices. Long-range interactions also play important roles in the study of coupled phase oscillators in diverse physical settings [26], heat transport in oscillator chains coupled to thermal reservoirs [52,53], and more. (1) with frequency f b ≈5.…”

Section: Discussionmentioning

confidence: 99%

Nonlinear excitations in magnetic lattices with long-range interactions

et al. 2019

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We study-experimentally, theoretically, and numerically-nonlinear excitations in lattices of magnets with long-range interactions. We examine breather solutions, which are spatially localized and periodic in time, in a chain with algebraically-decaying interactions. It was established two decades ago (Flach 1998 Phys. Rev. E 58 R4116) that lattices with long-range interactions can have breather solutions in which the spatial decay of the tails has a crossover from exponential to algebraic decay. In this article, we revisit this problem in the setting of a chain of repelling magnets with a mass defect and verify, both numerically and experimentally, the existence of breathers with such a crossover.

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“…In Refs. [20][21][22], the coupled rotor model was studied. This model shows a transition from the diffusive transport to the thermal insulator, as δ decreases from infinity.…”

Section: Introductionmentioning

confidence: 99%

“…[22,23], the Fermi-Pasta-Ulam (FPU) model was investigated, and it was found that the transport behavior is generally anomalous, except at δ = 2, where it exhibits ballistic behavior [23]. In stud-arXiv:1906.08457v1 [cond-mat.stat-mech] 20 Jun 2019 ies on the FPU model, long-range interactions can be added in several ways, e.g., long-range quadratic potential terms [24], long-range quartic potential terms [13,23], and a combination of both [8,22]. From these studies, many intriguing transport properties have been numerically shown.…”

Section: Introductionmentioning

confidence: 99%

Energy current correlation in solvable long-range interacting systems

Tamaki

Saito

2020

Phys. Rev. E

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We consider heat transfer in one-dimensional systems with long-range interactions. It is known that short-range interacting systems generally shows anomalous behavior in heat transport when total momentum is conserved, whereas momentum-nonconserving systems do not exhibit anomaly. In this study, we focus on the effect of long-range interaction. We propose an exactly solvable model that reduces to the so-called momentum-exchange model in the short-range interaction limit. We exactly calculate the asymptotic time-decay in the energy current correlation function, which is related to the thermal conductivity via the Green-Kubo formula. From the time-decay of the current correlation, we show two qualitatively crucial results. First, the anomalous exponent in the time-decay continuously changes as a function of the index of the long-range interaction. Second, even momentum-nonconserving systems can show the anomalous exponent indicating anomalous heat transport.

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Heat transport in oscillator chains with long-range interactions coupled to thermal reservoirs

Cited by 36 publications

References 42 publications

Generalization of Fourier’s Law into Viscous Heat Equations

Generalization of Fourier’s Law into Viscous Heat Equations

Nonlinear excitations in magnetic lattices with long-range interactions

Energy current correlation in solvable long-range interacting systems

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