Heat Conduction in Chains of Nonlinear Oscillators

Lepri, Stefano; Livi, Roberto; Politi, Antonio

doi:10.1103/physrevlett.78.1896

Cited by 491 publications

(520 citation statements)

References 22 publications

Supporting

Mentioning

485

Contrasting

Unclassified

Order By: Relevance

“…II is rather standard in the study of heat transport along harmonic chains with a single mass per unit cell, including terms beyond the usual intermass coupling but within the harmonic approximation. 10 In our case, we have considered a time-dependent version of those extensions in order to model the moving barrier.…”

Section: Discussionmentioning

confidence: 99%

“…9 Several studies of different classical and quantum models have analyzed the local temperature profile of chains of coupled oscillators in contact with two reservoirs at different temperatures. 10 The striking feature found in these studies was the violation of the Fourier law, according to which the local temperature is expected to drop linearly along the chain. This behavior is the phononic counterpart of the abrupt drop of the local voltage at the connections between a finite size electronic system to two reservoirs at different chemical potentials, which has been characterized by the concept of "contact resistance".…”

mentioning

confidence: 99%

See 1 more Smart Citation

Microscopic model of a phononic refrigerator

et al. 2012

View full text Add to dashboard Cite

We analyze a simple microscopic model to pump heat from a cold to a hot reservoir in a nanomechanical system. The model consists of a one-dimensional chain of masses and springs coupled to a back gate through which a time-dependent perturbation is applied. The action of the gate creates a moving phononic barrier by locally pinning a mass. We solve the problem numerically using a nonequilibrium Green function technique. For low driving frequencies and for sharp traveling barriers, we show that this microscopic model realizes a phonon refrigerator.

show abstract

Section: Discussionmentioning

confidence: 99%

mentioning

confidence: 99%

Microscopic model of a phononic refrigerator

et al. 2012

View full text Add to dashboard Cite

show abstract

“…Within this general context, one of the issues that attracted a renewed interest in the last decade is the problem of anomalous heat conduction in low-dimensional manyparticle systems [9,10]. In this case, the anomalous features amount to the divergence of the finite-size heat conductivity κ(L) ∝ L α in the limit L → ∞ and, correspondingly, to a nonintegrable decay of equilibrium correlations of the energy current (the GreenKubo integrand), J(t)J(0) ∝ t −(1−α) (0 ≤ α < 1) for long times t → ∞.…”

Section: Introductionmentioning

confidence: 99%

Anomalous kinetics and transport from 1D self-consistent mode-coupling theory

et al. 2007

Self Cite

View full text Add to dashboard Cite

Abstract. We study the dynamics of long-wavelength fluctuations in onedimensional (1D) many-particle systems as described by self-consistent modecoupling theory. The corresponding nonlinear integro-differential equations for the relevant correlators are solved analytically and checked numerically. In particular, we find that the memory functions exhibit a power-law decay accompanied by relatively fast oscillations. Furthermore, the scaling behaviour and, correspondingly, the universality class depends on the order of the leading nonlinear term. In the cubic case, both viscosity and thermal conductivity diverge in the thermodynamic limit. In the quartic case, a faster decay of the memory functions leads to a finite viscosity, while thermal conductivity exhibits an even faster divergence. Finally, our analysis puts on a more firm basis the previously conjectured connection between anomalous heat conductivity and anomalous diffusion.

show abstract

“…The increase in computer power led to a revival of the heat conduction problem inbetween the mid-1980s and the mid-1990s, when nonequilibrium simulations of the FPU model [106,107] and of the diatomic Toda chain [108,109,110,111] of alternating light and heavy masses were performed. Subsenquently, there were systematic studies on the size dependence of the heat conductivity for the FPU chain with quartic [112,113,114] or cubic [115] nonlinear potential as well as for the diatomic Toda chain [116,117]. They indicated a divergence of the heat conductivity with N , the number of mass points, which was interpreted as due to ballistic transport of energy through the chain.…”

Section: Heat Transport In Lattice Modelsmentioning

confidence: 99%

Dynamics of Oscillator Chains

Lichtenberg

Livi

Pettini

et al.

The Fermi-Pasta-Ulam Problem

Self Cite

View full text Add to dashboard Cite

Abstract. The Fermi-Pasta-Ulam (FPU) nonlinear oscillator chain has proved to be a seminal system for investigating problems in nonlinear dynamics. First proposed as a nonlinear system to elucidate the foundations of statistical mechanics, the initial lack of confirmation of the researchers expectations eventually led to a number of profound insights into the behavior of high-dimensional nonlinear systems. The initial numerical studies, proposed to demonstrate that energy placed in a single mode of the linearized chain would approach equipartition through nonlinear interactions, surprisingly showed recurrences. Although subsequent work showed that the origin of the recurrences is nonlinear resonance, the question of lack of equipartition remained. The attempt to understand the regularity bore fruit in a profound development in nonlinear dynamics: the birth of soliton theory. A parallel development, related to numerical observations that, at higher energies, equipartition among modes could be approached, was the understanding that the transition with increasing energy is due to resonance overlap. Further numerical investigations showed that time-scales were also important, with a transition between faster and slower evolution. This was explained in terms of mode overlap at higher energy and resonance overlap at lower energy. Numerical limitations to observing a very slow approach to equipartition and the problem of connecting high-dimensional Hamiltonian systems to lower dimensional studies of Arnold diffusion, which indicate transitions from exponentially slow diffusion along resonances to power-law diffusion across resonances, have been considered. Most of the work, both numerical and theoretical, started from low frequency (long wavelength) initial conditions. Coincident with developments to understand equipartition was another program to connect a statistical phenomenon to nonlinear dynamics, that of understanding classical heat conduction. The numerical studies were quite different, involving the excitation of a boundary oscillator with chaotic motion, rather than the excitation of

show abstract

Heat Conduction in Chains of Nonlinear Oscillators

Cited by 491 publications

References 22 publications

Microscopic model of a phononic refrigerator

Microscopic model of a phononic refrigerator

Anomalous kinetics and transport from 1D self-consistent mode-coupling theory

Dynamics of Oscillator Chains

Contact Info

Product

Resources

About