Thermal Conductivity in Harmonic Lattices with Random Collisions

Basile, Giada; Bernardin, Cédric; Jara, Milton; Komorowski, Tomasz; Olla, Stefano

doi:10.1007/978-3-319-29261-8_5

Cited by 18 publications

(32 citation statements)

References 47 publications

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“…have come to a satisfactory explanation. General theoretical approaches like nonlinear fluctuating hydrodynamics provides us a way of predicting the basic features of anomalous heat conductivity in one-dimensional chains of nonlinearly-coupled oscillators [4,5,6,7], while rigorous predictions of the anomalous behavior in stochastic conservative evolution of similar chains have been obtained [8,9,10,11]. Anyway, a good deal of numerical studies have paved the path of most of these achievements and still allow us to obtain inference about many still open problems, like the way anomalous behaviors depend on the kind of nonlinearity [12,13,14], dimension (e.g.…”

Section: Introductionmentioning

confidence: 99%

Transport in perturbed classical integrable systems: The pinned Toda chain

Cintio

Iubini

Lepri

et al. 2018

Chaos, Solitons & Fractals

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Nonequilibrium and thermal transport properties of the Toda chain, a prototype of classically integrable system, subject to additional (nonintegrable) terms are considered. In particular, we study via equilibrium and nonequilibrium simulations, the Toda lattice with a power-law pinning potential, recently analyzed by Lebowitz and Scaramazza [arXiv:1801.07153]. We show that, according to general expectations, even the case with quadratic pinning is genuinely non-integrable, as demonstrated by computing the Lyapunov exponents, and displays normal (diffusive) conductivity for very long chains. However, the model has unexpected dynamical features and displays strong finite-size effects and slow decay of correlations to be traced back to the propagation of soliton-like excitations, weakly affected by the harmonic pinning potential. Some novel results on current correlations for the standard integrable Toda model are also reported.

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Section: Introductionmentioning

confidence: 99%

Transport in perturbed classical integrable systems: The pinned Toda chain

Cintio

Iubini

Lepri

et al. 2018

Chaos, Solitons & Fractals

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“…Results in [12] extends also to the nonstationary superdiffusive evolution of the energy density, while the other two quantities evolve diffusively [15]. See also the review [1] and the other articles in the same volume about the numerical evidence in non-linear dynamics. The extension of such superdiffusive results to the non-linear dynamics is one of the most challenging problem.…”

Section: Introductionmentioning

confidence: 75%

Equilibrium fluctuation for an anharmonic chain with boundary conditions in the Euler scaling limit

Olla

2020

Nonlinearity

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We study the evolution in equilibrium of the fluctuations for the conserved quantities of a chain of anharmonic oscillators in the hyperbolic space-time scaling. Boundary conditions are determined by applying a constant tension at one side, while the position of the other side is kept fixed. The Hamiltonian dynamics is perturbed by random terms conservative of such quantities. We prove that these fluctuations evolve macroscopically following the linearized Euler equations with the corresponding boundary conditions, even in some time scales larger than the hyperbolic one.

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“…Similarly, our results could be relevant to discuss diffusion in amorphous materials at low temperature, when the system can be seen as hopping through different minima of its energy landscape. In this case, the heat bath is provided by the scattering of phonons, whose collision frequency is small at low temperatures23.…”

Section: Discussionmentioning

confidence: 99%

Escape rate and diffusion of a Stochastically Driven particle

Piscitelli

Ciamarra

2017

Sci Rep

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The dynamical properties of a tracer repeatedly colliding with heat bath particles can be described within a Langevin framework provided that the tracer is more massive than the bath particles, and that the collisions are frequent. Here we consider the escape of a particle from a potential well, and the diffusion coefficient in a periodic potential, without making these assumptions. We have thus investigated the dynamical properties of a Stochastically Driven particle that moves under the influence of the confining potential in between successive collisions with the heat bath. In the overdamped limit, both the escape rate and the diffusion coefficient coincide with those of a Langevin particle. Conversely, in the underdamped limit the two dynamics have a different temperature dependence. In particular, at low temperature the Stochastically Driven particle has a smaller escape rate, but a larger diffusion coefficient.

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Thermal Conductivity in Harmonic Lattices with Random Collisions

Cited by 18 publications

References 47 publications

Transport in perturbed classical integrable systems: The pinned Toda chain

Transport in perturbed classical integrable systems: The pinned Toda chain

Equilibrium fluctuation for an anharmonic chain with boundary conditions in the Euler scaling limit

Escape rate and diffusion of a Stochastically Driven particle

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