Diffusive Propagation of Energy in a Non-acoustic Chain

We consider heat transport via systems with broken time-reversal symmetry. We apply magnetic fields to the one-dimensional charged particle systems with transverse motions. The standard momentum conservation is not satisfied. To focus on this effect clearly, we introduce a solvable model. We exactly demonstrate that the anomalous transport with a new exponent can appear. We numerically show the violation of the standard relation between the power-law decay in the equilibrium correlation and the diverging exponent of the thermal conductivity in the open system. Introduction.-It is generally believed that heat conduction in low-dimensional nonlinear systems is anomalous from many theoretical and experimental studies [24][25][26]. In a one-dimensional system of N particles connected at the ends to heat baths with a small temperature difference ∆T , the thermal conductivity is defined as κ = JN/∆T , where J is the steady state current per site. The anomalous heat transport is given by the divergence of κ with increasing system size:

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“…(r j a −r a ))r 0a eq . (S. 34) We note here that the following relation from the simple calculation is satisfied, regardless of a = x, y:…”

Section: (S25)mentioning

confidence: 73%

Heat Transport via Low-Dimensional Systems with Broken Time-Reversal Symmetry

2017

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“…Such universality class was subsequently demonstrated in Fermi-Pasta-Ulam (FPU) chains with asymmetric potentials [22], and generalized to an arbitrary anharmonic chain but with another universality class γ = 3/2 (for symmetric potentials under zero pressure) reported [31]. Recently, two research groups studied the systems when the sound modes are absent [25,26]. Based on explicitly solvable models of stochastic dynamics [15], they observed normal [25] and anomalous (with new exponents reported) [26] transport, respectively.…”

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confidence: 92%

Observing golden-mean universality class in the scaling of thermal transport

Xiong

2018

Phys. Rev. E

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We address the issue of whether the golden mean ψ = ( √ 5 + 1)/2 ≃ 1.618 universality class, as predicted by several theoretical models, can be observed in the dynamical scaling of thermal transport. Remarkably, we show estimate with unprecedented precision, that ψ appears to be the scaling exponent of heat mode correlation in a purely quartic anharmonic chain. This observation seems somewhat deviation from the previous expectation and we explain it by the unusual slow decay of the cross-correlation between heat and sound modes. Whenever the cubic anharmonicity is included, this cross-correlation is gradually died out and another universality class with scaling exponent γ = 5/3, as commonly predicted by theories, seems recovered. However, this recovery is accompanied by two interesting phase transition processes characterized by a change of symmetry of the potential and a clear variation of the dynamic structure factor, respectively. Due to these transitions, an additional exponent close to γ ≃ 1.580 emerges. All these evidences suggest that, to gain a full prediction of the scaling of thermal transport, more ingredients should be taken into account.Introduction.-Despite decades of intensive studies , our understanding of thermal transport in onedimensional (1D) systems is still scarce. Macroscopically, such transport is described by an empirical law, i.e., the Fourier's law: J = −κ∇T with J the heat current, ∇T the spatial temperature gradient, and κ a material constant named as thermal conductivity. Nevertheless, now it has been generally realized that Fourier's law is not always valid; instead, an anomalous transport will be shown in most cases [1][2][3]. In particular, in the momentum-conserving systems which are of particular interest, this anomaly is mainly characterized by [27]: α describing the divergence of κ with increasing space size L as κ ∼ L α with 0 < α ≤ 1 (normal transport, α = 0) [6, 8-11, 13-15, 17-19, 24, 26], and γ giving the space(m)-time(t) scaling of energy/heat correlation ρ E/Q (m, t) by t

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“…Harmonic chains with energy conserving random perturbations of the dynamics have recently received attention in the study of the macroscopic evolution of energy [1,2,5,8,10,12]. They provide models that have a non-trivial macroscopic behavior which can be explicitly computed.…”

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confidence: 99%

Macroscopic evolution of mechanical and thermal energy in a harmonic chain with random flip of velocities

Komorowski¹,

Olla²,

Simon³

2018

Kinetic &Amp; Related Models

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We consider an unpinned chain of harmonic oscillators with periodic boundary conditions, whose dynamics is perturbed by a random flip of the sign of the velocities. The dynamics conserves the total volume (or elongation) and the total energy of the system. We prove that in a diffusive space-time scaling limit the profiles corresponding to the two conserved quantities converge to the solution of a diffusive system of differential equations. While the elongation follows a simple autonomous linear diffusive equation, the evolution of the energy depends on the gradient of the square of the elongation.

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Diffusive Propagation of Energy in a Non-acoustic Chain

Cited by 13 publications

References 10 publications

Heat Transport via Low-Dimensional Systems with Broken Time-Reversal Symmetry

Heat Transport via Low-Dimensional Systems with Broken Time-Reversal Symmetry

Observing golden-mean universality class in the scaling of thermal transport

Macroscopic evolution of mechanical and thermal energy in a harmonic chain with random flip of velocities

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