Diffusion of heat, energy, momentum, and mass in one-dimensional systems

Chen, Shunda; Zhang, Yong; Wang, Jiao; Zhao, Hong

doi:10.1103/physreve.87.032153

Cited by 50 publications

(80 citation statements)

References 45 publications

(69 reference statements)

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“…This should be compared with Refs. [29] that challenged the predictions of the NFH theory by claiming that thermal conductivity could turn to a normal behavior in the low-energy region of oscillators chain. Our results, along with Refs.…”

Section: Discussionmentioning

confidence: 99%

Anomalous dynamical scaling in anharmonic chains and plasma models with multiparticle collisions

et al. 2015

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We study the anomalous dynamical scaling of equilibrium correlations in one-dimensional systems. Two different models are compared: the Fermi-Pasta-Ulam chain with cubic and quartic nonlinearity and a gas of point particles interacting stochastically through multiparticle collision dynamics. For both models-that admit three conservation laws-by means of detailed numerical simulations we verify the predictions of nonlinear fluctuating hydrodynamics for the structure factors of density and energy fluctuations at equilibrium. Despite this, violations of the expected scaling in the currents correlation are found in some regimes, hindering the observation of the asymptotic scaling predicted by the theory. In the case of the gas model this crossover is clearly demonstrated upon changing the coupling constant.

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Section: Discussionmentioning

confidence: 99%

Anomalous dynamical scaling in anharmonic chains and plasma models with multiparticle collisions

et al. 2015

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“…However simulations of correlations of the conserved fields have been fairly scarce until recently. The peak structure was noted already in [54], see also [55,56]. But surprisingly enough, even such a basic issue as the quantitative comparison between the measured speed of sound and formula (2.31) is apparently not a routine check.…”

Section: Mode-coupling Theorymentioning

confidence: 99%

Fluctuating Hydrodynamics Approach to Equilibrium Time Correlations for Anharmonic Chains

Spohn

2016

Thermal Transport in Low Dimensions

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Abstract. Linear fluctuating hydrodynamics is a useful and versatile tool for describing fluids, as well as other systems with conserved fields, on a mesoscopic scale. In one spatial dimension, however, transport is anomalous, which requires to develop a nonlinear extension of fluctuating hydrodynamics. The relevant nonlinearity turns out to be the quadratic part of the Euler currents when expanding relative to a uniform background. We outline the theory and compare with recent molecular dynamics simulations. 1 arXiv:1505.05987v2 [cond-mat.stat-mech]

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“…It is also relevant to the dynamical exponents in general transport processes far away from equilibrium, such as that described by the famous Kardar Nevertheless, simulations to precisely identify the dynamical exponents, especially the exponent γ for heat transport, from direct dynamics, are actually hard to carry out, causing quite few numerical results reliable [22,23,29,30]. With this question in mind, in this work, by employing a direct dynamic simulation method [35] we provide a very precise estimate of γ from the new perspective of different phonon dispersions and under various system's parameter regimes, from which a crossover between the different universality classes of γ can be clearly identified. We argue that different dispersions along with nonlinearity could result in quite different microscopic enp-1…”

mentioning

confidence: 99%

“…With this question in mind, in this work, by employing a direct dynamic simulation method [35] we provide a very precise estimate of γ from the new perspective of different phonon dispersions and under various system's parameter regimes, from which a crossover between the different universality classes of γ can be clearly identified. We argue that different dispersions along with nonlinearity could result in quite different microscopic enp-1 vironments surrounding phonons continuous-time random walking (CTRW), which then leads to the different scaling exponents.…”

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confidence: 99%

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Crossover between different universality classes: Scaling for thermal transport in one dimension

Xiong

2016

EPL

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-For thermal transport in one-dimensional (1D) systems, recent studies have suggested that employing different theoretical models and different numerical simulations under different system's parameter regimes might lead to different universality classes of the scaling exponents. In order to well understand the universality class(es), here we perform a direct dynamics simulation for two archetype 1D oscillator systems with quite different phonon dispersions under various system's parameters and find that there is a crossover between the different universality classes. We show that by varying anharmonicity and temperatures, the space-time scaling exponents for the systems with different dispersions can be feasibly tuned in different ways. The underlying picture is suggested to be understood by phonons performing various kinds of continuous-time random walks (in most cases, be the Lévy walks but not always), probably induced by the peculiar phonon dispersions along with nonlinearity. The results and suggested mechanisms may provide insights into controlling the transport of heat in some 1D materials.Transport in one dimension has, for a long time, been realized to be anomalous in most cases [1,2], with signatures of a universal power-law scaling of transport coefficients, among which the heat transport has been extensively investigated in the recent decades, both by various theoretical techniques, such as the renormalization group [3], mode coupling [4,5] or cascade [6][7][8], nonlinear fluctuating hydrodynamics [9][10][11], and Lévy walks [12][13][14][15]; and also by computer simulations [16][17][18][19][20][21][22][23][24][25][26]. For all studied cases two main scaling exponents have been given the most focus, i.e., α describing the divergence of heat conductivity with space size L as L α and γ characterizing the space(x)-time(t) scaling of heat spreading density ρ(x, t) as t −1/γ ρ(t −1/γ x, t). Unfortunately, however, depending on the focused system's different parameter regimes, different theoretical models have been employed, and different predictions have been suggested. Thus, the universality classes of both scaling exponents and their relationship [27,28] The discussion of the latter scaling exponent γ is currently very hot [9-15, 20-23, 29, 30] because it involves more detailed space and time information [31], thus it can present a very detailed prediction for heat transport. It is also relevant to the dynamical exponents in general transport processes far away from equilibrium, such as that described by the famous Kardar Nevertheless, simulations to precisely identify the dynamical exponents, especially the exponent γ for heat transport, from direct dynamics, are actually hard to carry out, causing quite few numerical results reliable [22,23,29,30]. With this question in mind, in this work, by employing a direct dynamic simulation method [35] we provide a very precise estimate of γ from the new perspective of different phonon dispersions and under various system's parameter regimes, from whi...

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Diffusion of heat, energy, momentum, and mass in one-dimensional systems

Cited by 50 publications

References 45 publications

Anomalous dynamical scaling in anharmonic chains and plasma models with multiparticle collisions

Anomalous dynamical scaling in anharmonic chains and plasma models with multiparticle collisions

Fluctuating Hydrodynamics Approach to Equilibrium Time Correlations for Anharmonic Chains

Crossover between different universality classes: Scaling for thermal transport in one dimension

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