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

Abstract

-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...

Subdiffusive Energy Transport and Antipersistent Correlations Due to the Scattering of Phonons and Discrete Breathers

“…This is indeed indicated in Fig. 3(d) where the low frequency can be clearly identified (see also [34]). But after introducing the anharmonic LRIs, the situation reverses, i.e., as the anharmonicity increases we always see the attenuation of phonons beginning at the low frequency components [see Fig.…”

“…3(a,b)]. Secondly, it is known that in lattices with only NN couplings supporting superdiffusive transport, the low frequency phonons are weakly damped due to the conserved feature of momentum [34,35]. As the NN anharmonicity increases we always see the damping of phonons starting from the high frequency components.…”

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

“…More-interestingly, the second transition process seems discontinous ( Fig. 4), suggesting a feature similarly to that of structure phase transition [24,47]. Phase transitions.-We employ Fig.…”

Temperature profile and boundary conditions in an anomalous heat transport model

“…Anomalous heat conduction, typically characterized by κ = aN α with 0 < α ≤ 1, has however been shown to be a generic feature of one-dimensional momentum-conserving systems [31,17,29]. Violations of Fourier's law have been reported for a large variety of systems over the last decades both in theoretical models [30,22,36,11,23,48,15,7,38,42,40,2,24,26,3] and in nanotube experiments [8]. This phenomenon is usually accompanied by other puzzling features such as divergence of the time integral of the equilibrium currentcurrent correlations, superdiffusive propagation of local energy perturbations [35] and boundary singularities in the nonequilibrium stationary temperature profile [29].…”