Nonintegrability and thermalization of one-dimensional diatomic lattices

Chaotic route to classical thermalization: A real-space analysis

Most of the previous studies on classical thermalization focus on the wave-vector space, encountering limitations when extended beyond quasi-integrable regions. In this study, we propose a scheme to study the thermalization of the classical Hamiltonian chain of interacting oscillators in real space by developing a thermalization indicator proposed by Parisi [Europhys. Lett. 40, 357 (1997)0295-507510.1209/epl/i1997-00471-9], which approaches zero in the thermal state. Upon reaching the steady state characterized by the generalized Gibbs ensemble for a harmonic chain, a quench protocol is implemented to change the Hamiltonian to a nonintegrable form instantaneously, thereby preparing nonequilibrium initial states. This approach enables investigations of thermalization in real space, particularly valuable for exploring regions beyond quasi-integrability. For the FPUT-β lattice, we observe that the thermalization time as a function of the nonintegrable strength follows a -2 scaling law in the quasi-integrable region and -1/4 in the strongly integrable region. Moreover, numerical results reveal the thermalization time is proportional to the Lyapunov time, which bridges microscopic chaotic dynamics and the macroscopic thermalization process.

Thermalization of Two- and Three-Dimensional Classical Lattices

Understanding how systems achieve thermalization is a fundamental task in statistical physics. This Letter presents both analytical and numerical evidence showing that thermalization can be universally achieved in sufficiently large two- and three-dimensional lattices via weak nonlinear interactions. Thermalization time follows a universal scaling law unaffected by lattice structures, types of interaction potentials, or whether the lattice is ordered or not. Moreover, this study highlights the critical impact of dimensionality and degeneracy on thermalization dynamics.

Effect of pressure on thermalization of one-dimensional nonlinear chains

Pressure plays a vital role in changing the transport properties of matter. To understand this phenomenon at a microscopic level, we here focus on a more fundamental problem, i.e., how pressure affects the thermalization properties of solids. As illustrating examples, we study the thermalization behavior of the monatomic chain and the mass-disordered chain of Fermi-Pasta-Ulam-Tsingou-β under different strains in the thermodynamic limit. It is found that the pressure-induced change in integrability results in qualitatively different thermalization processes for the two kinds of chains. However, for both cases, the thermalization time follows the same law-it is inversely proportional to the square of the nonintegrability strength. This result suggests that pressure can significantly change the integrability of a system, which provides a new perspective for understanding the pressure-dependent thermal transport behavior.

Analytical approach to Lyapunov time: Universal scaling and thermalization

Based on the geometrization of dynamics and self-consistent phonon theory, we develop an analytical approach to derive the Lyapunov time, the reciprocal of the largest Lyapunov exponent, for general nonlinear lattices of coupled oscillators. The Fermi-Pasta-Ulam-Tsingou-like lattices are exemplified by using the method, which agree well with molecular dynamical simulations for the cases of quartic and sextic interactions. A universal scaling behavior of the Lyapunov time with the nonintegrability strength is observed for the quasi-integrable regime. Interestingly, the scaling exponent of the Lyapunov time is the same as the thermalization time, which indicates a proportional relationship between the two timescales. This relation illustrates how the thermalization process is related to the intrinsic chaotic property.

Too Close to Integrable: Crossover from Normal to Anomalous Heat Diffusion

Energy transport in one-dimensional chains of particles with three conservation laws is generically anomalous and belongs to the Kardar-Parisi-Zhang dynamical universality class. Surprisingly, some examples where an apparent normal heat diffusion is found over a large range of length scales were reported. We propose a novel physical explanation of these intriguing observations. We develop a scaling analysis that explains how this may happen in the vicinity of an integrable limit, such as, but not only, the famous Toda model. In this limit, heat transport is mostly supplied by quasiparticles with a very large mean free path ℓ. Upon increasing the system size L, three different regimes can be observed: a ballistic one, an intermediate diffusive range, and, eventually, the crossover to the anomalous (hydrodynamic) regime. Our theoretical considerations are supported by numerical simulations of a gas of diatomic hard-point particles for almost equal masses and of a weakly perturbed Toda chain. Finally, we discuss the case of the perturbed harmonic chain, which exhibits a yet different scenario.