22 June 2021 Tue 5 pm

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Whether dynamical systems can be thermalized and how they are thermalized are fundamental problems of statistical mechanics. It has been shown that thermalization time is related to the chaotic nature of the system, but its quantitative relationship is not clear. In this talk, I will present an analytical approach to Lyapunov time for nonlinear lattices of coupled oscillators based on the dynamical geometrization and self-consistent phonon theory. The Fermi-Pasta-Ulam-Tsingou-like lattices are exemplified by using the method, which agree well with molecular dynamical simulations. 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. In the non-integrable regime, we find that the proportional relationship is also established, which gives the scaling behavior of the thermalization time in the regime of strong nonintegrability. Finally, we explain the proportional relationship in terms of the production rate of the Kolmogorov-Sinai entropy. Our study not only provides a novel theoretical method to quantify the Lyapunov exponent, but also tentatively build a bridge between dynamics and statistical physics.

Bio：

Dr. Dahai He is a full professor in Department of Physics, Xiamen University. He mainly works on non-equilibrium statistical physics. His research interest in recent years includes thermalization, quantum and classical thermal conduction, and non-equilibrium fluctuation theorem in low-dimensional lattices.

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