title: Dynamical thermalization of Frenkel-Kontorova model in the thermodynamic limit.
abstract: We study numerically the process of dynamical thermalization in the Frenkel-Kontorova (FK) model with weak nonlinearity. The total energy has initially equidistributed among some of the lowest frequency linear modes. It is found that the energy transfers continuously to the high-frequency modes and finally evolves towards energy equipartition in the FK model. However, the metastable state, which was found in Fermi-Pasta-Ulam (FPU) model and φ(4) model in a relatively short time scale, is not found in the FK model. We further perform a very accurate systematic study of the equipartition time T(eq) as functions of the particle number N, the nonlinear parameter β, and the energy density ɛ. In the thermodynamic limit, the dependence of T(eq) on β and ɛ is found to display a power law behavior: T(eq)∝β(a)ɛ(b). The exponents a and b are numerically found to be approximately -2.0 and 1.43. This scaling law is also quite different from those of the FPU-β model and φ(4) model.
authors.affiliation: College of Science, Hohai University, Nanjing, Jiangsu 210098, People's Republic of China.
authors.forename: Zhenjun
authors.initials: Z
authors.lastname: Zhang
authors.affiliation: College of Science, Hohai University, Nanjing, Jiangsu 210098, People's Republic of China.
authors.forename: Chunmei
authors.initials: C
authors.lastname: Tang
authors.affiliation: School of Physics Science and Technology, Nanjing Normal University, Nanjing, Jiangsu 210023, People's Republic of China.|Jiangsu Provincial Key Laboratory for Numerical Simulation of Large Scale Complex Systems, Nanjing Normal University, Nanjing, Jiangsu 210023, People's Republic of China.
authors.forename: Peiqing
authors.initials: P
authors.lastname: Tong