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Universal Time Scale for Thermalization in Two-dimensional Systems
The Fermi-Pasta-Ulam-Tsingou problem, i.e., the problem of energy
equipartition among normal modes in a weakly nonlinear lattice, is here studied
in two types of two-dimensional (2D) lattices, more precisely in lattices with
square cell and triangular cell. We apply the wave-turbulence approach to
describe the dynamics and find multi-wave resonances play a major role in the
transfer of energy among the normal modes. We show that, in general, the
thermalization time in 2D systems is inversely proportional to the squared
perturbation strength in the thermodynamic limit. Numerical simulations confirm
that the results are consistent with the theoretical prediction no matter
systems are translation-invariant or not. It leads to the conclusion that such
systems can always be thermalized by arbitrarily weak many-body interactions.
Moreover, the validity for disordered lattices implies that the localized
states are unstable.Comment: 6 pages, 4 figure
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