Effects of weak disorder on the thermalization of Fermi–Pasta–Ulam–Tsingou model

Abstract

We study the effects of two kinds of weak disorders on the thermalization of the Fermi–Pasta–Ulam–Tsingou model by extensive numerical simulations. The disorders are introduced to the mass of atom or coefficient of the quadratic term of potential energy. The initial energy is distributed equally among some lowest frequency modes. We find that the energy transports to high-frequency modes with time t and eventually approaches energy equipartition faster with either weak disorder than that in the homogeneous case. That means weak disorders accelerate the process of thermalization. We further study the effects of two kinds of disorders on the scaling law of equipartition time T _eq . We find that T _eq satisfies the following scaling law: T _eq ∼ ( ɛ ) ^− ^a (| α |) ^− ^b for different disorder strengths in the thermodynamic limit. It is found that the exponent a ≈ 1.0 while b depends on the strength of disorder, which are different from b = 2 a in the homogeneous case.

Keywords

• energy equipartition
• weak disorder
• nonlinearity
• Fermi–Pasta–Ulam–Tsingou model