We study the effects of two kinds of weak disorders on the thermalization of the Fermi-Pasta-Ulam-Tsingou model(FPUT) 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 Teq. We find that Teq satisfies the following scaling law: Teq~(")a(||)b for different disorder strengths in the thermodynamic limit. It's found that the exponent a ≈ 1:0 while b depends on the strength of disorder, which are different from b=2a in the homogeneous case.

中文翻译：

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弱无序对Fermi-Pasta-Ulam-Tsingou模型热化的影响

我们通过广泛的数值模拟研究了两种弱无序对 Fermi-Pasta-Ulam-Tsingou 模型 (FPUT) 热化的影响。无序被引入原子的质量或势能的二次项的系数。初始能量在一些最低频率模式之间平均分配。我们发现能量在时间 t 内传输到高频模式，并最终在弱无序下比在均质情况下更快地接近能量均分。这意味着弱无序会加速热化过程。我们进一步研究了两种紊乱对均分时间 Teq 标度律的影响。我们发现 Teq 满足以下标度定律：Teq~(")a(||)b 对于热力学极限中的不同无序强度。它'