Conundrum of weak-noise limit for diffusion in a tilted periodic potential,Physical Review E

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Conundrum of weak-noise limit for diffusion in a tilted periodic potential
Physical Review E ( IF 2.2 ) Pub Date : 2021-09-07 , DOI: 10.1103/physreve.104.034104
J Spiechowicz ₁ , J Łuczka ₁

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The weak-noise limit of dissipative dynamical systems is often the most fascinating one. In such a case fluctuations can interact with a rich complexity, frequently hidden in deterministic systems, to give rise to phenomena that are absent for both noiseless and strong fluctuations regimes. Unfortunately, this limit is also notoriously hard to approach analytically or numerically. We reinvestigate in this context the paradigmatic model of nonequilibrium statistical physics consisting of inertial Brownian particles diffusing in a tilted periodic potential by exploiting state-of-the-art computer simulations of an extremely long timescale. In contrast to previous results on this longstanding problem, we draw an inference that in the parameter regime for which the particle velocity is bistable the lifetime of ballistic diffusion diverges to infinity when the thermal noise intensity tends to zero, i.e., an everlasting ballistic diffusion emerges. As a consequence, the diffusion coefficient does not reach its stationary constant value.

中文翻译：

倾斜周期势中扩散的弱噪声极限难题

耗散动力系统的弱噪声极限通常是最吸引人的。在这种情况下，波动会与通常隐藏在确定性系统中的丰富复杂性相互作用，从而产生无噪声和强波动机制都不存在的现象。不幸的是，众所周知，这个限制也很难通过分析或数值方式接近。在这种情况下，我们通过利用极长时间尺度的最先进计算机模拟，重新研究了非平衡统计物理学的范式模型，该模型由以倾斜周期势扩散的惯性布朗粒子组成。与之前关于这个长期存在的问题的结果相反，我们得出一个推论，在粒子速度双稳态的参数范围内，当热噪声强度趋于零时，弹道扩散的寿命发散到无穷大，即出现了永久弹道扩散。因此，扩散系数不会达到其固定常数值。

更新日期：2021-09-07

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