Non-equilibrium attractor for non-linear stochastic dynamics

IF 1.8 4区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

EPL Pub Date : 2024-01-11 DOI:10.1209/0295-5075/ad1d70

Antonio Patrón, Bernardo Sánchez-Rey, Emmanuel Trizac, Antonio Prados

引用次数: 0

Abstract We study the dynamical behaviour of mesoscopic systems in contact with a thermal bath, described either via a non-linear Langevin equation at the trajectory level---or the corresponding Fokker-Planck equation for the probability distribution function at the ensemble level. Our focus is put on one-dimensional---or $d$-dimensional isotropic---systems in confining potentials, with detailed balance---fluctuation-dissipation thus holds, and the stationary probability distribution has the canonical form at the bath temperature. When quenching the bath temperature to low enough values, a far-from-equilibrium state emerges that rules the dynamics over a characteristic intermediate timescale. Such a long-lived state has a Dirac-delta probability distribution function and attracts all solutions over this intermediate timescale, in which the initial conditions are immaterial while the influence of the bath is still negligible. Numerical evidence and qualitative physical arguments suggest that the above picture extends to higher-dimensional systems, with anisotropy and interactions.

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非线性随机动力学的非平衡吸引子

摘要我们研究了与热浴接触的介观系统的动力学行为，在轨迹水平上通过非线性朗格文方程进行描述--或在集合水平上通过概率分布函数的相应福克-普朗克方程进行描述。我们的研究重点是约束势中的一维--或各向同性的 $d$维--系统，其详细平衡--波动--耗散因此成立，静态概率分布在浴槽温度下具有典型形式。当把熔池温度淬火到足够低的值时，就会出现一种远离平衡态的状态，这种状态会在一个特征性的中间时间尺度上控制动力学。这种长寿命状态具有 Dirac-delta 概率分布函数，并吸引着这一中间时间尺度上的所有解，在这一中间时间尺度上，初始条件无关紧要，而浴液的影响仍然可以忽略不计。数值证据和定性物理论证表明，上述情况可以扩展到具有各向异性和相互作用的高维系统。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

EPL 物理-物理：综合

CiteScore

3.30

自引率

5.60%

发文量

332

审稿时长

1.9 months

期刊介绍： General physics – physics of elementary particles and fields – nuclear physics – atomic, molecular and optical physics – classical areas of phenomenology – physics of gases, plasmas and electrical discharges – condensed matter – cross-disciplinary physics and related areas of science and technology. Letters submitted to EPL should contain new results, ideas, concepts, experimental methods, theoretical treatments, including those with application potential and be of broad interest and importance to one or several sections of the physics community. The presentation should satisfy the specialist, yet remain understandable to the researchers in other fields through a suitable, clearly written introduction and conclusion (if appropriate). EPL also publishes Comments on Letters previously published in the Journal.