{"title":"Non-equilibrium phase transitions in active rank diffusions","authors":"Leo Touzo, Pierre Le Doussal","doi":"10.1209/0295-5075/ad222b","DOIUrl":null,"url":null,"abstract":"<jats:title>Abstract</jats:title> We consider N run-and-tumble particles in one dimension interacting via a linear 1D Coulomb potential, an active version of the rank diffusion problem. It was solved previously for N=2 leading to a stationary bound state in the attractive case. Here the evolution of the density fields is obtained in the large N limit in terms of two coupled Burger’s type equations. In the attractive case the exact stationary solution describes a non-trivial N-particle bound state, which exhibits transitions between a phase where the density is smooth with infinite support, a phase where the density has finite support and exhibits ”shocks”, i.e. clusters of particles, at the edges, and a fully clustered phase. In presence of an additional linear potential, the phase diagram, obtained for either sign of the interaction, is even richer, with additional partially expanding phases, with or without shocks. Finally, a general self-consistent method is introduced to treat more general interactions. The predictions are tested through numerical simulations.","PeriodicalId":11738,"journal":{"name":"EPL","volume":"35 1","pages":""},"PeriodicalIF":1.8000,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"EPL","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1209/0295-5075/ad222b","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract We consider N run-and-tumble particles in one dimension interacting via a linear 1D Coulomb potential, an active version of the rank diffusion problem. It was solved previously for N=2 leading to a stationary bound state in the attractive case. Here the evolution of the density fields is obtained in the large N limit in terms of two coupled Burger’s type equations. In the attractive case the exact stationary solution describes a non-trivial N-particle bound state, which exhibits transitions between a phase where the density is smooth with infinite support, a phase where the density has finite support and exhibits ”shocks”, i.e. clusters of particles, at the edges, and a fully clustered phase. In presence of an additional linear potential, the phase diagram, obtained for either sign of the interaction, is even richer, with additional partially expanding phases, with or without shocks. Finally, a general self-consistent method is introduced to treat more general interactions. The predictions are tested through numerical simulations.
摘要 我们考虑了一维中通过线性一维库仑势相互作用的 N 个奔跑和翻滚粒子，这是等级扩散问题的主动版本。该问题曾在 N=2 的情况下求解，并得出了吸引力情况下的静止束缚态。在这里，密度场的演化是通过两个耦合伯格方程在大 N 极限得到的。在有吸引力的情况下，精确的静态解描述了一个非三维的 N 粒子束缚态，该束缚态在以下三个阶段之间发生转变：密度为无限支撑的平滑阶段；密度为有限支撑并在边缘表现出 "冲击"（即粒子群）的阶段；以及完全成团的阶段。在存在额外线性势的情况下，在相互作用的任一符号下得到的相图甚至更加丰富，有额外的部分膨胀相，有或没有冲击。最后，引入了一种一般自洽方法来处理更一般的相互作用。预测结果通过数值模拟进行了检验。
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.
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