Tagged particle behavior in a harmonic chain of direction-reversing active Brownian particles

IF 2.2 3区 物理与天体物理 Q2 MECHANICS Journal of Statistical Mechanics: Theory and Experiment Pub Date : 2024-08-28 DOI:10.1088/1742-5468/ad6133
Shashank Prakash, Urna Basu, Sanjib Sabhapandit
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For well-separated time-scales, <inline-formula>\n<tex-math><?CDATA $k^{-1}, D_R^{-1}$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:msup><mml:mi>k</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mo>,</mml:mo><mml:msubsup><mml:mi>D</mml:mi><mml:mi>R</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math><inline-graphic xlink:href=\"jstatad6133ieqn1.gif\"></inline-graphic></inline-formula> and <italic toggle=\"yes\">γ</italic><sup>−1</sup>, the strength of the spring constant <italic toggle=\"yes\">k</italic> relative to <italic toggle=\"yes\">D</italic><sub><italic toggle=\"yes\">R</italic></sub> and <italic toggle=\"yes\">γ</italic> gives rise to different coupling limits, and for each coupling limit there are short, intermediate, and long-time regimes. In the thermodynamic limit, we show that, to the leading order, the tagged particle variance exhibits an algebraic growth <italic toggle=\"yes\">t</italic><sup><italic toggle=\"yes\">ν</italic></sup>, where the value of the exponent <italic toggle=\"yes\">ν</italic> depends on the specific regime. For a quenched initial orientation, the exponent <italic toggle=\"yes\">ν</italic> crosses over from 3 to <inline-formula>\n<tex-math><?CDATA $1/2$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mn>1</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href=\"jstatad6133ieqn2.gif\"></inline-graphic></inline-formula>, via intermediate values <inline-formula>\n<tex-math><?CDATA $5/2$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mn>5</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href=\"jstatad6133ieqn3.gif\"></inline-graphic></inline-formula> or 1, depending on the specific coupling limits. However, for the annealed initial orientation, <italic toggle=\"yes\">ν</italic> crosses over from 2 to <inline-formula>\n<tex-math><?CDATA $1/2$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mn>1</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href=\"jstatad6133ieqn4.gif\"></inline-graphic></inline-formula> via an intermediate value <inline-formula>\n<tex-math><?CDATA $3/2$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mn>3</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href=\"jstatad6133ieqn5.gif\"></inline-graphic></inline-formula> or 1 for the strong coupling limit and the weak coupling limit, respectively. An additional time-scale <inline-formula>\n<tex-math><?CDATA $t_N = N^2/k$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mi>N</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msup><mml:mi>N</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:math><inline-graphic xlink:href=\"jstatad6133ieqn6.gif\"></inline-graphic></inline-formula> emerges for a system with a finite number of oscillators <italic toggle=\"yes\">N</italic>. We show that the behavior of the tagged particle variance across <italic toggle=\"yes\">t<sub>N</sub></italic> can be expressed in terms of a crossover scaling function, which we find exactly. Moreover, we study the velocity autocorrelation. Finally, we characterize the stationary state behavior of the separation between two consecutive particles by calculating the corresponding spatio-temporal correlation function.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Statistical Mechanics: Theory and Experiment","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1088/1742-5468/ad6133","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
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Abstract

We study the tagged particle dynamics in a harmonic chain of direction-reversing active Brownian particles, with the spring constant k, rotation diffusion coefficient DR, and directional reversal rate γ. We exactly compute the tagged particle position variance for quenched and annealed initial orientations of the particles. For well-separated time-scales, k1,DR1 and γ−1, the strength of the spring constant k relative to DR and γ gives rise to different coupling limits, and for each coupling limit there are short, intermediate, and long-time regimes. In the thermodynamic limit, we show that, to the leading order, the tagged particle variance exhibits an algebraic growth tν, where the value of the exponent ν depends on the specific regime. For a quenched initial orientation, the exponent ν crosses over from 3 to 1/2, via intermediate values 5/2 or 1, depending on the specific coupling limits. However, for the annealed initial orientation, ν crosses over from 2 to 1/2 via an intermediate value 3/2 or 1 for the strong coupling limit and the weak coupling limit, respectively. An additional time-scale tN=N2/k emerges for a system with a finite number of oscillators N. We show that the behavior of the tagged particle variance across tN can be expressed in terms of a crossover scaling function, which we find exactly. Moreover, we study the velocity autocorrelation. Finally, we characterize the stationary state behavior of the separation between two consecutive particles by calculating the corresponding spatio-temporal correlation function.
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反方向主动布朗粒子谐波链中的标记粒子行为
我们研究了具有弹簧常数 k、旋转扩散系数 DR 和方向逆转率 γ 的方向逆转主动布朗粒子谐波链中的标记粒子动力学。我们精确计算了粒子淬火和退火初始方向的标记粒子位置方差。对于完全不同的时间尺度 k-1、DR-1 和 γ-1,弹簧常数 k 相对于 DR 和 γ 的强度会产生不同的耦合极限,而对于每种耦合极限,都存在短时、中时和长时区。在热力学极限中,我们表明,在先导阶,标记粒子方差表现出代数增长 tν,其中指数 ν 的值取决于特定制度。对于淬火初始取向,指数ν从 3 到 1/2,中间值为 5/2 或 1,取决于特定的耦合极限。然而,对于退火初始取向,ν从 2 到 1/2,中间值分别为强耦合极限和弱耦合极限的 3/2 或 1。我们的研究表明,标记粒子方差在 tN 上的行为可以用交叉缩放函数来表示,我们精确地找到了这个函数。此外,我们还研究了速度自相关性。最后,我们通过计算相应的时空相关函数来描述两个连续粒子之间分离的静态行为。
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来源期刊
CiteScore
4.50
自引率
12.50%
发文量
210
审稿时长
1.0 months
期刊介绍: JSTAT is targeted to a broad community interested in different aspects of statistical physics, which are roughly defined by the fields represented in the conferences called ''Statistical Physics''. Submissions from experimentalists working on all the topics which have some ''connection to statistical physics are also strongly encouraged. The journal covers different topics which correspond to the following keyword sections. 1. Quantum statistical physics, condensed matter, integrable systems Scientific Directors: Eduardo Fradkin and Giuseppe Mussardo 2. Classical statistical mechanics, equilibrium and non-equilibrium Scientific Directors: David Mukamel, Matteo Marsili and Giuseppe Mussardo 3. Disordered systems, classical and quantum Scientific Directors: Eduardo Fradkin and Riccardo Zecchina 4. Interdisciplinary statistical mechanics Scientific Directors: Matteo Marsili and Riccardo Zecchina 5. Biological modelling and information Scientific Directors: Matteo Marsili, William Bialek and Riccardo Zecchina
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