{"title":"Tagged particle behavior in a harmonic chain of direction-reversing active Brownian particles","authors":"Shashank Prakash, Urna Basu, Sanjib Sabhapandit","doi":"10.1088/1742-5468/ad6133","DOIUrl":null,"url":null,"abstract":"We study the tagged particle dynamics in a harmonic chain of direction-reversing active Brownian particles, with the spring constant <italic toggle=\"yes\">k</italic>, rotation diffusion coefficient <italic toggle=\"yes\">D</italic><sub><italic toggle=\"yes\">R</italic></sub>, and directional reversal rate <italic toggle=\"yes\">γ</italic>. We exactly compute the tagged particle position variance for quenched and annealed initial orientations of the particles. 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}
引用次数: 0
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, k−1,DR−1 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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