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Silvano N, Barci DG. Emergent gauge symmetry in active Brownian matter. Phys Rev E 2024; 109:044605. [PMID: 38755850 DOI: 10.1103/physreve.109.044605] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2023] [Accepted: 04/04/2024] [Indexed: 05/18/2024]
Abstract
We investigate a two-dimensional system of interacting active Brownian particles. Using the Martin-Siggia-Rose-Janssen-de Dominicis formalism, we built up the generating functional for correlation functions. We study in detail the hydrodynamic regime with a constant density stationary state. Our findings reveal that, within a small density fluctuations regime, an emergent U(1) gauge symmetry arises, originated from the conservation of fluid vorticity. Consequently, the interaction between the orientational order parameter and density fluctuations can be cast into a gauge theory, where the concept of "electric charge density" aligns with the local vorticity of the original fluid. We study in detail the case of a microscopic local two-body interaction. We show that, upon integrating out the gauge fields, the stationary states of the rotational degrees of freedom satisfy a nonlocal Frank free energy for a nematic fluid. We give explicit expressions for the splay and bend elastic constants as a function of the Péclet number (Pe) and the diffusion interaction constant (k_{d}).
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Affiliation(s)
- Nathan Silvano
- Center for Advanced Systems Understanding, Untermarkt 20, 02826 Görlitz, Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstraße 400, 01328 Dresden, Germany
- Departamento de Física Teórica, 20270-004 Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier 524, 20550-013, Rio de Janeiro, RJ, Brazil
| | - Daniel G Barci
- Departamento de Física Teórica, 20270-004 Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier 524, 20550-013, Rio de Janeiro, RJ, Brazil
- Sorbonne Université, Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589, 4 Place Jussieu, 75252 Paris Cedex 05, France
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2
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Burenev IN, Majumdar SN, Rosso A. Occupation time of a system of Brownian particles on the line with steplike initial condition. Phys Rev E 2024; 109:044150. [PMID: 38755944 DOI: 10.1103/physreve.109.044150] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/30/2023] [Accepted: 02/29/2024] [Indexed: 05/18/2024]
Abstract
We consider a system of noninteracting Brownian particles on the line with steplike initial condition and study the statistics of the occupation time on the positive half-line. We demonstrate that even at large times, the behavior of the occupation time exhibits long-lasting memory effects of the initialization. Specifically, we calculate the mean and the variance of the occupation time, demonstrating that the memory effects in the variance are determined by a generalized compressibility (or Fano factor), associated with the initial condition. In the particular case of the uncorrelated uniform initial condition we conduct a detailed study of two probability distributions of the occupation time: annealed (averaged over all possible initial configurations) and quenched (for a typical configuration). We show that at large times both the annealed and the quenched distributions admit large deviation form and we compute analytically the associated rate functions. We verify our analytical predictions via numerical simulations using importance sampling Monte Carlo strategy.
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Affiliation(s)
- Ivan N Burenev
- LPTMS, CNRS, Université Paris-Saclay, 91405 Orsay, France
| | | | - Alberto Rosso
- LPTMS, CNRS, Université Paris-Saclay, 91405 Orsay, France
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3
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Santra S, Singh P. Exact fluctuation and long-range correlations in a single-file model under resetting. Phys Rev E 2024; 109:034123. [PMID: 38632800 DOI: 10.1103/physreve.109.034123] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2023] [Accepted: 01/24/2024] [Indexed: 04/19/2024]
Abstract
Resetting is a renewal mechanism in which a process is intermittently repeated after a random or fixed time. This simple act of stop and repeat profoundly influences the behavior of a system as exemplified by the emergence of nonequilibrium properties and expedition of search processes. Herein we explore the ramifications of stochastic resetting in the context of a single-file system called random average process (RAP) in one dimension. In particular, we focus on the dynamics of tracer particles and analytically compute the variance, equal time correlation, autocorrelation, and unequal time correlation between the positions of different tracer particles. Our study unveils that resetting gives rise to rather different behaviors depending on whether the particles move symmetrically or asymmetrically. For the asymmetric case, the system for instance exhibits a long-range correlation which is not seen in absence of the resetting. Similarly, in contrast to the reset-free RAP, the variance shows distinct scalings for symmetric and asymmetric cases. While for the symmetric case, it decays (towards its steady value) as ∼e^{-rt}/sqrt[t], we find ∼te^{-rt} decay for the asymmetric case (r being the resetting rate). Finally, we examine the autocorrelation and unequal time correlation in the steady state and demonstrate that they obey interesting scaling forms at late times. All our analytical results are substantiated by extensive numerical simulations.
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Affiliation(s)
- Saikat Santra
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India
| | - Prashant Singh
- Niels Bohr International Academy, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100 Copenhagen, Denmark
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Burenev IN, Majumdar SN, Rosso A. Local time of a system of Brownian particles on the line with steplike initial condition. Phys Rev E 2023; 108:064113. [PMID: 38243455 DOI: 10.1103/physreve.108.064113] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2023] [Accepted: 10/30/2023] [Indexed: 01/21/2024]
Abstract
We consider a system of noninteracting Brownian particles on a line with a steplike initial condition, and we investigate the behavior of the local time at the origin at large times. We compute the mean and the variance of the local time, and we show that the memory effects are governed by the Fano factor associated with the initial condition. For the uniform initial condition, we show that the probability distribution of the local time admits a large deviation form, and we compute the corresponding large deviation functions for the annealed and quenched averaging schemes. The two resulting large deviation functions are very different. Our analytical results are supported by extensive numerical simulations.
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Affiliation(s)
- Ivan N Burenev
- LPTMS, CNRS, Université Paris-Saclay, 91405 Orsay, France
| | | | - Alberto Rosso
- LPTMS, CNRS, Université Paris-Saclay, 91405 Orsay, France
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Jose S, Rosso A, Ramola K. Generalized disorder averages and current fluctuations in run and tumble particles. Phys Rev E 2023; 108:L052601. [PMID: 38115454 DOI: 10.1103/physreve.108.l052601] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2023] [Accepted: 11/07/2023] [Indexed: 12/21/2023]
Abstract
We present exact results for the fluctuations in the number of particles crossing the origin up to time t in a collection of noninteracting run and tumble particles in one dimension. In contrast to passive systems, such active particles are endowed with two inherent degrees of freedom, positions and velocities, which can be used to construct density and magnetization fields. We introduce generalized disorder averages associated with both these fields and perform annealed and quenched averages over various initial conditions. We show that the variance σ^{2} of the current in annealed versus quenched magnetization situations exhibits a surprising difference at short times, σ^{2}∼t vs σ^{2}∼t^{2}, respectively, with a sqrt[t] behavior emerging at large times. Our analytical results demonstrate that in the strictly quenched scenario, where both the density and magnetization fields are initially frozen, the fluctuations in the current are strongly suppressed. Importantly, these anomalous fluctuations cannot be obtained solely by freezing the density field.
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Affiliation(s)
- Stephy Jose
- Tata Institute of Fundamental Research, Hyderabad 500046, India
| | - Alberto Rosso
- LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
| | - Kabir Ramola
- Tata Institute of Fundamental Research, Hyderabad 500046, India
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6
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Sorkin B, Dean DS. Single-file diffusion in spatially inhomogeneous systems. Phys Rev E 2023; 108:054125. [PMID: 38115401 DOI: 10.1103/physreve.108.054125] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2023] [Accepted: 09/06/2023] [Indexed: 12/21/2023]
Abstract
We study the effect of spatially varying potential and diffusivity on the dispersion of a tracer particle in single-file diffusion. Noninteracting particles in such a system exhibit normal diffusion at late times, which is characterized by an effective diffusion constant D_{eff}. Here we demonstrate the physically appealing result that the dispersion of single-file tracers in this system has the same long-time behavior as that for Brownian particles in a spatially homogeneous system with constant diffusivity D_{eff}. Our results are based on a late-time analysis of the Fokker-Planck equation, motivated by the mathematical theory of homogenization. The findings are confirmed by numerical simulations for both annealed and quenched initial conditions.
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Affiliation(s)
- Benjamin Sorkin
- School of Chemistry and Center for Physics and Chemistry of Living Systems, Tel Aviv University, 69978 Tel Aviv, Israel
| | - David S Dean
- Univ. Bordeaux, CNRS, LOMA, UMR 5798, F-33400 Talence, France
- Team MONC, INRIA Bordeaux Sud Ouest, CNRS UMR 5251, Bordeaux INP, Univ. Bordeaux, F-33400 Talence, France
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Semeraro M, Gonnella G, Suma A, Zamparo M. Work Fluctuations for a Harmonically Confined Active Ornstein-Uhlenbeck Particle. PHYSICAL REVIEW LETTERS 2023; 131:158302. [PMID: 37897759 DOI: 10.1103/physrevlett.131.158302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/21/2023] [Accepted: 09/13/2023] [Indexed: 10/30/2023]
Abstract
We study the active work fluctuations of an active Ornstein-Uhlenbeck particle in the presence of a confining harmonic potential. We tackle the problem analytically both for stationary and generic uncorrelated initial states. Our results show that harmonic confinement can induce singularities in the active work rate function, with linear stretches at large positive and negative active work, at sufficiently large active and harmonic force constants. These singularities originate from big jumps in the displacement and in the active force, occurring at the initial or ending points of trajectories and marking the relevance of boundary terms in this problem.
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Affiliation(s)
- Massimiliano Semeraro
- Dipartimento Interateneo di Fisica, Università degli Studi di Bari and INFN, Sezione di Bari, via Amendola 173, Bari I-70126, Italy
| | - Giuseppe Gonnella
- Dipartimento Interateneo di Fisica, Università degli Studi di Bari and INFN, Sezione di Bari, via Amendola 173, Bari I-70126, Italy
| | - Antonio Suma
- Dipartimento Interateneo di Fisica, Università degli Studi di Bari and INFN, Sezione di Bari, via Amendola 173, Bari I-70126, Italy
| | - Marco Zamparo
- Dipartimento Interateneo di Fisica, Università degli Studi di Bari and INFN, Sezione di Bari, via Amendola 173, Bari I-70126, Italy
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Di Bello C, Hartmann AK, Majumdar SN, Mori F, Rosso A, Schehr G. Current fluctuations in stochastically resetting particle systems. Phys Rev E 2023; 108:014112. [PMID: 37583217 DOI: 10.1103/physreve.108.014112] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/07/2023] [Accepted: 04/28/2023] [Indexed: 08/17/2023]
Abstract
We consider a system of noninteracting particles on a line with initial positions distributed uniformly with density ρ on the negative half-line. We consider two different models: (i) Each particle performs independent Brownian motion with stochastic resetting to its initial position with rate r and (ii) each particle performs run-and-tumble motion, and with rate r its position gets reset to its initial value and simultaneously its velocity gets randomized. We study the effects of resetting on the distribution P(Q,t) of the integrated particle current Q up to time t through the origin (from left to right). We study both the annealed and the quenched current distributions and in both cases, we find that resetting induces a stationary limiting distribution of the current at long times. However, we show that the approach to the stationary state of the current distribution in the annealed and the quenched cases are drastically different for both models. In the annealed case, the whole distribution P_{an}(Q,t) approaches its stationary limit uniformly for all Q. In contrast, the quenched distribution P_{qu}(Q,t) attains its stationary form for QQ_{crit}(t). We show that Q_{crit}(t) increases linearly with t for large t. On the scale where Q∼Q_{crit}(t), we show that P_{qu}(Q,t) has an unusual large deviation form with a rate function that has a third-order phase transition at the critical point. We have computed the associated rate functions analytically for both models. Using an importance sampling method that allows to probe probabilities as tiny as 10^{-14000}, we were able to compute numerically this nonanalytic rate function for the resetting Brownian dynamics and found excellent agreement with our analytical prediction.
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Affiliation(s)
- Costantino Di Bello
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
| | | | - Satya N Majumdar
- LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
| | - Francesco Mori
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
| | - Alberto Rosso
- LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
| | - Grégory Schehr
- Sorbonne Université, Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589, 75252 Paris Cedex 05, France
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Schweers S, Antonov AP, Ryabov A, Maass P. Scaling laws for single-file diffusion of adhesive particles. Phys Rev E 2023; 107:L042102. [PMID: 37198860 DOI: 10.1103/physreve.107.l042102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/16/2023] [Accepted: 03/29/2023] [Indexed: 05/19/2023]
Abstract
Single-file diffusion refers to the Brownian motion in narrow channels where particles cannot pass each other. In such processes, the diffusion of a tagged particle is typically normal at short times and becomes subdiffusive at long times. For hard-sphere interparticle interaction, the time-dependent mean squared displacement of a tracer is well understood. Here we develop a scaling theory for adhesive particles. It provides a full description of the time-dependent diffusive behavior with a scaling function that depends on an effective strength of adhesive interaction. Particle clustering induced by the adhesive interaction slows down the diffusion at short times, while it enhances subdiffusion at long times. The enhancement effect can be quantified in measurements irrespective of how tagged particles are injected into the system. Combined effects of pore structure and particle adhesiveness should speed up translocation of molecules through narrow pores.
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Affiliation(s)
- Sören Schweers
- Universität Osnabrück, Fachbereich Physik, Barbarastraße 7, D-49076 Osnabrück, Germany
| | - Alexander P Antonov
- Universität Osnabrück, Fachbereich Physik, Barbarastraße 7, D-49076 Osnabrück, Germany
| | - Artem Ryabov
- Charles University, Faculty of Mathematics and Physics, Department of Macromolecular Physics, V Holešovičkách 2, CZ-18000 Praha 8, Czech Republic
| | - Philipp Maass
- Universität Osnabrück, Fachbereich Physik, Barbarastraße 7, D-49076 Osnabrück, Germany
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