Construction of a coordinate Bethe ansatz for the asymmetric simple exclusion process with open boundaries

Simon, Damien

doi:10.1088/1742-5468/2009/07/p07017

Cited by 92 publications

(126 citation statements)

References 37 publications

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“…and interpret ∆V C as an 'effective potential' that acts to drive the system into the ν-ensemble (see also [6]). If ∆V C is known then steady state averages of one-time quantities may be obtained by the methods of equilibrium statistical mechanics, using the energy function βE(C) = β i n i + ∆V C .…”

Section: Large Deviationsmentioning

confidence: 99%

Large deviations of the dynamical activity in the East model: analysing structure in biased trajectories

Jack¹,

Sollich²

2013

J. Phys. A: Math. Theor.

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Abstract. We consider large deviations of the dynamical activity in the East model. We bias this system to larger than average activity and investigate the structure that emerges. To best characterise this structure, we exploit the fact that there are effective interactions that would reproduce the same behaviour in an equilibrium system. We combine numerical results with linear response theory and variational estimates of these effective interactions, giving the first insights into such interactions in a many-body system, across a wide range of biases. The system exhibits a hierarchy of responses to the bias, remaining quasi-equilibrated on short length scales, but deviating far from equilibrium on large length scales. We discuss the connection between this hierarchy and the hierarchical aging behaviour of the system.

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Section: Large Deviationsmentioning

confidence: 99%

Large deviations of the dynamical activity in the East model: analysing structure in biased trajectories

Jack¹,

Sollich²

2013

J. Phys. A: Math. Theor.

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“…A well-know difficulty is that this deformed Markov operator no longer conserves probability, and cannot straightforwardly be interpreted as describing a bona fide probability-preserving dynamics. It has however been shown [16,17,18,19] how a relatively simple but formal transformation of the deformed Markov operator allows one to define a closely related probability-conserving Markov operator.…”

Section: Introductionmentioning

confidence: 99%

Effective driven dynamics for one-dimensional conditioned Langevin processes in the weak-noise limit

Tizón-Escamilla¹,

Lecomte²,

Bertin³

2019

J. Stat. Mech.

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In this work we focus on fluctuations of time-integrated observables for a particle diffusing in a one-dimensional periodic potential in the weak-noise asymptotics. Our interest goes to rare trajectories presenting an atypical value of the observable, that we study through a biased dynamics in a largedeviation framework. We determine explicitly the effective probability-conserving dynamics which makes rare trajectories of the original dynamics become typical trajectories of the effective one. Our approach makes use of a weak-noise path-integral description in which the action is minimised by the rare trajectories of interest. For 'current-type' additive observables, we find the emergence of a propagative trajectory minimising the action for large enough deviations, revealing the existence of a dynamical phase transition at a fluctuating level. In addition, we provide a new method to determine the scaled cumulant generating function of the observable without having to optimise the action. It allows one to show that the weak-noise and the large-time limits commute in this problem. Finally, we show how the biased dynamics can be mapped in practice to an effective driven dynamics, which takes the form of a driven Langevin dynamics in an effective potential. The non-trivial shape of this effective potential is key to understand the link between the dynamical phase transition in the large deviations of current and the standard depinning transition of a particle in a tilted potential. ‡ During the preparation of this manuscript, we became aware that works parallel to ours were completed using similar approaches [22,23].

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“…We present the exact analytical solution of the ASEP with reflecting boundaries using the Bethe ansatz method [38][39][40]. The master equation and boundary conditions which define the dynamics of the system as well as further technical details are provided in appendix B.…”

Section: Exact Solution Of Asep Dynamics With Reflecting Boundariesmentioning

confidence: 99%

Exactly solvable dynamics of forced polymer loops

et al. 2018

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Here, we show that a problem of forced polymer loops can be mapped to an asymmetric simple exclusion process with reflecting boundary conditions. The dynamics of the particle system can be solved exactly using the Bethe ansatz. We thus can fully describe the relaxation dynamics of forced polymer loops. In the steady state, the conformation of the loop can be approximated by a combination of Fermi-Dirac and Brownian bridge statistics, while the exact solution is found by using the fermion integer partition theory. With the theoretical framework presented here we establish a link between the physics of polymers and statistics of many-particle systems opening new paths of exploration in both research fields. Our result can be applied to the dynamics of the biopolymers which form closed loops. One such example is the active pulling of chromosomal loops during meiosis in yeast cells which helps to align chromosomes for recombination in the viscous environment of the cell nucleus.

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Construction of a coordinate Bethe ansatz for the asymmetric simple exclusion process with open boundaries

Cited by 92 publications

References 37 publications

Large deviations of the dynamical activity in the East model: analysing structure in biased trajectories

Large deviations of the dynamical activity in the East model: analysing structure in biased trajectories

Effective driven dynamics for one-dimensional conditioned Langevin processes in the weak-noise limit

Exactly solvable dynamics of forced polymer loops

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