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We study phase transitions of a system of particles on the one-dimensional integer lattice moving with constant acceleration, with a collision law respecting slower particles. This simple deterministic ``particle-hopping'' traffic flow…

Dynamical Systems · Mathematics 2009-11-10 Michael Blank

The transport equation of active motion is generalised to consider time-fractional dynamics for describing the anomalous diffusion of self-propelled particles observed in many different systems. In the present study, we consider an…

Statistical Mechanics · Physics 2023-10-27 Francisco J. Sevilla , Guillermo Chacón-Acosta , Trifce Sandev

The dynamics of a closed quantum system is often studied with the direct evolution of the Schrodinger equation. In this paper, we propose that the gauge choice (i.e. degrees of freedom irrelevant to physical observables) of the Schrodinger…

Numerical Analysis · Mathematics 2020-02-20 Dong An , Lin Lin

Exact solutions of interacting random walk models, such as 1D lattice gases, offer precise insight into the origin of nonequilibrium phenomena. Here, we study a model of run-and-tumble particles on a ring lattice interacting via hardcore…

Statistical Mechanics · Physics 2019-02-21 Emil Mallmin , Richard A Blythe , Martin R Evans

We derive the thermodynamic Bethe ansatz equation for the situation inwhich the statistical interaction of a multi-particle system is governed by Haldane statistics. We formulate a macroscopical equivalence principle for such systems.…

High Energy Physics - Theory · Physics 2009-10-31 A. G. Bytsko , A. Fring

Dynamical universality classes are distinguished by their dynamical exponent $z$ and unique scaling functions encoding space-time asymmetry for, e.g. slow-relaxation modes or the distribution of time-integrated currents. So far the…

Statistical Mechanics · Physics 2019-11-20 Jan de Gier , Andreas Schadschneider , Johannes Schmidt , Gunter M. Schütz

By combining the algebraic Bethe ansatz and the off-diagonal Bethe ansatz, we investigate the supersymmetric t-J model with generic open boundaries. The eigenvalues of the transfer matrix are given in terms of an inhomogeneous T-Q relation,…

Mathematical Physics · Physics 2017-07-13 Pei Sun , Fakai Wen , Kun Hao , Junpeng Cao , Guang-Liang Li , Wen-Li Yang , Kangjie Shi

The algebraic structure underlying the totally asymmetric exclusion process is studied by using the Bethe Ansatz technique. From the properties of the algebra generated by the local jump operators, we explicitly construct the hierarchy of…

Statistical Mechanics · Physics 2007-06-07 O. Golinelli , K. Mallick

The implementation of the algebraic Bethe ansatz for the XXZ Heisenberg spin chain, of arbitrary spin-$s$, in the case, when both reflection matrices have the upper-triangular form is analyzed. The general form of the Bethe vectors is…

Exactly Solvable and Integrable Systems · Physics 2017-08-21 N. Manojlović , and I. Salom

This work deals with the one-dimensional Stefan problem with a general time-dependent boundary condition at the fixed boundary. Stochastic solutions are obtained using discrete random walks, and the results are compared with analytic…

Analysis of PDEs · Mathematics 2023-02-06 M. Ogren

The spin-1/2 XYZ model with both periodic and anti-periodic boundary conditions is studied via the off-diagonal Bethe ansatz method. The exact spectra of the Hamiltonians and the Bethe ansatz equations are derived by constructing the…

Statistical Mechanics · Physics 2015-06-16 Junpeng Cao , Shuai Cui , Wen-Li Yang , Kangjie Shi , Yupeng Wang

In this paper, we investigate the convergence rate of the averaging principle for stochastic differential equations (SDEs) with $\beta$-H\"older drift driven by $\alpha$-stable processes. More specifically, we first derive the Schauder…

Dynamical Systems · Mathematics 2024-09-20 Mengyu Cheng , Zimo Hao , Xicheng Zhang

This paper extends the results of Ma, Wu, Zhang, Zhang [11] to the context of path-dependent multidimensional forward-backward stochastic differential equations (FBSDE). By path-dependent we mean that the coefficients of the…

Probability · Mathematics 2022-01-14 Kaitong Hu , Zhenjie Ren , Nizar Touzi

We consider partial exclusion processes~(PEPs) on the one-dimensional square lattice, that is, a system of interacting particles where each particle random walks according to a jump rate satisfying an exclusion rule that allows up to a…

Probability · Mathematics 2026-04-15 Patrícia Gonçalves , Kohei Hayashi , Makiko Sasada

We consider open systems where cars move according to the deterministic Nagel-Schreckenberg rules and with maximum velocity ${v}_{max} > 1$, what is an extension of the Asymmetric Exclusion Process (ASEP). It turns out that the behaviour of…

Statistical Mechanics · Physics 2009-10-31 S. Cheybani , J. Kertesz , M. Schreckenberg

We consider the one-dimensional totally asymmetric simple exclusion model (TASEP model) with open boundary conditions and present the analytical computations leading to the exact formula for distance clearance distribution, i.e. probability…

Cellular Automata and Lattice Gases · Physics 2018-01-08 Milan Krbalek , Pavel Hrabak

The nested off-diagonal Bethe ansatz is generalized to study the quantum spin chain associated with the $SU_q(3)$ R-matrix and generic integrable non-diagonal boundary conditions. By using the fusion technique, certain closed operator…

Mathematical Physics · Physics 2016-08-24 Guang-Liang Li , Junpeng Cao , Kun Hao , Fakai Wen , Wen-Li Yang , Kangjie Shi

Many biological processes are supported by special molecules, called motor proteins or molecular motors, that transport cellular cargoes along linear protein filaments and can reversibly associate to their tracks. Stimulated by these…

Statistical Mechanics · Physics 2021-11-17 Akriti Jindal , Anatoly B. Kolomeisky , Arvind Kumar Gupta

The one-dimensional totally asymmetric simple exclusion process (TASEP), a Markov process describing classical hard-core particles hopping in the same direction, is considered on a periodic lattice of $L$ sites. The relaxation to the…

Statistical Mechanics · Physics 2016-03-09 Sylvain Prolhac

Stationary probability distributions for stochastic processes on linear chains with closed or open ends are obtained using the matrix product Ansatz. The matrices are representations of some quadratic algebras. The algebras and the types of…

Statistical Mechanics · Physics 2009-10-30 F. C. Alcaraz , S. Dasmahapatra , V. Rittenberg