Exact solution of the totally asymmetric simple exclusion process: Shock profiles
TLDR
In this paper, the microscopic structure of macroscopic shocks in the one-dimensional, totally asymmetric simple exclusion process is obtained exactly from the complete solution of the stationary state of a model system containing two types of particles.Abstract:
The microscopic structure of macroscopic shocks in the one-dimensional, totally asymmetric simple exclusion process is obtained exactly from the complete solution of the stationary state of a model system containing two types of particles-“first” and “second” class. This nonequilibrium steady state factorizes about any second-class particle, which implies factorization in the one-component system about the (random) shock position. It also exhibits several other interesting features, including long-range correlations in the limit of zero density of the second-class particles. The solution also shows that a finite number of second-class particles in a uniform background of first-class particles form a weakly bound state.read more
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References
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TL;DR: The construction, and other general results are given in this paper, with values in [0, ] s. The voter model, the contact process, the nearest-particle system, and the exclusion process.
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TL;DR: In this article, the authors present a model of a Tracer Particle in a Fluid with Hard Core Exclusion (TPE) and a Brownian Particle with hard core exclusion.
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Exact solution of a 1d asymmetric exclusion model using a matrix formulation
TL;DR: In this paper, a new approach based on representing the weights of each configuration in the steady state as a product of noncommuting matrices is presented, and the whole solution of the fully asymmetric exclusion problem is reduced to finding two matrices and two vectors which satisfy very simple algebraic rules.
Journal ArticleDOI
An exact solution of a one-dimensional asymmetric exclusion model with open boundaries
TL;DR: In this paper, a simple asymmetric exclusion model with open boundaries is solved exactly in one dimension by deriving a recursion relation for the steady state, which gives the closed expressions for the average occupations of all sites.
Journal ArticleDOI
Finite-size effects and shock fluctuations in the asymmetric simple-exclusion process.
TL;DR: This work considers a system of particles on a lattice of L sites, evolving according to the asymmetric simple-exclusion process, and finds that fluctuations of the shock position about its average value grow like ${\mathit{L}}^{1/2}$ or £1/3$ depending upon whether particle-hole symmetry exists.
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