159 research outputs found
Time-dependent correlation functions in a one-dimensional asymmetric exclusion process
We study a one-dimensional anisotropic exclusion process describing particles
injected at the origin, moving to the right on a chain of sites and being
removed at the (right) boundary. We construct the steady state and compute the
density profile, exact expressions for all equal-time n-point density
correlation functions and the time-dependent two-point function in the steady
state as functions of the injection and absorption rates. We determine the
phase diagram of the model and compare our results with predictions from
dynamical scaling and discuss some conjectures for other exclusion models.Comment: LATEX-file, 32 pages, Weizmann preprint WIS/93/01/Jan-P
Large Deviation Function of the Partially Asymmetric Exclusion Process
The large deviation function obtained recently by Derrida and Lebowitz for
the totally asymmetric exclusion process is generalized to the partially
asymmetric case in the scaling limit. The asymmetry parameter rescales the
scaling variable in a simple way. The finite-size corrections to the universal
scaling function and the universal cumulant ratio are also obtained to the
leading order.Comment: 10 pages, 2 eps figures, minor changes, submitted to PR
Spectral gap of the totally asymmetric exclusion process at arbitrary filling
We calculate the spectral gap of the Markov matrix of the totally asymmetric
simple exclusion process (TASEP) on a ring of L sites with N particles. Our
derivation is simple and self-contained and extends a previous calculation that
was valid only for half-filling. We use a special property of the Bethe
equations for TASEP to reformulate them as a one-body problem. Our method is
closely related to the one used to derive exact large deviation functions of
the TASEP
Bethe Ansatz for the Weakly Asymmetric Simple Exclusion Process and phase transition in the current distribution
The probability distribution of the current in the asymmetric simple
exclusion process is expected to undergo a phase transition in the regime of
weak asymmetry of the jumping rates. This transition was first predicted by
Bodineau and Derrida using a linear stability analysis of the hydrodynamical
limit of the process and further arguments have been given by Mallick and
Prolhac. However it has been impossible so far to study what happens after the
transition. The present paper presents an analysis of the large deviation
function of the current on both sides of the transition from a Bethe ansatz
approach of the weak asymmetry regime of the exclusion process.Comment: accepted to J.Stat.Phys, 1 figure, 1 reference, 2 paragraphs adde
Universal Distributions for Growth Processes in 1+1 Dimensions and Random Matrices
We develop a scaling theory for KPZ growth in one dimension by a detailed
study of the polynuclear growth (PNG) model. In particular, we identify three
universal distributions for shape fluctuations and their dependence on the
macroscopic shape. These distribution functions are computed using the
partition function of Gaussian random matrices in a cosine potential.Comment: 4 pages, 3 figures, 1 table, RevTeX, revised version, accepted for
publication in PR
Exact Solution of the Asymmetric Exclusion Model with Particles of Arbitrary Size
A generalization of the simple exclusion asymmetric model is introduced. In
this model an arbitrary mixture of molecules with distinct sizes , in units of lattice space, diffuses asymmetrically on the lattice.
A related surface growth model is also presented. Variations of the
distribution of molecules's sizes may change the excluded volume almost
continuously. We solve the model exactly through the Bethe ansatz and the
dynamical critical exponent is calculated from the finite-size corrections
of the mass gap of the related quantum chain. Our results show that for an
arbitrary distribution of molecules the dynamical critical behavior is on the
Kardar-Parizi-Zhang (KPZ) universality.Comment: 28 pages, 2 figures. To appear in Phys. Rev. E (1999
General Reaction-Diffusion Processes With Separable Equations for Correlation Functions
We consider general multi-species models of reaction diffusion processes and
obtain a set of constraints on the rates which give rise to closed systems of
equations for correlation functions. Our results are valid in any dimension and
on any type of lattice. We also show that under these conditions the evolution
equations for two point functions at different times are also closed. As an
example we introduce a class of two species models which may be useful for the
description of voting processes or the spreading of epidemics.Comment: 17 pages, Latex, No figure
Asymptotic behavior of A + B --> inert for particles with a drift
We consider the asymptotic behavior of the (one dimensional) two-species
annihilation reaction A + B --> 0, where both species have a uniform drift in
the same direction and like species have a hard core exclusion. Extensive
numerical simulations show that starting with an initially random distribution
of A's and B's at equal concentration the density decays like t^{-1/3} for long
times. This process is thus in a different universality class from the cases
without drift or with drift in different directions for the different species.Comment: LaTeX, 6pp including 3 figures in LaTeX picture mod
Spectral Degeneracies in the Totally Asymmetric Exclusion Process
We study the spectrum of the Markov matrix of the totally asymmetric
exclusion process (TASEP) on a one-dimensional periodic lattice at ARBITRARY
filling. Although the system does not possess obvious symmetries except
translation invariance, the spectrum presents many multiplets with degeneracies
of high order. This behaviour is explained by a hidden symmetry property of the
Bethe Ansatz. Combinatorial formulae for the orders of degeneracy and the
corresponding number of multiplets are derived and compared with numerical
results obtained from exact diagonalisation of small size systems. This
unexpected structure of the TASEP spectrum suggests the existence of an
underlying large invariance group.
Keywords: ASEP, Markov matrix, Bethe Ansatz, Symmetries.Comment: 19 pages, 1 figur
Algebraic Bethe Ansatz for the two species ASEP with different hopping rates
An ASEP with two species of particles and different hopping rates is
considered on a ring. Its integrability is proved and the Nested Algebraic
Bethe Ansatz is used to derive the Bethe Equations for states with arbitrary
numbers of particles of each type, generalizing the results of Derrida and
Evans. We present also formulas for the total velocity of particles of a given
type and their limit for large size of the system and finite densities of the
particles.Comment: 14 page
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