8 research outputs found
Anomalous tag diffusion in the asymmetric exclusion model with particles of arbitrary sizes
Anomalous behavior of correlation functions of tagged particles are studied
in generalizations of the one dimensional asymmetric exclusion problem. In
these generalized models the range of the hard-core interactions are changed
and the restriction of relative ordering of the particles is partially brocken.
The models probing these effects are those of biased diffusion of particles
having size S=0,1,2,..., or an effective negative "size" S=-1,-2,..., in units
of lattice space. Our numerical simulations show that irrespective of the range
of the hard-core potential, as long some relative ordering of particles are
kept, we find suitable sliding-tag correlation functions whose fluctuations
growth with time anomalously slow (), when compared with the normal
diffusive behavior (). These results indicate that the critical
behavior of these stochastic models are in the Kardar-Parisi-Zhang (KPZ)
universality class. Moreover a previous Bethe-ansatz calculation of the
dynamical critical exponent , for size particles is extended to
the case and the KPZ result is predicted for all values of .Comment: 4 pages, 3 figure
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
Equilibrium and dynamical properties of the ANNNI chain at the multiphase point
We study the equilibrium and dynamical properties of the ANNNI (axial
next-nearest-neighbor Ising) chain at the multiphase point. An interesting
property of the system is the macroscopic degeneracy of the ground state
leading to finite zero-temperature entropy. In our equilibrium study we
consider the effect of softening the spins. We show that the degeneracy of the
ground state is lifted and there is a qualitative change in the low temperature
behaviour of the system with a well defined low temperature peak of the
specific heat that carries the thermodynamic ``weight'' of the ground state
entropy. In our study of the dynamical properties, the stochastic Kawasaki
dynamics is considered. The Fokker-Planck operator for the process corresponds
to a quantum spin Hamiltonian similar to the Heisenberg ferromagnet but with
constraints on allowed states. This leads to a number of differences in its
properties which are obtained through exact numerical diagonalization,
simulations and by obtaining various analytic bounds.Comment: 9 pages, RevTex, 6 figures (To appear in Phys. Rev. E
Two ways to solve ASEP
The purpose of this article is to describe the two approaches to compute
exact formulas (which are amenable to asymptotic analysis) for the probability
distribution of the current of particles past a given site in the asymmetric
simple exclusion process (ASEP) with step initial data. The first approach is
via a variant of the coordinate Bethe ansatz and was developed in work of Tracy
and Widom in 2008-2009, while the second approach is via a rigorous version of
the replica trick and was developed in work of Borodin, Sasamoto and the author
in 2012.Comment: 10 pages, Chapter in "Topics in percolative and disordered systems
Transient behavior in Single-File Systems
We have used Monte-Carlo methods and analytical techniques to investigate the
influence of the characteristics, such as pipe length, diffusion, adsorption,
desorption and reaction rates on the transient properties of Single-File
Systems. The transient or the relaxation regime is the period in which the
system is evolving to equilibrium. We have studied the system when all the
sites are reactive and when only some of them are reactive. Comparisons between
Mean-Field predictions, Cluster Approximation predictions, and Monte Carlo
simulations for the relaxation time of the system are shown. We outline the
cases where Mean-Field analysis gives good results compared to Dynamic
Monte-Carlo results. For some specific cases we can analytically derive the
relaxation time. Occupancy profiles for different distribution of the sites
both for Mean-Field and simulations are compared. Different results for slow
and fast reaction systems and different distribution of reactive sites are
discussed.Comment: 18 pages, 19 figure
Determinant representation for some transition probabilities in the TASEP with second class particles
We study the transition probabilities for the totally asymmetric simple
exclusion process (TASEP) on the infinite integer lattice with a finite, but
arbitrary number of first and second class particles. Using the Bethe ansatz we
present an explicit expression of these quantities in terms of the Bethe wave
function. In a next step it is proved rigorously that this expression can be
written in a compact determinantal form for the case where the order of the
first and second class particles does not change in time. An independent
geometrical approach provides insight into these results and enables us to
generalize the determinantal solution to the multi-class TASEP.Comment: Minor revision; journal reference adde