413 research outputs found
Bethe anzats derivation of the Tracy-Widom distribution for one-dimensional directed polymers
The distribution function of the free energy fluctuations in one-dimensional
directed polymers with -correlated random potential is studied by
mapping the replicated problem to a many body quantum boson system with
attractive interactions. Performing the summation over the entire spectrum of
excited states the problem is reduced to the Fredholm determinant with the Airy
kernel which is known to yield the Tracy-Widom distributionComment: 5 page
Replica Bethe ansatz derivation of the Tracy-Widom distribution of the free energy fluctuations in one-dimensional directed polymers
The distribution function of the free energy fluctuations in one-dimensional
directed polymers with -correlated random potential is studied by
mapping the replicated problem to the -particle quantum boson system with
attractive interactions. We find the full set of eigenfunctions and eigenvalues
of this many-body system and perform the summation over the entire spectrum of
excited states. It is shown that in the thermodynamic limit the problem is
reduced to the Fredholm determinant with the Airy kernel yielding the universal
Tracy-Widom distribution, which is known to describe the statistical properties
of the Gaussian unitary ensemble as well as many other statistical systems.Comment: 23 page
Current moments of 1D ASEP by duality
We consider the exponential moments of integrated currents of 1D asymmetric
simple exclusion process using the duality found by Sch\"utz. For the ASEP on
the infinite lattice we show that the th moment is reduced to the problem of
the ASEP with less than or equal to particles.Comment: 13 pages, no figur
Construction of a matrix product stationary state from solutions of finite size system
Stationary states of stochastic models, which have states per site, in
matrix product form are considered. First we give a necessary condition for the
existence of a finite -dimensional matrix product state for any .
Second, we give a method to construct the matrices from the stationary states
of small size system when the above condition and are satisfied.
Third, the method by which one can check that the obtained matrices are valid
for any system size is presented for the case where is satisfied. The
application of our methods is explained using three examples: the asymmetric
exclusion process, a model studied in [F. H. Jafarpour: J. Phys. A: Math. Gen.
36 (2003) 7497] and a hybrid of both of the models.Comment: 22 pages, no figure. Major changes: sec.3 was shortened; the list of
references were changed. This is the final version, which will appear in
J.Phys.
Exact solution of a partially asymmetric exclusion model using a deformed oscillator algebra
We study the partially asymmetric exclusion process with open boundaries. We
generalise the matrix approach previously used to solve the special case of
total asymmetry and derive exact expressions for the partition sum and currents
valid for all values of the asymmetry parameter q. Due to the relationship
between the matrix algebra and the q-deformed quantum harmonic oscillator
algebra we find that q-Hermite polynomials, along with their orthogonality
properties and generating functions, are of great utility. We employ two
distinct sets of q-Hermite polynomials, one for q1. It
turns out that these correspond to two distinct regimes: the previously studied
case of forward bias (q1) where the
boundaries support a current opposite in direction to the bulk bias. For the
forward bias case we confirm the previously proposed phase diagram whereas the
case of reverse bias produces a new phase in which the current decreases
exponentially with system size.Comment: 27 pages LaTeX2e, 3 figures, includes new references and further
comparison with related work. To appear in J. Phys.
Power-law behavior in the power spectrum induced by Brownian motion of a domain wall
We show that Brownian motion of a one-dimensional domain wall in a large but
finite system yields a power spectrum. This is successfully
applied to the totally asymmetric simple exclusion process (TASEP) with open
boundaries. An excellent agreement between our theory and numerical results is
obtained in a frequency range where the domain wall motion dominates and
discreteness of the system is not effective.Comment: 4 pages, 4 figure
Multiple Shocks in a Driven Diffusive System with Two Species of Particles
A one-dimensional driven diffusive system with two types of particles and
nearest neighbors interactions has been considered on a finite lattice with
open boundaries. The particles can enter and leave the system from both ends of
the lattice and there is also a probability for converting the particle type at
the boundaries. We will show that on a special manifold in the parameters space
multiple shocks evolve in the system for both species of particles which
perform continuous time random walks on the lattice.Comment: 11 pages, 1 figure, accepted for publication in Physica
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