595 research outputs found
Formulas for ASEP with Two-Sided Bernoulli Initial Condition
For the asymmetric simple exclusion process on the integer lattice with
two-sided Bernoulli initial condition, we derive exact formulas for the
following quantities: (1) the probability that site x is occupied at time t;
(2) a correlation function, the probability that site 0 is occupied at time 0
and site x is occupied at time t; (3) the distribution function for the total
flux across 0 at time t and its exponential generating function.Comment: 18 page
Superdiffusivity of Finite-Range Asymmetric Exclusion Processes on
We consider finite-range asymmetric exclusion processes on with
non-zero drift. The diffusivity is expected to be of . We prove that in the weak (Tauberian) sense
that as . The proof employs the resolvent method to make a direct comparison with the
totally asymmetric simple exclusion process, for which the result is a
consequence of the scaling limit for the two-point function recently obtained
by Ferrari and Spohn. In the nearest neighbor case, we show further that
is monotone, and hence we can conclude that in the usual sense.Comment: Version 3. Statement of Theorem 3 is correcte
On the partial connection between random matrices and interacting particle systems
In the last decade there has been increasing interest in the fields of random
matrices, interacting particle systems, stochastic growth models, and the
connections between these areas. For instance, several objects appearing in the
limit of large matrices arise also in the long time limit for interacting
particles and growth models. Examples of these are the famous Tracy-Widom
distribution functions and the Airy_2 process. The link is however sometimes
fragile. For example, the connection between the eigenvalues in the Gaussian
Orthogonal Ensembles (GOE) and growth on a flat substrate is restricted to
one-point distribution, and the connection breaks down if we consider the joint
distributions. In this paper we first discuss known relations between random
matrices and the asymmetric exclusion process (and a 2+1 dimensional
extension). Then, we show that the correlation functions of the eigenvalues of
the matrix minors for beta=2 Dyson's Brownian motion have, when restricted to
increasing times and decreasing matrix dimensions, the same correlation kernel
as in the 2+1 dimensional interacting particle system under diffusion scaling
limit. Finally, we analyze the analogous question for a diffusion on (complex)
sample covariance matrices.Comment: 31 pages, LaTeX; Added a section concerning the Markov property on
space-like path
On the Two Species Asymmetric Exclusion Process with Semi-Permeable Boundaries
We investigate the structure of the nonequilibrium stationary state (NESS) of
a system of first and second class particles, as well as vacancies (holes), on
L sites of a one-dimensional lattice in contact with first class particle
reservoirs at the boundary sites; these particles can enter at site 1, when it
is vacant, with rate alpha, and exit from site L with rate beta. Second class
particles can neither enter nor leave the system, so the boundaries are
semi-permeable. The internal dynamics are described by the usual totally
asymmetric exclusion process (TASEP) with second class particles. An exact
solution of the NESS was found by Arita. Here we describe two consequences of
the fact that the flux of second class particles is zero. First, there exist
(pinned and unpinned) fat shocks which determine the general structure of the
phase diagram and of the local measures; the latter describe the microscopic
structure of the system at different macroscopic points (in the limit L going
to infinity in terms of superpositions of extremal measures of the infinite
system. Second, the distribution of second class particles is given by an
equilibrium ensemble in fixed volume, or equivalently but more simply by a
pressure ensemble, in which the pair potential between neighboring particles
grows logarithmically with distance. We also point out an unexpected feature in
the microscopic structure of the NESS for finite L: if there are n second class
particles in the system then the distribution of first class particles
(respectively holes) on the first (respectively last) n sites is exchangeable.Comment: 28 pages, 4 figures. Changed title and introduction for clarity,
added reference
Fluctuation properties of the TASEP with periodic initial configuration
We consider the joint distributions of particle positions for the continuous
time totally asymmetric simple exclusion process (TASEP). They are expressed as
Fredholm determinants with a kernel defining a signed determinantal point
process. We then consider certain periodic initial conditions and determine the
kernel in the scaling limit. This result has been announced first in a letter
by one of us and here we provide a self-contained derivation. Connections to
last passage directed percolation and random matrices are also briefly
discussed.Comment: 33 pages, 4 figure, LaTeX; We added several references to the general
framework and techniques use
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
On the asymmetric simple exclusion process with multiple species
In the asymmetric simple exclusion process on the integers each particle
waits exponential time, then with probability p it moves one step to the right
if the site is unoccupied, otherwise it stays put; and with probability q=1-p
it moves one step to the left if the site is unoccupied, otherwise it stays
put. In previous work the authors, using the Bethe Ansatz, found for N-particle
ASEP a formula --- a sum of multiple integrals --- for the probability that a
system is in a particular configuration at time t given an initial
configuration. The present work extends this to the case where particles are of
different species, with particles of a higher species having priority over
those of a lower species. Here the integrands in the multiple integrals are
defined by a system of relations whose consistency requires verifying that the
Yang-Baxter equations are satisfied.Comment: 17 pages. Version 3 corrects misprints, clarifies some points, and
adds reference
Zitterbewegung in External Magnetic Field: Classic versus Quantum Approach
We investigate variations of the Zitterbewegung frequency of electron due to
an external static and uniform magnetic field employing the expectation value
quantum approach, and compare our results with the classical model of spinning
particles. We demonstrate that these two so far compatible approaches are not
in agreement in the presence of an external uniform static magnetic field, in
which the classical approach breaks the usual symmetry of free particles and
antiparticles states, i.e. it leads to CP violation. Hence, regarding the
Zitterbewegung frequency of electron, the classical approach in the presence of
an external magnetic field is unlikely to correctly describe the spin of
electron, while the quantum approach does, as expected. We also show that the
results obtained via the expectation value are in close agreement with the
quantum approach of the Heisenberg picture derived in the literature. However,
the method we use is capable of being compared with the classical approach
regarding the spin aspects. The classical interpretation of spin produced by
the altered Zitterbewegung frequency, in the presence of an external magnetic
field, are discussed.Comment: 16 pages, no figure
X-boson cumulant approach to the periodic Anderson model
The Periodic Anderson Model (PAM) can be studied in the infinite U limit by
employing the Hubbard X operators to project out the unwanted states. We have
already studied this problem employing the cumulant expansion with the
hybridization as perturbation, but the probability conservation of the local
states (completeness) is not usually satisfied when partial expansions like the
Chain Approximation (CHA) are employed. Here we treat the problem by a
technique inspired in the mean field approximation of Coleman's slave-bosons
method, and we obtain a description that avoids the unwanted phase transition
that appears in the mean-field slave-boson method both when the chemical
potential is greater than the localized level Ef at low temperatures (T) and
for all parameters at intermediate T.Comment: Submited to Physical Review B 14 pages, 17 eps figures inserted in
the tex
Thermodynamic Limit for the Invariant Measures in Supercritical Zero Range Processes
We prove a strong form of the equivalence of ensembles for the invariant
measures of zero range processes conditioned to a supercritical density of
particles. It is known that in this case there is a single site that
accomodates a macroscopically large number of the particles in the system. We
show that in the thermodynamic limit the rest of the sites have joint
distribution equal to the grand canonical measure at the critical density. This
improves the result of Gro\ss kinsky, Sch\"{u}tz and Spohn, where convergence
is obtained for the finite dimensional marginals. We obtain as corollaries
limit theorems for the order statistics of the components and for the
fluctuations of the bulk
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