arXiv subjects

V. B. Priezzhev

Publications and source records attributed to V. B. Priezzhev.

At least 37 records · Page 2Linked to original sources

arXiv2010

Green functions for the TASEP with sublattice parallel update

We consider the totally asymmetric simple exclusion process (TASEP) in discrete time with the sublattice parallel dynamics describing particles moving to the right on the one-dimensional infinite chain with equal hoping probabilities. Using sequentially two mappings, we show that the model is equivalent to the TASEP with the backward-ordered sequential update in the case when particles start and finish their motion not simultaneously. The Green functions are obtained exactly in a determinant form for different initial and final conditions.

cond-mat.stat-mech↗

arXiv2009

Three-leg correlations in the two component spanning tree on the upper half-plane

We present a detailed asymptotic analysis of correlation functions for the two component spanning tree on the two-dimensional lattice when one component contains three paths connecting vicinities of two fixed lattice sites at large distance $s$ apart. We extend the known result for correlations on the plane to the case of the upper half-plane with closed and open boundary conditions. We found asymptotics of correlations for distance $r$ from the boundary to one of the fixed lattice sites for the cases $r\gg s \gg 1$ and $s \gg r \gg 1$.

cond-mat.stat-mech↗

arXiv2008

From Vicious Walkers to TASEP

We propose a model of semi-vicious walkers, which interpolates between the totally asymmetric simple exclusion process and the vicious walkers model, having the two as limiting cases. For this model we calculate the asymptotics of the survival probability for $m$ particles and obtain a scaling function, which describes the transition from one limiting case to another. Then, we use a fluctuation-dissipation relation allowing us to reinterpret the result as the particle current generating function in the totally asymmetric simple exclusion process. Thus we obtain the particle current distribution asymptotically in the large time limit as the number of particles is fixed. The results apply to the large deviation scale as well as to the diffusive scale. In the latter we obtain a new universal distribution, which has a skew non-Gaussian form. For $m$ particles its asymptotic behavior is shown to be $e^{-\frac{y^{2}}{2m^{2}}}$ as $y\to -\infty $ and $e^{-\frac{y^{2}}{2m}}y^{-\frac{m(m-1)}{2}}$ as $y\to \infty $.

cond-mat.stat-mech↗

arXiv2008

Two-dimensional spanning webs as (1,2) logarithmic minimal model

A lattice model of critical spanning webs is considered for the finite cylinder geometry. Due to the presence of cycles, the model is a generalization of the known spanning tree model which belongs to the class of logarithmic theories with central charge $c=-2$. We show that in the scaling limit the universal part of the partition function for closed boundary conditions at both edges of the cylinder coincides with the character of symplectic fermions with periodic boundary conditions and for open boundary at one edge and closed at the other coincides with the character of symplectic fermions with antiperiodic boundary conditions.

cond-mat.stat-mech↗

arXiv2008

Exact solution of the Bernoulli matching model of sequence alignment

Through a series of exact mappings we reinterpret the Bernoulli model of sequence alignment in terms of the discrete-time totally asymmetric exclusion process with backward sequential update and step function initial condition. Using earlier results from the Bethe ansatz we obtain analytically the exact distribution of the length of the longest common subsequence of two sequences of finite lengths $X,Y$. Asymptotic analysis adapted from random matrix theory allows us to derive the thermodynamic limit directly from the finite-size result.

cond-mat.stat-mech↗

arXiv2008

Jamming probabilities for a vacancy in the dimer model

Following the recent proposal made by Bouttier et al [Phys. Rev. E 76, 041140 (2007)], we study analytically the mobility properties of a single vacancy in the close-packed dimer model on the square lattice. Using the spanning web representation, we find determinantal expressions for various observable quantities. In the limiting case of large lattices, they can be reduced to the calculation of Toeplitz determinants and minors thereof. The probability for the vacancy to be strictly jammed and other diffusion characteristics are computed exactly.

cond-mat.stat-mech↗

arXiv2007

Pair correlations in sandpile model: a check of logarithmic conformal field theory

We compute the correlations of two height variables in the two-dimensional Abelian sandpile model. We extend the known result for two minimal heights to the case when one of the heights is bigger than one. We find that the most dominant correlation log r/r^4 exactly fits the prediction obtained within the logarithmic conformal approach.

cond-mat.stat-mech↗

arXiv2007

Determinant solution for the Totally Asymmetric Exclusion Process with parallel update II. Ring geometry

Using the Bethe ansatz we obtain the determinant expression for the time dependent transition probabilities in the totally asymmetric exclusion process with parallel update on a ring. Developing a method of summation over the roots of Bethe equations based on the multidimensional analogue of the Cauchy residue theorem, we construct the resolution of the identity operator, which allows us to calculate the matrix elements of the evolution operator and its powers. Representation of results in the form of an infinite series elucidates connection to other results obtained for the ring geometry. As a byproduct we also obtain the generating function of the joint probability distribution of particle configurations and the total distance traveled by the particles.

cond-mat.stat-mech↗

arXiv2006

Determinant solution for the TASEP with particle-dependent hopping probabilities on a ring

We consider the totally asymmetric exclusion process on a ring in discrete time with the backward-ordered sequential update and particle-dependent hopping probabilities. Using a combinatorial treatment of the Bethe ansatz, we derive the determinant expression for the non-stationary probability of transitions between particle configurations. In the continuous-time limit, we find a generalization of the recent result, obtained by A. Rákos and G.M. Schütz for infinite lattice, to the case of ring geometry.

cond-mat.stat-mech↗

arXiv2006

Determinant solution for the Totally Asymmetric Exclusion Process with parallel update

We consider the totally asymmetric exclusion process in discrete time with the parallel update. Constructing an appropriate transformation of the evolution operator, we reduce the problem to that solvable by the Bethe ansatz. The non-stationary solution of the master equation for the infinite 1D lattice is obtained in a determinant form. Using a modified combinatorial treatment of the Bethe ansatz, we give an alternative derivation of the resulting determinant expression.

cond-mat.stat-mech↗

arXiv2006

Logarithmic Conformal Field Theory and Boundary Effects in the Dimer Model

We study the finite-size corrections of the dimer model on $\infty \times N$ square lattice with two different boundary conditions: free and periodic. We find that the finite-size corrections in a crucial way depend on the parity of $N$; we also show that such unusual finite-size behavior can be fully explained in the framework of the $c=-2$ logarithmic conformal field theory.

cond-mat.stat-mech↗

arXiv2005

The totally asymmetric exclusion process on a ring: Exact relaxation dynamics and associated model of clustering transition

The totally asymmetric simple exclusion process in discrete time is considered on finite rings with fixed number of particles. A translation-invariant version of the backward-ordered sequential update is defined for periodic boundary conditions. We prove that the so defined update leads to a stationary state in which all possible particle configurations have equal probabilities. Using the exact analytical expression for the propagator, we find the generating function for the conditional probabilities, average velocity and diffusion constant at all stages of evolution. An exact and explicit expression for the stationary velocity of TASEP on rings of arbitrary size and particle filling is derived. The evolution of small systems towards a steady state is clearly demonstrated. Considering the generating function as a partition function of a thermodynamic system, we study its zeros in planes of complex fugacities. At long enough times, the patterns of zeroes for rings with increasing size provide evidence for a transition of the associated two-dimensional lattice paths model into a clustered phase at low fugacities.

cond-mat.soft↗

arXiv2003

Transition from KPZ to Tilted Interface Critical Behavior in a Solvable Asymmetric Avalanche Model

We use a discrete-time formulation to study the asymmetric avalanche process [Phys. Rev. Lett. vol. 87, 084301 (2001)] on a finite ring and obtain an exact expression for the average avalanche size of particles as a function of toppling probabilities depending on parameters $μ$ and $α$. By mapping the model below and above the critical line onto driven interface problems, we show how different regimes of avalanches may lead to different types of critical interface behavior characterized by either annealed or quenched disorders and obtain exactly the related critical exponents which violate a well-known scaling relation when $α\ne 2$.

cond-mat.stat-mech↗

arXiv2003

The Asymmetric Avalanche Process

An asymmetric stochastic process describing the avalanche dynamics on a ring is proposed. A general kinetic equation which incorporates the exclusion and avalanche processes is considered. The Bethe ansatz method is used to calculate the generating function for the total distance covered by all particles. It gives the average velocity of particles which exhibits a phase transition from an intermittent to continuous flow. We calculated also higher cumulants and the large deviation function for the particle flow. The latter has the universal form obtained earlier for the asymmetric exclusion process and conjectured to be common for all models of the Kardar-Parisi-Zhang universality class .

cond-mat.stat-mech↗

arXiv2002

Exact Non-Stationary Probabilities in the Asymmetric Exclusion Process on a Ring

By a geometrical treatment of the Bethe ansatz, we obtain an exact solution for the totally asymmetric exclusion process on a ring. We derive an explicit determinant expression for the non-stationary conditional probability $Prob(x_1,...,x_P;t|x_1^0,...,x_P^0;0)$ of finding $P$ particles on sites $x_1,...,x_P$ at time $t$ provided they are on sites $x_1^0,...,x_P^0$ at time $t=0$.

cond-mat.stat-mech↗

arXiv2000

Exact velocity of dispersive flow in the asymmetric avalanche process

Using the Bethe ansatz we obtain the exact solution for the one-dimensional asymmetric avalanche process. We evaluate the velocity of dispersive flow as a function of driving force and the density of particles. The obtained solution shows a dynamical transition from intermittent to continuous flow.

cond-mat.stat-mech↗

arXiv2000

Distribution of consecutive waves in the sandpile model on the Sierpinski gasket

The scaling properties of waves of topplings in the sandpile model on the Sierpinski gasket are investigated. The exponent describing the asymptotics of the distribution of last waves in an avalanche is found. Predictions for scaling exponents in the forward and backward conditional probabilites for two consecutive waves are given. All predictions were examined by numerical simulations and were found to be in reasonable agreement with the obtained data.

cond-mat.stat-mech↗

arXiv1999

Inversion Symmetry and Critical Exponents of Dissipating Waves in the Sandpile Model

Statistics of waves of topplings in the Sandpile model is analysed both analytically and numerically. It is shown that the probability distribution of dissipating waves of topplings that touch the boundary of the system obeys power-law with critical exponent 5/8. This exponent is not indeendent and is related to the well-known exponent of the probability distribution of last waves of topplings by exact inversion symmetry s -> 1/s.

cond-mat.stat-mech↗