arXiv subjects

A. M. Povolotsky

Publications and source records attributed to A. M. Povolotsky.

25 records · Page 2Linked to original sources

arXiv2003

Bethe Ansatz solution of the stochastic process with nonuniform stationary state

The eigenfunctions and eigenvalues of the master-equation for zero range process on a ring are found exactly via the Bethe ansatz. The rates of particle exit from a site providing the Bethe ansatz applicability are shown to be expressed in terms of single parameter. Continuous variation of this parameter leads to the transition of driving diffusive system from positive to negative driving through purely diffusive point. The relation of the model with other Bethe ansatz solvable models is discussed.

cond-mat.stat-mech↗

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↗

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↗

arXiv1998

Dynamics of Eulerian walkers

We investigate the dynamics of Eulerian walkers as a model of self-organized criticality. The evolution of the system is subdivided into characteristic periods which can be seen as avalanches. The structure of avalanches is described and the critical exponent in the distribution of first avalanches $τ=2$ is determined. We also study a mean square displacement of Eulerian walkers and obtain a simple diffusion law in the critical state. The evolution of underlying medium from a random state to the critical one is also described.

cond-mat.stat-mech↗

arXiv1996

Renormalization Group Study of Sandpile on the Triangular Lattice

We apply the renormalization group approach to the sandpile on the triangular lattice. The only attractive fixed point is found. The obtained fixed point height probabilities are compared with numerical simulations. The value of critical exponent of avalanche size distribution is found to be $τ=1.36$. The probabilities of the sand transition are compared with the branching probabilities of the spanning trees on the triangular lattice which are also evaluated.

cond-mat↗

arXiv1996

Critical Dynamics of Self-Organizing Eulerian Walkers

The model of self-organizing Eulerian walkers is numerically investigated on the square lattice. The critical exponents for the distribution of a number of steps ($τ_l$) and visited sites ($τ_s$) characterizing the process of transformation from one recurrent configuration to another are calculated using the finite-size scaling analysis. Two different kinds of dynamical rules are considered. The results of simulations show that both the versions of the model belong to the same class of universality with the critical exponents $τ_l=τ_s=1.75\pm 0.1$.

cond-mat↗