Hydrodynamic behavior of “fluxoid'” in type II - superconductor
based on the asymmetric zero-range process

I.B. Krasniyk, V.M Yurchenko

A.A.Galkin Physical & Technical Institute NASU,
R. Luxemburg Str., 72,  83114, Donetsk., Ukraine.

The points where the order parameter turns into zero and their phase experience a leap by multiple of 2, are known as phase slip centers (B.Ivlev,N.Kopnin [1984]). PCSs can be formed as a result of  thermodynamic fluctuations of the system. The probability of such  an event is proportional to exp (-F /T) where F is the free-energy barrier between two uniform states before and after the phase slippage.  This process is more probable near the critical temperature where the  barrier is small  (L.Langer, V.Ambegaokar [1967]). If Xt  denotes this process then it is described by the following hyperbolic equation
                                                                             (*)
(J.Fouque, A.Benassi [1989] and E.Andjel, C.Kipnis [1984]) where the expectation 

and  a  small  parameter  .  For  we set  and  is called a configuration (1 for sites occupied with intensity  and 0 for vacant ones). In the asymmetric case , the right scaling is  and as  and setting   converges to . If  (in the symmetric case),  is the right scaling and the limiting equation is parabolic. Simulations is a Monte-Carlo method solving Burger-type equation (*). This equation rules the hydrodynamic limit behavior of a simple exclusion  process: particles are on a linear lattice and wait an exponential amount of time before jumping to the right if there is no particle already there.