Explicit solution of the optimal fluctuation problem for an elastic string in a random medium
Abstract
The freeenergy distribution function of an elastic string in a quenched random potential, P_{L}(F) , is investigated with the help of the optimal fluctuation approach. The form of the farright tail of P_{L}(F) is found by constructing the exact solution of the nonlinear saddlepoint equations describing the asymptotic form of the optimal fluctuation. The solution of the problem is obtained for two different types of boundary conditions and for an arbitrary dimension of the imbedding space 1+d with d from the interval 0<d<2 . The results are also applicable for the description of the farleft tail of the height distribution function in the stochastic growth problem described by the d dimensional KardarParisiZhang equation.
 Publication:

Physical Review E
 Pub Date:
 September 2009
 DOI:
 10.1103/PhysRevE.80.031107
 arXiv:
 arXiv:0904.1673
 Bibcode:
 2009PhRvE..80c1107K
 Keywords:

 46.65.+g;
 75.10.Nr;
 05.20.y;
 74.25.Qt;
 Random phenomena and media;
 Spinglass and other random models;
 Classical statistical mechanics;
 Vortex lattices flux pinning flux creep;
 Condensed Matter  Disordered Systems and Neural Networks;
 Condensed Matter  Statistical Mechanics
 EPrint:
 9 pages, RevTex4