Explicit solution of the optimal fluctuation problem for an elastic string in a random medium
Abstract
The free-energy distribution function of an elastic string in a quenched random potential, PL(F) , is investigated with the help of the optimal fluctuation approach. The form of the far-right tail of PL(F) is found by constructing the exact solution of the nonlinear saddle-point 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 far-left tail of the height distribution function in the stochastic growth problem described by the d -dimensional Kardar-Parisi-Zhang 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;
- Spin-glass and other random models;
- Classical statistical mechanics;
- Vortex lattices flux pinning flux creep;
- Condensed Matter - Disordered Systems and Neural Networks;
- Condensed Matter - Statistical Mechanics
- E-Print:
- 9 pages, RevTex4