Equivalence of Fokker-Planck approach and non-linear σ-model for disordered wires in the unitary symmetry class

Quantum transport in disordered wires: Equivalence of one-dimensional σ model and Dorokhov-Mello-Pereyra-Kumar equation

The two known non-perturbative theories of localization in disordered wires, the Fokker-Planck approach due to Dorokhov, Mello, Pereyra, and Kumar, and the field-theoretic approach due to Efetov and Larkin, are shown to be equivalent for all symmetry classes. The equivalence had been questioned as a result of field-theoretic calculations of the average conductance by Zirnbauer [PRL 69, 1584 (19...

Iterative methods for solving non linear Fokker-Planck equation

Typeset Using Revt E X 2

The parametric correlations of the transmission eigenvalues Ti of a N -channel quantum scatterer are calculated assuming two different Brownian motion ensembles. The first one is the original ensemble introduced by Dyson and assumes an isotropic diffusion for the S-matrix. We derive the corresponding Fokker-Planck equation for the transmission eigenvalues, which can be mapped for the unitary ca...

Pseudo-spectral ‎M‎atrix and Normalized Grunwald Approximation for Numerical Solution of Time Fractional Fokker-Planck Equation

This paper presents a new numerical method to solve time fractional Fokker-Planck equation. The space dimension is discretized to the Gauss-Lobatto points, then we apply pseudo-spectral successive integration matrix for this dimension. This approach shows that with less number of points, we can approximate the solution with more accuracy. The numerical results of the examples are displayed.

CONTROL OF CHAOS IN A DRIVEN NON LINEAR DYNAMICAL SYSTEM

We present a numerical study of a one-dimensional version of the Burridge-Knopoff model [16] of N-site chain of spring-blocks with stick-slip dynamics. Our numerical analysis and computer simulations lead to a set of different results corresponding to different boundary conditions. It is shown that we can convert a chaotic behaviour system to a highly ordered and periodic behaviour by making on...