SCIENCE@home

Loschmidt echo and Lyapunov exponent in a quantum disordered system.

Y. Adamov,I. Gornyi,A. Mirlin

Published 2002 in Physical review. E, Statistical, nonlinear, and soft matter physics

ABSTRACT

We investigate the sensitivity of a disordered system with diffractive scatterers to a weak external perturbation. Specifically, we calculate the fidelity M(t) (also called the Loschmidt echo) characterizing a return probability after a propagation for a time t followed by a backward propagation governed by a slightly perturbed Hamiltonian. For short-range scatterers, we perform a diagrammatic calculation showing that the fidelity decays first exponentially according to the golden rule, and then follows a power law governed by the diffusive dynamics. For long-range disorder (when the diffractive scattering is of small-angle character), an intermediate regime emerges where the diagrammatics is not applicable. Using the path-integral technique, we derive a kinetic equation and show that M(t) decays exponentially with a rate governed by the classical Lyapunov exponent.

PUBLICATION RECORD

CITATION MAP

EXTRACTION MAP

CLAIMS

  • No claims are published for this paper.

CONCEPTS

  • No concepts are published for this paper.

REFERENCES

Showing 1-30 of 30 references · Page 1 of 1

CITED BY

Showing 1-24 of 24 citing papers · Page 1 of 1