Long-time saturation of the Loschmidt echo in quantum chaotic billiards

Gutiérrez, Martha and Goussev, Arseni (2009) Long-time saturation of the Loschmidt echo in quantum chaotic billiards. Physical Review E, 79 (4). 046211. ISSN 1539-3755

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Official URL: http://dx.doi.org/10.1103/PhysRevE.79.046211

Abstract

The Loschmidt echo (LE) (or fidelity) quantifies the sensitivity of the time evolution of a quantum system with respect to a perturbation of the Hamiltonian. In a typical chaotic system the LE has been previously argued to exhibit a long-time saturation at a value inversely proportional to the effective size of the Hilbert space of the system. However, until now no quantitative results have been known and, in particular, no explicit expression for the proportionality constant has been proposed. In this paper we perform a quantitative analysis of the phenomenon of the LE saturation and provide the analytical expression for its long-time saturation value for a semiclassical particle in a two-dimensional chaotic billiard. We further perform extensive (fully quantum mechanical) numerical calculations of the LE saturation value and find the numerical results to support the semiclassical theory.

Item Type: Article
Subjects: F300 Physics
G100 Mathematics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: Arseni Goussev
Date Deposited: 08 Nov 2012 10:22
Last Modified: 13 May 2017 20:19
URI: http://nrl.northumbria.ac.uk/id/eprint/10197

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