Regensburg 2007 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 25: Quantum chaos II

DY 25.2: Talk

Thursday, March 29, 2007, 10:00–10:15, H2

Chaotic billiards: Loschmidt echo decay due to local deformations of boundaries — •Arseni Goussev and Klaus Richter — Institute for Theoretical Physics, University of Regensburg, Germany

We study the stability of the quantum dynamics against perturbations of the Hamiltonian in systems that are chaotic in the classical limit. For this purpose, we address the time dependence of the Loschmidt echo (LE), also known as fidelity, for semiclassical wave packets in two-dimensional chaotic billiards. The LE is the overlap between two wave functions that are obtained in the course of time evolution of the same initial quantum state under two different Hamiltonians. We investigate, analytically and numerically, the time decay of the LE for the case that the difference between the two Hamiltonians, i.e. the Hamiltonian perturbation, is due to a local deformation of the billiard's boundary. We find the LE to decay exponentially in time, with the rate equal to the classical escape rate from an open billiard obtained from the original one by removing the deformation-affected region of its boundary. This result provides an appealing connection between the quantum fidelity in the regime of strong Hamiltonian perturbations and properties of the chaotic dynamics of the underlying classical system.