Sensitivity to perturbations in a quantum chaotic billiard

D. A. WISNIACKI; E. G. VERGINI; H. M. PASTAWSKI; FERNANDO M. CUCCHIETTI

PHYSICAL REVIEW E - STATISTICAL PHYSICS, PLASMAS, FLUIDS AND RELATED INTERDISCIPLINARY TOPICS

The American Physical Society

Año: 2002 vol. 65 p. 55206 - 55206

1063-651X

Sensitivity to perturbations in a quantum chaotic billiard             D. A. Wisniacki, E.G. Vergini, H. M. Pastawski, F. M. Cucchietti,             Phys. Rev. E. 65 055206(R) (2002) Abstract The Loschmidt echo (LE) measures the ability of a system to return to the initial state after a forward quantum evolution followed by a backward perturbed one. It has been conjectured that the echo of a classically chaotic system decays exponentially, with a decay rate given by the minimum between the width G of the local density of states and the Lyapunov exponent. As the perturbation strength is increased one obtains a crossover between both regimes. These predictions are based on situations where the Fermi golden rule (FGR) is valid. By considering a paradigmatic fully chaotic system, the Bunimovich stadium billiard, with a perturbation in aregime for which the FGR manifestly does not work, we find a crossover from G to Lyapunov decay. We find that, challenging the analytic interpretation, these conjectures are valid even beyond the expected range.DOI: 10.1103/PhysRevE.65.055206 PACS number~s!: 05.45.Mt, 03.65.Sq