Sensitivity to perturbations in a quantum chaotic billiard.
PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002;
65:055206. [PMID:
12059633 DOI:
10.1103/physreve.65.055206]
[Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/27/2001] [Indexed: 05/23/2023]
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 Gamma 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 a regime for which the FGR manifestly does not work, we find a crossover from Gamma to Lyapunov decay. We find that, challenging the analytic interpretation, these conjectures are valid even beyond the expected range.
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