West CT, Prosen T, Kottos T. Short-time Loschmidt gap in dynamical systems with critical chaos.
PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009;
79:050107. [PMID:
19518402 DOI:
10.1103/physreve.79.050107]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/16/2008] [Indexed: 05/27/2023]
Abstract
We study the Loschmidt echo F(t) for a class of dynamical systems showing critical chaos. Using a kicked rotor with singular potential as a prototype model, we found that the classical echo shows a gap (initial drop) 1-F_{g} , where F_{g} scales as F_{g}(alpha,,eta)=f_{cl}(chi_{cl} identical witheta;{3-alpha}/) ; alpha is the order of singularity of the potential, eta is the spread of the initial phase-space density, and is the perturbation strength. Instead, the quantum echo gap is insensitive to alpha , described by a scaling law F_{g}=f_{q}(chi_{q}=eta;{2}/) which can be captured by a random matrix theory modeling of critical systems. We trace this quantum-classical discrepancy to strong diffraction effects that dominate the dynamics.
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