Fidelity Gap in Dynamical Systems with Critical Chaos

ORAL

Abstract

We analyze the fidelity decay for a class of dynamical systems showing {\it critical chaos}, using a Kicked Rotor with singular kicking potential as a prototype model. We found that the classical fidelity shows a gap $F_g$ (initial drop of fidelity) which scales as $F_g(\alpha, \epsilon, \eta ) = f(\chi\equiv\frac{\eta^{3-\alpha}}{\epsilon})$ where $\alpha$ is the order of singularity of the non-analytical potential, $\eta$ is the characteristic spread of the initial phase space density and $\epsilon$ is the perturbation strength. Instead, the corresponding quantum fidelity gap is insensitive to $\alpha$ due to strong diffraction effects that dominate the quantum dynamics.

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Authors

  • Carl T. West

    Department of Physics, Wesleyan University, Middletown, Connecticut 06459, USA and MPI for Dynamics and Self-Organization, 37073 Goettingen, Germany

  • Tomaz Prosen

    Physics Department, Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia

  • Tsampikos Kottos

    Department of Physics, Wesleyan University, Middletown CT-USA and MPI for Dynamics and Self-Organization, G\"ottingen-Germany, Department of Physics, Wesleyan University, Middletown, Connecticut 06459, USA and MPI for Dynamics and Self-Organization, 37073 Goettingen, Germany, Department of Physics, Wesleyan University, Middletown, Connecticut, Department of Physics, Wesleyan University, Middletown CT-USA and MPI for Dynamics and Self-Organization, Goettingen-Germany, Max Planck Institute for Dynamics \& Self-Organization. AND Dept. of Physics, Wesleyan University