Short time decay of the Loschmidt echo

Abstract

The Loschmidt echo measures the sensitivity to perturbations of quantum evolutions. We study its short time decay in classically chaotic systems. Using perturbation theory and throwing out all correlation imposed by the initial state and the perturbation, we show that the characteristic time of this regime is well described by the inverse of the width of the local density of states. This result is illustrated and discussed in a numerical study in a 2-dimensional chaotic billiard system perturbed by various contour deformations and using different types of initial conditions. Moreover, the influence to the short time decay of sub-Planck structures developed by time evolution is also investigated.

7 pages, 7 figures, published version

References in corpus (9)

• Sub-Planck spots of Schroedinger cats and quantum decoherence
• Golden rule decay versus Lyapunov decay of the quantum Loschmidt echo
• Sensitivity of Wave Field Evolution and Manifold Stability in Chaotic Systems
• Stability of quantum motion and correlation decay
• Quantum Chaotic Environments, The Butterfly Effect, And Decoherence
• Measuring the Lyapunov exponent using quantum mechanics
• Decay of the Loschmidt Echo for quantum states with sub-Planck scale structures
• Quantum irreversibility, perturbation independent decay, and the parametric theory of the local density of states
• Sensitivity to perturbations in a quantum chaotic billiard

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