Universal Response of Quantum Systems with Chaotic Dynamics

Abstract

The prediction of the response of a closed system to external perturbations is one of the central problems in quantum mechanics, and in this respect, the local density of states (LDOS) provides an in- depth description of such a response. The LDOS is the distribution of the overlaps squared connecting the set of eigenfunctions with the perturbed one. Here, we show that in the case of closed systems with classically chaotic dynamics, the LDOS is a Breit-Wigner distribution under very general perturbations of arbitrary high intensity. Consequently, we derive a semiclassical expression for the width of the LDOS which is shown to be very accurate for paradigmatic systems of quantum chaos. This Letter demonstrates the universal response of quantum systems with classically chaotic dynamics.

4 pages, 3 figures

References in corpus (5)

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• Dephasing representation of quantum fidelity for general pure and mixed states
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• Quantum to classical transition in the work distribution for chaotic systems
• Beating the efficiency of both quantum and classical simulations with semiclassics
• Loschmidt echo in quantum maps: the elusive nature of the Lyapunov regime
• An initial value representation for the Loschmidt echo
• Evaluation of the importance of spin-orbit couplings in the nonadiabatic quantum dynamics with quantum fidelity and with its efficient "on-the-fly" ab initio semiclassical approximation
• Improving the accuracy and efficiency of time-resolved electronic spectra calculations: Cellular dephasing representation with a prefactor
• Proliferation of effective interactions: decoherence-induced equilibration in a closed many-body system
• Path integral approach to the quantum fidelity amplitude
• Sensitivity to perturbations and quantum phase transitions
• Perturbations and chaos in quantum maps