Lyapunov decay in quantum irreversibility

I. GARCIA-MATA; A. RONCAGLIA; D. A. WISNIACKI

PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES

ROYAL SOC

Lugar: Londres; Año: 2016 p. 1 - 12

0080-4614

The Loschmidt echo?also known as fidelity?is avery useful tool to study irreversibility in quantummechanics due to perturbations or imperfections.Many different regimes, as a function of time andstrength of the perturbation, have been identified.For chaotic systems, there is a range of perturbationstrengths where the decay of the Loschmidt echo isperturbation independent, and given by the classicalLyapunov exponent. But observation of the Lyapunovdecay depends strongly on the type of initial stateupon which an average is done. This dependencecan be removed by averaging the fidelity over theHaar measure, and the Lyapunov regime is recovered,as it was shown for quantum maps. In this work,we introduce an analogous quantity for systems withinfinite dimensional Hilbert space, in particular thequantum stadium billiard, and we show clearly theuniversality of the Lyapunov regime.