Quantum chaos versus noise environment

Yaroslav A. Kharkov, Valentin V. Sokolov, Oleg V. Zhirov

Budker's Institute of Nuclear Physics, Novosibirsk State University, Novosibirsk, Russia

Abstract: Quantum dynamics of a classically chaotic 1D system in the presence of external noise is studied. Stability and reversibility properties of the motion (characterized by the Peres fidelity) as functions of the noise level $\sigma$ are considered. We calculate fidelity analytically in the cases of weak and very strong noise and find critical value, $\sigma_c(t)$, below which the effect of perturbation remains small. Decay of critical perturbation with time is found to be power-like after the Ehrenfest time $t_E$. An estimation of the decoherence time $t_d(\sigma)$ is presented after which the averaged density matrix becomes diagonal and its evolution turns into a Markovian process.

Keywords: quantum chaos, Wigner function, Fidelity, stability, reversibility, markov's chain, entropy, purity.

UDC: 530.145.1

Received: 10.04.2010
Received in revised form: 10.05.2010
Accepted: 12.06.2010

Language: English