Geodesic
Quantum chaos versus noise environment
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 3 (2010) no. 3, pp. 303-310

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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, entropy, purity.
Mots-clés : markov's chain 
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Yaroslav A. Kharkov; Valentin V. Sokolov; Oleg V. Zhirov. Quantum chaos versus noise environment. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 3 (2010) no. 3, pp. 303-310. http://geodesic.mathdoc.fr/item/JSFU_2010_3_3_a4/