[en] Motivated by neutron scattering experiments, we investigate the decay of the fidelity with which a wave packet is reconstructed by a perfect time-reversal operation performed after a phase-space displacement. In the semiclassical limit, we show that the decay rate is generically given by the Lyapunov exponent of the classical dynamics. For small displacements, we additionally show that, following a short-time Lyapunov decay, the decay freezes well above the ergodic value because of quantum effects. Our analytical results are corroborated by numerical simulations.
Disciplines :
Physics
Author, co-author :
Petitjean, Cyril ; Université de Liège - ULiège > Département de physique > Physique quantique statistique
Bevilaqua, Diego V.; Harvard Univ, Dept Phys, Cambridge, MA 02138 USA.
Heller, Eric J.; Harvard Univ, Dept Chem & Chem Biol, Cambridge, MA 02138 USA.
Jacquod, Philippe; Univ Arizona, Dept Phys, Tucson, AZ 85721 USA.
Language :
English
Title :
Displacement echoes: Classical decay and quantum freeze
Publication date :
2007
Journal title :
Physical Review Letters
ISSN :
0031-9007
eISSN :
1079-7114
Publisher :
American Physical Soc, College Pk, United States - Maryland
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The fidelity freeze reported here differs from the one found by T. Prosen and M. Žnidarič, Phys. Rev. Lett. 94, 044101 (2005). In particular, because the spectrum is left unchanged by phase-space displacements, the freeze of MD(t) found here persists up to t→. PRLTAO 0031-9007 10.1103/PhysRevLett.94.044101
The situation bears similarities with spectral and wavefunction variations in perturbed billiards. When the perturbation is an homogeneous spatial displacement, the spectrum is left unchanged. See: D. Cohen, A. Barnett, and E.J. Heller, Phys. Rev. E 63, 046207 (2001). PLEEE8 1063-651X 10.1103/PhysRevE.63.046207
The reduced Lyapunov exponent is somehow smaller than λ=ln[K/2] because Cγ exp[-λt] exp [-λt]. See: P.G. Silvestrov, J. Tworzydło, and C.W.J. Beenakker, Phys. Rev. E 67, 025204(R) (2003). PLEEE8 1063-651X 10.1103/PhysRevE.67.025204
