A phase-space study of the quantum Loschmidt Echo in the semiclassical limit

Details A phase-space study of the quantum Loschmidt Echo in the semiclassical limit A phase-space study of the quantum Loschmidt Echo in the semiclassical limit

2005-10-19

arxiv.org/abs/quant-ph/0510151v2

Annales de l'Institut Henri Poincare Physique Theorique 8 (2007) 91-108

Physics

Quantum Physics

Scientific paper

10.1007/s00023-006-0301-9

The notion of Loschmidt echo (also called "quantum fidelity") has been introduced in order to study the (in)-stability of the quantum dynamics under perturbations of the Hamiltonian. It has been extensively studied in the past few years in the physics literature, in connection with the problems of "quantum chaos", quantum computation and decoherence. In this paper, we study this quantity semiclassically (as $\hbar \to 0$), taking as reference quantum states the usual coherent states. The latter are known to be well adapted to a semiclassical analysis, in particular with respect to semiclassical estimates of their time evolution. For times not larger than the so-called "Ehrenfest time" $C | \log \hbar |$, we are able to estimate semiclassically the Loschmidt Echo as a function of $t$ (time), $\hbar$ (Planck constant), and $\delta$ (the size of the perturbation). The way two classical trajectories merging from the same point in classical phase-space, fly apart or come close together along the evolutions governed by the perturbed and unperturbed Hamiltonians play a major role in this estimate. We also give estimates of the "return probability" (again on reference states being the coherent states) by the same method, as a function of $t$ and $\hbar$.

Affiliated with

Also associated with

No associations

Rating

A phase-space study of the quantum Loschmidt Echo in the semiclassical limit does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A phase-space study of the quantum Loschmidt Echo in the semiclassical limit, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A phase-space study of the quantum Loschmidt Echo in the semiclassical limit will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-242276