Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2003-07-31
Physics
Condensed Matter
Disordered Systems and Neural Networks
33 pages, 17 figures, uses Revtex 4
Scientific paper
10.1103/PhysRevB.70.035311
The Loschmidt echo (LE) is a magnitude that measures the sensitivity of quantum dynamics to perturbations in the Hamiltonian. For a certain regime of the parameters, the LE decays exponentially with a rate given by the Lyapunov exponent of the underlying classically chaotic system. We develop a semiclassical theory, supported by numerical results in a Lorentz gas model, which allows us to establish and characterize the universality of this Lyapunov regime. In particular, the universality is evidenced by the semiclassical limit of the Fermi wavelength going to zero, the behavior for times longer than Ehrenfest time, the insensitivity with respect to the form of the perturbation and the behavior of individual (non-averaged) initial conditions. Finally, by elaborating a semiclassical approximation to the Wigner function, we are able to distinguish between classical and quantum origin for the different terms of the LE. This approach renders an understanding for the persistence of the Lyapunov regime after the Ehrenfest time, as well as a reinterpretation of our results in terms of the quantum--classical transition.
Cucchietti Fernando M.
Jalabert Rodolfo A.
Pastawski Horacio Miguel
No associations
LandOfFree
Universality of the Lyapunov regime for the Loschmidt echo 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 Universality of the Lyapunov regime for the Loschmidt echo, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Universality of the Lyapunov regime for the Loschmidt echo will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-333302