Energy absorption in time-dependent unitary random matrix ensembles: dynamic vs. Anderson localization
M. A. Skvortsov*, D. M. Basko+, V. E. Kravtsov*+
*L.D.Landau Institute for Theoretical Physics RAS, 117940 Moscow, Russia
+The Abdus Salam International Centre for Theoretical Physics, 34100 Trieste, Italy
PACS: 03.65.-w, 72.10.Bg, 73.23.-b
We consider energy absorption in an externally driven complex system
of noninteracting fermions with the chaotic underlying dynamics
described by the unitary random matrices. In the absence of
quantum interference the energy absorption rate W(t) can be calculated
with the help of the linear-response Kubo formula.
We calculate the leading two-loop interference correction
to the semiclassical absorption rate for an arbitrary time
dependence of the external perturbation.
Based on the results for periodic perturbations, we make
a conjecture that the dynamics of the periodically-driven random
matrices can be mapped onto the one-dimensional Anderson model.
We predict that in the regime of strong dynamic localization
rather than decays exponentially.