Abstract:
Classical chaotic systems proceed to equilibrium by a mixing process in the phase
space. We study this relaxation to equilibrium for quantized, bound chaotic maps
on the torus. The Ruelle-Pollicott resonances that describe the mixing of classical
chaotic system has been derived for the lazy-baker map, which is a non-uniformly
hyperbolic system. The corresponding issue of quantifying mixing in Hilbert space
has been discussed in this thesis and a correspondence between the classical and
quantum relaxation has been shown for the same map. Later the e ect of a random
unitary transformation on the quantum relaxation has been shown to be an immediate
relaxation to the equilibrium. An average of the quantum relaxation over all such
random unitary transformations has been analytically performed. The average of the
relaxation
uctuations about the equilibrium is derived to have a simple structure
under certain conditions, re
ecting the universal properties of the concerned random
matrix ensemble.
