Abstract

Tunneling between two classically disconnected regular regions can be
strongly affected by the presence of a chaotic sea in between.
This phenomenon, known as chaos-assisted tunneling, gives rise to large
fluctuations of the tunneling rate.
We study chaos-assisted tunneling in the presence of Anderson
localization effects in the chaotic sea. Our results show that the
standard tunneling rate distribution is strongly modified by localization,
going from the known Cauchy distribution in the ergodic regime to a
log-normal distribution in the strongly localized case.
We develop an analytical single-parameter scaling theory which
accurately describes the numerical data, for both a deterministic and a
disordered model.
Time permitting, I will also discuss some preliminary numerical results
pertaining to the superfluid to Bose glass transition in the
one-dimensional t-V-model, i.e. hard-core bosons with nearest-neighbour
interactions and on-site disorder.