7 research outputs found
An Exactly Solvable Model for the Integrability-Chaos Transition in Rough Quantum Billiards
A central question of dynamics, largely open in the quantum case, is to what
extent it erases a system's memory of its initial properties. Here we present a
simple statistically solvable quantum model describing this memory loss across
an integrability-chaos transition under a perturbation obeying no selection
rules. From the perspective of quantum localization-delocalization on the
lattice of quantum numbers, we are dealing with a situation where every lattice
site is coupled to every other site with the same strength, on average. The
model also rigorously justifies a similar set of relationships recently
proposed in the context of two short-range-interacting ultracold atoms in a
harmonic waveguide. Application of our model to an ensemble of uncorrelated
impurities on a rectangular lattice gives good agreement with ab initio
numerics.Comment: 29 pages, 5 figure
Dynamics of a Quantum Phase Transition and Relaxation to a Steady State
We review recent theoretical work on two closely related issues: excitation
of an isolated quantum condensed matter system driven adiabatically across a
continuous quantum phase transition or a gapless phase, and apparent relaxation
of an excited system after a sudden quench of a parameter in its Hamiltonian.
Accordingly the review is divided into two parts. The first part revolves
around a quantum version of the Kibble-Zurek mechanism including also phenomena
that go beyond this simple paradigm. What they have in common is that
excitation of a gapless many-body system scales with a power of the driving
rate. The second part attempts a systematic presentation of recent results and
conjectures on apparent relaxation of a pure state of an isolated quantum
many-body system after its excitation by a sudden quench. This research is
motivated in part by recent experimental developments in the physics of
ultracold atoms with potential applications in the adiabatic quantum state
preparation and quantum computation.Comment: 117 pages; review accepted in Advances in Physic