title: An exactly solvable model for the integrability-chaos transition in rough quantum billiards.
abstract: 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.
authors.affiliation: Department of Physics, University of Massachusetts Boston, Boston, Massachusetts 02125, USA. Maxim.Olchanyi@umb.edu
authors.forename: Maxim
authors.initials: M
authors.lastname: Olshanii
authors.forename: Kurt
authors.initials: K
authors.lastname: Jacobs
authors.forename: Marcos
authors.initials: M
authors.lastname: Rigol
authors.forename: Vanja
authors.initials: V
authors.lastname: Dunjko
authors.forename: Harry
authors.initials: H
authors.lastname: Kennard
authors.forename: Vladimir A
authors.initials: VA
authors.lastname: Yurovsky