An exactly solvable model for the integrability-chaos transition in rough quantum billiards
|Title||An exactly solvable model for the integrability-chaos transition in rough quantum billiards|
|Publication Type||Journal Article|
|Year of Publication||2012|
|Authors||Olshanii, M., Jacobs K., Rigol M., Dunjko V., Kennard H., and Yurovsky V. A.|
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.