An exactly solvable model for the integrability-chaos transition in rough quantum billiards

作者：Olshanii Maxim^*; Jacobs Kurt; Rigol Marcos; Dunjko Vanja; Kennard Harry; Yurovsky Vladimir A

来源：Nature Communications, 2012, 3(1): 641.

DOI：10.1038/ncomms1653

A central question of dynamics, largely open in the quantum case, is to what extent it erases a system%26apos;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.

• 出版日期2012-1