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

Maxim Olshanii (), Kurt Jacobs, Marcos Rigol, Vanja Dunjko, Harry Kennard and Vladimir A. Yurovsky
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Maxim Olshanii: University of Massachusetts Boston
Kurt Jacobs: University of Massachusetts Boston
Marcos Rigol: Georgetown University
Vanja Dunjko: University of Massachusetts Boston
Harry Kennard: University of Massachusetts Boston
Vladimir A. Yurovsky: School of Chemistry, Tel Aviv University

Nature Communications, 2012, vol. 3, issue 1, 1-9

Abstract: 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.

Date: 2012
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DOI: 10.1038/ncomms1653

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