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

Maxim Olshanii, Kurt Jacobs, Marcos Rigol, Vanja Dunjko, Harry Kennard, Vladimir A. Yurovsky

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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.

Original languageEnglish (US)
Article number641
JournalNature communications
Volume3
DOIs
StatePublished - Jan 1 2012

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All Science Journal Classification (ASJC) codes

  • Chemistry(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Physics and Astronomy(all)

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