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

Author

Listed:
  • 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
    Cavendish Laboratory, University of Cambridge)

  • Vladimir A. Yurovsky

    (School of Chemistry, Tel Aviv University)

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.

Suggested Citation

  • Maxim Olshanii & Kurt Jacobs & Marcos Rigol & Vanja Dunjko & Harry Kennard & Vladimir A. Yurovsky, 2012. "An exactly solvable model for the integrability–chaos transition in rough quantum billiards," Nature Communications, Nature, vol. 3(1), pages 1-9, January.
  • Handle: RePEc:nat:natcom:v:3:y:2012:i:1:d:10.1038_ncomms1653
    DOI: 10.1038/ncomms1653
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    Cited by:

    1. Ferenc Iglói & Csaba Zoltán Király, 2024. "Entanglement detection in postquench nonequilibrium states: thermal Gibbs vs. generalized Gibbs ensemble," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(6), pages 1-12, June.

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