An Exactly Solvable Model for the Integrability-Chaos Transition in Rough Quantum Billiards

Details An Exactly Solvable Model for the Integrability-Chaos Transition in Rough Quantum Billiards An Exactly Solvable Model for the Integrability-Chaos Transition in Rough Quantum Billiards

2012-03-09

arxiv.org/abs/1203.1972v1

Nature Communications 3, 641 (2012)

Physics

Condensed Matter

Quantum Gases

29 pages, 5 figures

Scientific paper

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.

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