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Open Quantum Systems Decoherence
Quantum Simulation
Partial Weyl Law for Billiards
arXiv
Authors: Arnd Bäcker, Roland Ketzmerick, Steffen Löck, Holger Schanz
Year
2010
Paper ID
10706
Status
Preprint
Abstract Read
~2 min
Abstract Words
98
Citations
N/A
Abstract
For two-dimensional quantum billiards we derive the partial Weyl law, i.e. the average density of states, for a subset of eigenstates concentrating on an invariant region Γ of phase space. The leading term is proportional to the area of the billiard times the phase-space fraction of Γ. The boundary term is proportional to the fraction of the boundary where parallel trajectories belong to Γ. Our result is numerically confirmed for the mushroom billiard and the generic cosine billiard, where we count the number of chaotic and regular states, and for the elliptical billiard, where we consider rotating and oscillating states.
Why This Paper Matters
- This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
- It adds a 2010 reference point for readers tracking recent quantum research.
- For two-dimensional quantum billiards we derive the partial Weyl law, i.e.
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