Journal
PHYSICS LETTERS A
Volume 380, Issue 34, Pages 2637-2643Publisher
ELSEVIER
DOI: 10.1016/j.physleta.2016.06.031
Keywords
Stationary points; Semiclassical level density; Level dynamics
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Funding
- Czech Science Foundation [P203-13-07117S]
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Classical stationary points of an analytic Hamiltonian induce singularities of the density of quantum energy levels and their flow with a control parameter in the system's infinite-size limit. We show that for a system with f degrees of freedom, a non-degenerate stationary point with index r causes a discontinuity (for r even) or divergence (r odd) of the (f-1)th derivative of both density and flow of the spectrum. An increase of flatness for a degenerate stationary point shifts the singularity to lower derivatives. The findings are verified in an f = 3 toy model. (C) 2016 Elsevier B.V. All rights reserved.
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