Equidistribution of phase shifts in semiclassical potential scattering

Jesse Gell-Redman, Andrew Hassell, Steve Zelditch

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

Consider the Hamiltonian H:= h2 Δ +V-E where Δ is the positive Laplacian on Rd, V in C0(Rd) is a smooth, compactly supported potential, E >0 is an energy level, and h >0 is a semiclassical parameter. We study the eigenvalues of the scattering matrix Sh(E), which lie on the unit circle S1 C due to the unitarity of Sh(E). Under an appropriate hypothesis on the classical dynamical flow corresponding to H, we show that in the limit h to 0, the eigenvalues are asymptotically equidistributed on the unit circle away from the point 1 in S1.

Original languageEnglish (US)
Pages (from-to)159-179
Number of pages21
JournalJournal of the London Mathematical Society
Volume91
Issue number1
DOIs
StatePublished - Apr 17 2015

ASJC Scopus subject areas

  • Mathematics(all)

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