Equidistribution of phase shifts in semiclassical potential scattering

Jesse Gell-Redman; Andrew Hassell; Steve Zelditch

doi:10.1112/jlms/jdu068

Equidistribution of phase shifts in semiclassical potential scattering

Jesse Gell-Redman, Andrew Hassell, Steve Zelditch

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

Consider the Hamiltonian H:= h² Δ +V-E where Δ is the positive Laplacian on R^d, V in C₀(R^d) 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 S_h(E), which lie on the unit circle S¹ C due to the unitarity of S_h(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 language	English
Pages (from-to)	159-179
Number of pages	21
Journal	Journal of the London Mathematical Society
Volume	91
Issue number	1
DOIs	https://doi.org/10.1112/jlms/jdu068
Publication status	Published - 17 Apr 2015

Access to Document

10.1112/jlms/jdu068

Cite this

@article{d07273a775f049b6b112c62596d36087,

title = "Equidistribution of phase shifts in semiclassical potential scattering",

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.",

author = "Jesse Gell-Redman and Andrew Hassell and Steve Zelditch",

note = "Publisher Copyright: {\textcopyright} 2015 {\textcopyright} 2015 London Mathematical Society.",

year = "2015",

month = apr,

day = "17",

doi = "10.1112/jlms/jdu068",

language = "English",

volume = "91",

pages = "159--179",

journal = "Journal of the London Mathematical Society",

issn = "0024-6107",

publisher = "John Wiley & Sons Ltd.",

number = "1",

}

TY - JOUR

T1 - Equidistribution of phase shifts in semiclassical potential scattering

AU - Gell-Redman, Jesse

AU - Hassell, Andrew

AU - Zelditch, Steve

PY - 2015/4/17

Y1 - 2015/4/17

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84925218220&partnerID=8YFLogxK

U2 - 10.1112/jlms/jdu068

DO - 10.1112/jlms/jdu068

M3 - Article

SN - 0024-6107

VL - 91

SP - 159

EP - 179

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

IS - 1

ER -

Equidistribution of phase shifts in semiclassical potential scattering

Abstract

Access to Document

Other files and links

Fingerprint

Cite this