The high energy asymptotic distribution of the eigenvalues of the scattering matrix

We determine the high energy asymptotic density of the eigenvalues of the scat- tering matrix associated with the operators H0 = −∆ and H = (i∇ + A)2 + V (x), where V : Rd → R is a smooth short-range real-valued electric potential and<br/>A = (A1, . . . , Ad) : Rd → Rd is a smooth short-range magnetic vector-potential. Two cases are considered. The first case is where the magnetic vector-potential is non-zero. The spectral density of the associated scattering matrix in this case is expressed as an integral solely in terms of the magnetic vector-potential A. The second case considered is where the magnetic vector-potential is identically zero. Again the spectral density of the scattering matrix is expressed as an integral, this time in terms of the poten- tial V . These results share similar <br/>characteristics to results pertaining to semiclassical asymptotics for pseudodifferential <br/>operators.<br/>

Name dc:type.qualificationname

Doctor of Philosophy

Level dc:type.qualificationlevel

Doctoral Thesis

Grantor dc:publisher.institution

King's College London

Year dc:date.issued

2013

Author dc:creator

• Bulger, Daniel

Advisors dc:contributor.advisor

• Pushnitski, Alexander
• Shargorodsky, Eugene
• Safarov, Yuri

Language dc:language

eng

Identifier

oai:kclpure.kcl.ac.uk:studenttheses/541fc908-ff77-4f0f-b3ba-af1fe53e19dd

OAI identifier oai:identifier

oai:kclpure.kcl.ac.uk:studenttheses/541fc908-ff77-4f0f-b3ba-af1fe53e19dd