{"id":{"repo_id":"kings","oai_identifier":"oai:kclpure.kcl.ac.uk:studenttheses/541fc908-ff77-4f0f-b3ba-af1fe53e19dd"},"canonical_url":"https://search.dev.ndltd.org/etd/kings/oai:kclpure.kcl.ac.uk:studenttheses/541fc908-ff77-4f0f-b3ba-af1fe53e19dd","repository":{"repo_id":"kings","name":"King's College London","base_url":"https://kclpure.kcl.ac.uk/ws/oai"},"display":{"title":"The high energy asymptotic distribution of the eigenvalues of the scattering matrix","abstract":"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/>","abstract_html":"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&lt;br/&gt;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 &lt;br/&gt;characteristics to results pertaining to semiclassical asymptotics for pseudodifferential &lt;br/&gt;operators.&lt;br/&gt;","abstract_has_math":false,"creators":["Bulger, Daniel"],"institution":"King's College London","degree_name":"Doctor of Philosophy","degree_level":"Doctoral Thesis","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Pushnitski, Alexander","Shargorodsky, Eugene","Safarov, Yuri"],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013-6","date_published":"2013-6","updated_at":"2026-07-24T02:44:34Z","subjects":[],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["oai:kclpure.kcl.ac.uk:studenttheses/541fc908-ff77-4f0f-b3ba-af1fe53e19dd"],"render_values":[{"text":"oai:kclpure.kcl.ac.uk:studenttheses/541fc908-ff77-4f0f-b3ba-af1fe53e19dd","href":null,"code":true}]}]},"links":{"outbound_url":"https://kclpure.kcl.ac.uk/portal/en/studentTheses/541fc908-ff77-4f0f-b3ba-af1fe53e19dd","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Pushnitski, Alexander","Shargorodsky, Eugene","Safarov, Yuri"]},{"key":"dc:creator","label":"Author","values":["Bulger, Daniel"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2013-6"]},{"key":"dc:date.issued","label":"Date","values":["2013-6"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Mathematics"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["King's College London"]},{"key":"dc:relation.isreferencedby","label":"Dc Relation Isreferencedby","values":["https://kclpure.kcl.ac.uk/portal/en/studentTheses/541fc908-ff77-4f0f-b3ba-af1fe53e19dd"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Doctoral Thesis"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["Doctor of Philosophy"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["oai:kclpure.kcl.ac.uk:studenttheses/541fc908-ff77-4f0f-b3ba-af1fe53e19dd","https://kclpure.kcl.ac.uk/portal/en/studentTheses/541fc908-ff77-4f0f-b3ba-af1fe53e19dd"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://kclpure.kcl.ac.uk/portal/files/12503142/Studentthesis-Daniel_Bulger_2013.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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/>"]},{"key":"dc:title","label":"Title","values":["The high energy asymptotic distribution of the eigenvalues of the scattering matrix"]}]}],"canonical_facts":{"dc:contributor.advisor":["Pushnitski, Alexander","Shargorodsky, Eugene","Safarov, Yuri"],"dc:creator":["Bulger, Daniel"],"dc:date":["2013-6"],"dc:date.issued":["2013-6"],"dc:description.abstract":["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/>"],"dc:identifier":["oai:kclpure.kcl.ac.uk:studenttheses/541fc908-ff77-4f0f-b3ba-af1fe53e19dd","https://kclpure.kcl.ac.uk/portal/en/studentTheses/541fc908-ff77-4f0f-b3ba-af1fe53e19dd"],"dc:identifier.uri":["https://kclpure.kcl.ac.uk/portal/files/12503142/Studentthesis-Daniel_Bulger_2013.pdf"],"dc:language":["eng"],"dc:publisher.department":["Mathematics"],"dc:publisher.institution":["King's College London"],"dc:relation.isreferencedby":["https://kclpure.kcl.ac.uk/portal/en/studentTheses/541fc908-ff77-4f0f-b3ba-af1fe53e19dd"],"dc:title":["The high energy asymptotic distribution of the eigenvalues of the scattering matrix"],"dc:type":["Thesis"],"dc:type.qualificationlevel":["Doctoral Thesis"],"dc:type.qualificationname":["Doctor of Philosophy"]},"updated_at":"2026-07-24T02:44:34Z"}