Publication:
Renormalization of multi-delta-function point scatterers in two and three dimensions, the coincidence-limit problem, and its resolution

dc.contributor.coauthorLoran, Farhang
dc.contributor.departmentDepartment of Mathematics
dc.contributor.departmentDepartment of Physics
dc.contributor.kuauthorMostafazadeh, Ali
dc.contributor.schoolcollegeinstituteCollege of Sciences
dc.date.accessioned2024-11-09T12:25:02Z
dc.date.issued2022
dc.description.abstractIn two and three dimensions, the standard treatment of the scattering problem for a multi-delta-function potential, v(r)= n-expressionry sumexpressiontion (N)(n=1)z(n)delta(r-a(n)), leads to divergent terms. Regularization of these terms and renormalization of the coupling constants 3(n) give rise to a finite expression for the scattering amplitude of this potential, but this expression has an important short-coming; in the limit where the centers a(n) of the delta functions coincide, it does not reproduce the formula for the scattering amplitude of a single-delta-function potential, i.e., it seems to have a wrong coincidence limit. We provide a critical assessment of the standard treatment of these potentials and offer a resolution of its coincidence-limit problem. This reveals some previously unnoticed features of this treatment. For example, it turns out that the standard treatment is incapable of determining the dependence of the scattering amplitude on the distances between the centers of the delta functions. This is in sharp contrast to the treatment of this problem offered by a recently proposed dynamical formulation of stationary scattering. For cases where the centers of the delta functions lie on a straight line, this formulation avoids singularities of the standard approach and yields an expression for the scattering amplitude which has the correct coincidence limit.
dc.description.fulltextYES
dc.description.indexedbyWOS
dc.description.indexedbyScopus
dc.description.openaccessYES
dc.description.publisherscopeInternational
dc.description.sponsoredbyTubitakEuTÜBİTAK
dc.description.sponsorshipScientific and Technological Research Council of Turkey (TÜBİTAK)
dc.description.sponsorshipTurkish Academy of Sciences (TÜBA)
dc.description.versionAuthor's final manuscript
dc.description.volume443
dc.identifier.doi10.1016/j.aop.2022.168966
dc.identifier.eissn1096-035X
dc.identifier.embargoNO
dc.identifier.filenameinventorynoIR03841
dc.identifier.issn0003-4916
dc.identifier.quartileQ2
dc.identifier.scopus2-s2.0-85133277082
dc.identifier.urihttps://hdl.handle.net/20.500.14288/1527
dc.identifier.wos827535700008
dc.keywordsScattering
dc.keywordsRenormalization
dc.keywordsPoint scatterer
dc.keywordsLippmann-Schwinger equation
dc.keywordsTransfer matrix
dc.language.isoeng
dc.publisherElsevier
dc.relation.grantno120F061
dc.relation.ispartofAnnals of Physics
dc.relation.urihttp://cdm21054.contentdm.oclc.org/cdm/ref/collection/IR/id/10699
dc.subjectPhysics
dc.titleRenormalization of multi-delta-function point scatterers in two and three dimensions, the coincidence-limit problem, and its resolution
dc.typeJournal Article
dspace.entity.typePublication
local.contributor.kuauthorMostafazadeh, Ali
local.publication.orgunit1College of Sciences
local.publication.orgunit2Department of Physics
local.publication.orgunit2Department of Mathematics
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