An application of the Liouville resolvent method to the study of fermion-boson couplings

Simple item page
dc.contributor.authorBressler, Barry Leeen
dc.contributor.committeechairBowen, Samuel P.en
dc.contributor.committeememberRoper, L. Daviden
dc.contributor.committeememberWilliams, Clayton D.en
dc.contributor.committeememberZia, K.P.en
dc.contributor.committeememberLee, T.K.en
dc.contributor.departmentPhysicsen
dc.date.accessioned2014-08-13T14:38:58Zen
dc.date.available2014-08-13T14:38:58Zen
dc.date.issued1986en
dc.description.abstractThe Liouville resolvent method is an unconventional technique used for finding a Green function for a Hamiltonian. Implementation of the method entails the calculation of commutators of a second-quantized Hamiltonian operator with particular generalized stepping operators that are elements of a Hilbert space and that represent transitions between many-particle states. These commutators produce linear combinations of stepping operators, so the results can be arrayed as matrix elements of the Liouville operator L̂ in the Hilbert space of stepping operators. The resulting L̂ matrix is usually of infinite order, and in principle its eigenvalues and eigenvectors can be used to construct the Green function from the L̂ resolvent matrix. Approximations are usually necessary, at least in the form of truncation of the L̂ matrix, and if one produces a sequence of such matrices of increasing order and calculates the eigenvalues and eigenvectors of these matrices, a sequence of approximations for the L̂ resolvent matrix can be produced. This sequence is mathematically guaranteed to converge to the exact result for the L̂ resolvent matrix (except at its singularities). The accuracy of an approximation depends on the order of the matrix at which the sequence is truncated. Application of the method to a Hamiltonian representing interactions between fermions and bosons involves complications arising from the large number of terms generated by the commutation properties of boson operators. This dissertation describes the method and its use in the study of fermion-boson couplings. Approximations to second order in stepping operators are calculated for simplified Froehlich and Lee models. Limited thermodynamic results are obtained from the Lee model. Exact energy eigenvalues are obtained by operator algebra for simplified Froehlich, Lee and Dirac models. These exact solutions comprise the main contribution of this research and will prove to be valuable starting points for further research. Suggestions are made for further research.en
dc.description.adminincomplete_metadataen
dc.description.degreePh. D.en
dc.format.extentxviii, 198 leavesen
dc.format.mimetypeapplication/pdfen
dc.identifier.urihttp://hdl.handle.net/10919/49994en
dc.publisherVirginia Polytechnic Institute and State Universityen
dc.relation.isformatofOCLC# 14942697en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.lccLD5655.V856 1986.B737en
dc.subject.lcshGreen's functionsen
dc.subject.lcshHamiltonian operatoren
dc.subject.lcshFermionsen
dc.subject.lcshBosonsen
dc.titleAn application of the Liouville resolvent method to the study of fermion-boson couplingsen
dc.typeDissertationen
dc.type.dcmitypeTexten
thesis.degree.disciplinePhysicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
LD5655.V856_1986.B737.pdf
Size:
4.59 MB
Format:
Adobe Portable Document Format
Description:
Download

Collections

Doctoral Dissertations