{"id":{"repo_id":"must-thes","oai_identifier":"oai:scholarsmine.mst.edu:doctoral_dissertations-2667"},"canonical_url":"https://search.dev.ndltd.org/etd/must-thes/oai:scholarsmine.mst.edu:doctoral_dissertations-2667","repository":{"repo_id":"must-thes","name":"Missouri University of Science and Technology","base_url":"https://scholarsmine.mst.edu/do/oai/"},"display":{"title":"Classical Hamiltonian dynamics of a particle interacting with the vibrational modes of a one-dimensional medium","abstract":"\"The polaron and more generally the basic problem of a particle interacting with the vibrational modes of the local medium are important to a large range of physical processes. The complex behavior and underlying properties of polaron dynamics has been the focus of much research for many years. Since the exact quantum mechanical dynamics of the interacting particle/many-oscillator system remains computationally complex due to the enormous size of the man-body Hilbert space, it is difficult to computationally test perturbative or semi-classical calculations of such fundamental transport quantities as the polaron diffusion constant. This thesis introduces a classical model which incorporates the essential features of a particle coupling to the surrounding vibrational modes. With this simple model it is possible to numerically evaluate the equations of motion allowing detailed examination of the dynamics\"--Abstract, page iv.","abstract_html":""The polaron and more generally the basic problem of a particle interacting with the vibrational modes of the local medium are important to a large range of physical processes. The complex behavior and underlying properties of polaron dynamics has been the focus of much research for many years. Since the exact quantum mechanical dynamics of the interacting particle/many-oscillator system remains computationally complex due to the enormous size of the man-body Hilbert space, it is difficult to computationally test perturbative or semi-classical calculations of such fundamental transport quantities as the polaron diffusion constant. This thesis introduces a classical model which incorporates the essential features of a particle coupling to the surrounding vibrational modes. With this simple model it is possible to numerically evaluate the equations of motion allowing detailed examination of the dynamics"--Abstract, page iv.","abstract_has_math":false,"creators":["Silvius, Alex A."],"institution":"University of Missouri--Rolla","degree_name":"Ph. D. in Physics","degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-02-10T08:00:00Z","date_published":"2016-02-10T08:00:00Z","updated_at":"2026-07-24T03:19:54Z","subjects":["Holstein molecular crystal","Physics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarsmine.mst.edu/doctoral_dissertations/1665","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Silvius, Alex A."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2016-02-10T08:00:00Z"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation - Citation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph. 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Since the exact quantum mechanical dynamics of the interacting particle/many-oscillator system remains computationally complex due to the enormous size of the man-body Hilbert space, it is difficult to computationally test perturbative or semi-classical calculations of such fundamental transport quantities as the polaron diffusion constant. This thesis introduces a classical model which incorporates the essential features of a particle coupling to the surrounding vibrational modes. With this simple model it is possible to numerically evaluate the equations of motion allowing detailed examination of the dynamics\"--Abstract, page iv."]},{"key":"dc:title","label":"Title","values":["Classical Hamiltonian dynamics of a particle interacting with the vibrational modes of a one-dimensional medium"]}]}],"canonical_facts":{"dc:creator":["Silvius, Alex A."],"dc:date.available":["2016-02-10T08:00:00Z"],"dc:description.abstract":["\"The polaron and more generally the basic problem of a particle interacting with the vibrational modes of the local medium are important to a large range of physical processes. The complex behavior and underlying properties of polaron dynamics has been the focus of much research for many years. Since the exact quantum mechanical dynamics of the interacting particle/many-oscillator system remains computationally complex due to the enormous size of the man-body Hilbert space, it is difficult to computationally test perturbative or semi-classical calculations of such fundamental transport quantities as the polaron diffusion constant. This thesis introduces a classical model which incorporates the essential features of a particle coupling to the surrounding vibrational modes. With this simple model it is possible to numerically evaluate the equations of motion allowing detailed examination of the dynamics\"--Abstract, page iv."],"dc:identifier":["https://scholarsmine.mst.edu/doctoral_dissertations/1665"],"dc:subject":["Holstein molecular crystal","Physics"],"dc:title":["Classical Hamiltonian dynamics of a particle interacting with the vibrational modes of a one-dimensional medium"],"dc:type":["Dissertation - Citation"],"thesis:degree_name":["Ph. 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