{"id":{"repo_id":"waikato-masters","oai_identifier":"oai:researchcommons.waikato.ac.nz:10289/17627"},"canonical_url":"https://search.dev.ndltd.org/etd/waikato-masters/oai:researchcommons.waikato.ac.nz:10289/17627","repository":{"repo_id":"waikato-masters","name":"University Waikato","base_url":"https://researchcommons.waikato.ac.nz/server/oai/request"},"display":{"title":"A master equation approach to nonlinear optics and chemical reactions","abstract":"Part 1 of this thesis consists of a theoretical quantum statistical analysis of several nonlinear optical processes. As an introduction a master equation describing the time behaviour of the field in a general irreversible nonlinear interaction between an optical photon field and a number of two level atoms is given. This master equation is then used to calculate the exact time dependent statistical properties of the light fields in certain special processes: two photon emission by atoms, two photon absorption by atoms and Raman scattering of photons by atoms. The steady states of the emission-absorption processes are examined, and found to have interesting statistical properties not found in the field states normally met with. Part 1 is concluded with a brief examination of approximate methods of solutions for the nonlinear processes studied. Part 2 is a brief study of the nature of concentration fluctuations and correlations in chemically reacting systems, using the stochastic master equation approach. The time dependent fluctuations and spatial correlations are discussed for a space dependent model of a linear chemically reacting system. These results are compared with those obtained when correlations are ignored. The steady state behaviour of a particular nonlinear chemical system is then examined. Deterministic and non space-dependent stochastic analysis show that when certain system parameters are varied, the system’s behaviour is very similar to that of a thermodynamic system which undergoes a second order phase transition. A space-dependent analysis is then given, and this makes the analogy very close indeed.","abstract_html":"Part 1 of this thesis consists of a theoretical quantum statistical analysis of several nonlinear optical processes. As an introduction a master equation describing the time behaviour of the field in a general irreversible nonlinear interaction between an optical photon field and a number of two level atoms is given. This master equation is then used to calculate the exact time dependent statistical properties of the light fields in certain special processes: two photon emission by atoms, two photon absorption by atoms and Raman scattering of photons by atoms. The steady states of the emission-absorption processes are examined, and found to have interesting statistical properties not found in the field states normally met with. Part 1 is concluded with a brief examination of approximate methods of solutions for the nonlinear processes studied. Part 2 is a brief study of the nature of concentration fluctuations and correlations in chemically reacting systems, using the stochastic master equation approach. The time dependent fluctuations and spatial correlations are discussed for a space dependent model of a linear chemically reacting system. These results are compared with those obtained when correlations are ignored. The steady state behaviour of a particular nonlinear chemical system is then examined. Deterministic and non space-dependent stochastic analysis show that when certain system parameters are varied, the system’s behaviour is very similar to that of a thermodynamic system which undergoes a second order phase transition. A space-dependent analysis is then given, and this makes the analogy very close indeed.","abstract_has_math":false,"creators":["McNeil, Kenneth James"],"institution":"The University of Waikato","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Walls, D.F.","Gardiner, Crispin"],"committee_chairs":[],"committee_members":[],"year":1976,"date_issued":"1976","date_published":"1976","updated_at":"2026-07-24T05:57:41Z","subjects":[],"languages":[],"rights":["All items in Research Commons are provided for private study and research purposes and are protected by copyright with all rights reserved unless otherwise indicated."],"rights_urls":["https://researchcommons.waikato.ac.nz/bitstreams/fd46dd8a-9545-484f-8cd5-3679f2b5b725/download"],"identifier_entries":[]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Walls, D.F.","Gardiner, Crispin"]},{"key":"dc:creator","label":"Author","values":["McNeil, Kenneth James"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["1976"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["The University of Waikato"]},{"key":"dc:relation.isreferencedby","label":"Dc Relation Isreferencedby","values":["https://hdl.handle.net/10289/17627"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["https://researchcommons.waikato.ac.nz/bitstreams/fd46dd8a-9545-484f-8cd5-3679f2b5b725/download","All items in Research Commons are provided for private study and research purposes and are protected by copyright with all rights reserved unless otherwise indicated."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://researchcommons.waikato.ac.nz/bitstreams/07b1cefe-b7c8-40c6-9fce-47e2163d2aa3/download"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Part 1 of this thesis consists of a theoretical quantum statistical analysis of several nonlinear optical processes. As an introduction a master equation describing the time behaviour of the field in a general irreversible nonlinear interaction between an optical photon field and a number of two level atoms is given. This master equation is then used to calculate the exact time dependent statistical properties of the light fields in certain special processes: two photon emission by atoms, two photon absorption by atoms and Raman scattering of photons by atoms. The steady states of the emission-absorption processes are examined, and found to have interesting statistical properties not found in the field states normally met with. Part 1 is concluded with a brief examination of approximate methods of solutions for the nonlinear processes studied. Part 2 is a brief study of the nature of concentration fluctuations and correlations in chemically reacting systems, using the stochastic master equation approach. The time dependent fluctuations and spatial correlations are discussed for a space dependent model of a linear chemically reacting system. These results are compared with those obtained when correlations are ignored. The steady state behaviour of a particular nonlinear chemical system is then examined. Deterministic and non space-dependent stochastic analysis show that when certain system parameters are varied, the system’s behaviour is very similar to that of a thermodynamic system which undergoes a second order phase transition. A space-dependent analysis is then given, and this makes the analogy very close indeed."]},{"key":"dc:format.checksum.md5","label":"Dc Format Checksum Md5","values":["83aa581733b806ee072c9533ecd9de20","e14202ab27e47ddb00d33097327ba050","49ed755ab7818c875a6c8bfca336639d"]},{"key":"dc:title","label":"Title","values":["A master equation approach to nonlinear optics and chemical reactions"]}]}],"canonical_facts":{"dc:contributor.advisor":["Walls, D.F.","Gardiner, Crispin"],"dc:creator":["McNeil, Kenneth James"],"dc:date.issued":["1976"],"dc:description.abstract":["Part 1 of this thesis consists of a theoretical quantum statistical analysis of several nonlinear optical processes. As an introduction a master equation describing the time behaviour of the field in a general irreversible nonlinear interaction between an optical photon field and a number of two level atoms is given. This master equation is then used to calculate the exact time dependent statistical properties of the light fields in certain special processes: two photon emission by atoms, two photon absorption by atoms and Raman scattering of photons by atoms. The steady states of the emission-absorption processes are examined, and found to have interesting statistical properties not found in the field states normally met with. Part 1 is concluded with a brief examination of approximate methods of solutions for the nonlinear processes studied. Part 2 is a brief study of the nature of concentration fluctuations and correlations in chemically reacting systems, using the stochastic master equation approach. The time dependent fluctuations and spatial correlations are discussed for a space dependent model of a linear chemically reacting system. These results are compared with those obtained when correlations are ignored. The steady state behaviour of a particular nonlinear chemical system is then examined. Deterministic and non space-dependent stochastic analysis show that when certain system parameters are varied, the system’s behaviour is very similar to that of a thermodynamic system which undergoes a second order phase transition. A space-dependent analysis is then given, and this makes the analogy very close indeed."],"dc:format.checksum.md5":["83aa581733b806ee072c9533ecd9de20","e14202ab27e47ddb00d33097327ba050","49ed755ab7818c875a6c8bfca336639d"],"dc:identifier.uri":["https://researchcommons.waikato.ac.nz/bitstreams/07b1cefe-b7c8-40c6-9fce-47e2163d2aa3/download"],"dc:publisher.institution":["The University of Waikato"],"dc:relation.isreferencedby":["https://hdl.handle.net/10289/17627"],"dc:rights":["https://researchcommons.waikato.ac.nz/bitstreams/fd46dd8a-9545-484f-8cd5-3679f2b5b725/download","All items in Research Commons are provided for private study and research purposes and are protected by copyright with all rights reserved unless otherwise indicated."],"dc:title":["A master equation approach to nonlinear optics and chemical reactions"],"dc:type":["Thesis"]},"updated_at":"2026-07-24T05:57:41Z"}