{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/16094"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/16094","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Theoretical methods for the study of quantum dynamics","abstract":"Several theoretical methods for the computation of quantum dynamical quantities are formulated, implemented, and applied, in the overall context of overcoming the exponential scaling property of quantum mechanics. The convergence of the approximate forward-backward semiclassical dynamics (FBSD) method has been accelerated by working with only the imaginary part of the real-time position and momentum time correlation functions. Simple manipulations allow the computationally favorable limit of a single factorization (“bead”) of the Boltzmann operator to yield greatly improved results. Numerical examples for a one-dimensional anharmonic oscillator and Lennard-Jones fluids are presented. Bohm's trajectory formulation of quantum mechanics is an exact mapping of the time-dependent Schrödinger equation onto classical fluid dynamics, plus one extra term responsible for all non-classical effects, the dreaded quantum potential. A computational procedure has been introduced to stably solve Bohm’s hydrodynamic equations of motion in the forward-backward quantum dynamics (FBQD) formulation of time correlation functions, and applied to one-dimensional bound systems at zero and low temperature. A key step in the formulation of this procedure was the use of Hamilton's law of varying action, a generalization of Hamilton’s principle of stationary action applicable to initial-value problems. This has resulted in the first reported synthetic computation of non-stationary quantum trajectories for a fully anharmonic oscillator. Success in one dimension has laid the groundwork for future extension to a rigorous quantum-classical scheme, which is briefly discussed. Other unpublished methods for obtaining time correlation functions and propagators in quantum dynamics are also discussed.","abstract_html":"Several theoretical methods for the computation of quantum dynamical quantities are formulated, implemented, and applied, in the overall context of overcoming the exponential scaling property of quantum mechanics. The convergence of the approximate forward-backward semiclassical dynamics (FBSD) method has been accelerated by working with only the imaginary part of the real-time position and momentum time correlation functions. Simple manipulations allow the computationally favorable limit of a single factorization (“bead”) of the Boltzmann operator to yield greatly improved results. Numerical examples for a one-dimensional anharmonic oscillator and Lennard-Jones fluids are presented. Bohm's trajectory formulation of quantum mechanics is an exact mapping of the time-dependent Schrödinger equation onto classical fluid dynamics, plus one extra term responsible for all non-classical effects, the dreaded quantum potential. A computational procedure has been introduced to stably solve Bohm’s hydrodynamic equations of motion in the forward-backward quantum dynamics (FBQD) formulation of time correlation functions, and applied to one-dimensional bound systems at zero and low temperature. A key step in the formulation of this procedure was the use of Hamilton's law of varying action, a generalization of Hamilton’s principle of stationary action applicable to initial-value problems. This has resulted in the first reported synthetic computation of non-stationary quantum trajectories for a fully anharmonic oscillator. Success in one dimension has laid the groundwork for future extension to a rigorous quantum-classical scheme, which is briefly discussed. Other unpublished methods for obtaining time correlation functions and propagators in quantum dynamics are also discussed.","abstract_has_math":false,"creators":["Chen, Jonathan E."],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Chemical Physics","degree_department":null,"school":null,"contributors":["Makri, Nancy","Luthey-Schulten, Zaida A.","Bond, Stephen","Vishveshwara, Smitha"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2010,"date_issued":"2010-05-19T18:34:42Z","date_published":"2010-05-19T18:34:42Z","updated_at":"2026-07-22T22:25:08Z","subjects":["quantum dynamics","correlation functions","semiclassical approximation","quantum trajectories","Bohmian trajectories","Monte Carlo","forward-backward semiclassical dynamics","forward-backward quantum dynamics","sign problem","Hamilton's law of varying action"],"languages":["en"],"rights":["Copyright 2010 Jonathan E. Chen"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/16094","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Makri, Nancy","Luthey-Schulten, Zaida A.","Bond, Stephen","Vishveshwara, Smitha"]},{"key":"dc:creator","label":"Author","values":["Chen, Jonathan E."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2010-05-19T18:34:42Z","2010-5"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Chemical Physics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["quantum dynamics","correlation functions","semiclassical approximation","quantum trajectories","Bohmian trajectories","Monte Carlo","forward-backward semiclassical dynamics","forward-backward quantum dynamics","sign problem","Hamilton's law of varying action"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2010 Jonathan E. Chen"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/16094"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Several theoretical methods for the computation of quantum dynamical quantities are formulated, implemented, and applied, in the overall context of overcoming the exponential scaling property of quantum mechanics. The convergence of the approximate forward-backward semiclassical dynamics (FBSD) method has been accelerated by working with only the imaginary part of the real-time position and momentum time correlation functions. Simple manipulations allow the computationally favorable limit of a single factorization (“bead”) of the Boltzmann operator to yield greatly improved results. Numerical examples for a one-dimensional anharmonic oscillator and Lennard-Jones fluids are presented. Bohm's trajectory formulation of quantum mechanics is an exact mapping of the time-dependent Schrödinger equation onto classical fluid dynamics, plus one extra term responsible for all non-classical effects, the dreaded quantum potential. A computational procedure has been introduced to stably solve Bohm’s hydrodynamic equations of motion in the forward-backward quantum dynamics (FBQD) formulation of time correlation functions, and applied to one-dimensional bound systems at zero and low temperature. A key step in the formulation of this procedure was the use of Hamilton's law of varying action, a generalization of Hamilton’s principle of stationary action applicable to initial-value problems. This has resulted in the first reported synthetic computation of non-stationary quantum trajectories for a fully anharmonic oscillator. Success in one dimension has laid the groundwork for future extension to a rigorous quantum-classical scheme, which is briefly discussed. Other unpublished methods for obtaining time correlation functions and propagators in quantum dynamics are also discussed.","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2010-04-16T21:17:47Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 19 0a-Title.doc: 199168 bytes, checksum: 4337515b7d716d897bcad858941fa6f2 (MD5) 0b-Abstract.doc: 247296 bytes, checksum: c58727169be6850d498a6cba37aa823a (MD5) 0c-Front Matter.doc: 251392 bytes, checksum: bb7bc08cee087a18486c86eff742f267 (MD5) 1-background.doc: 784896 bytes, checksum: db3d710b2ba6d29e654f8a0012913155 (MD5) 2-fbsd.doc: 2568192 bytes, checksum: 16a2759fdfffc74411ee8b1dd229220d (MD5) 3-bohm1.doc: 2382848 bytes, checksum: 7be91f17beb5b238ad480df2e4c73c03 (MD5) 4-bohm1imag.doc: 1423360 bytes, checksum: 1cedfcf934fadde2269049db8d21f24f (MD5) 5-bohm2.doc: 2737152 bytes, checksum: 34926bbb02cda44d722e6ceed225a4f8 (MD5) C-bohm1_appendix.doc: 1356800 bytes, checksum: 080b31284a87781cffb17d2599166c09 (MD5) D-bohm1imag_appendix.doc: 837632 bytes, checksum: 76fbbae636056df4215644f3c5418f2d (MD5) E-bohm2_appendix.doc: 1492992 bytes, checksum: c583a31d684f66dca7b047e364b8f9bd (MD5) F-other_appendix.doc: 1552896 bytes, checksum: 82bf230ab12bf71bcc80e97c6d6a4829 (MD5) X-algorithms.doc: 569856 bytes, checksum: 53667431db98b87eb7763638d04ffc37 (MD5) thesis.doc: 621568 bytes, checksum: 3a69ffd01c3b9d46f2e0f41d36a5d657 (MD5) 6-other.doc: 13521920 bytes, checksum: 01bb39d38944d6febe40c1ff64243a0d (MD5) A-background_appendix.doc: 1235968 bytes, checksum: 21f7a4a0b70a2c0d8ce2046e5784ec54 (MD5) B-fbsd_appendix.doc: 1393152 bytes, checksum: f30f40e27c9393272105364beaf8078a (MD5) Chen_Jonathan.pdf: 3497296 bytes, checksum: cc073f42b710a8b71c33a05e6b74a2ac (MD5) source.zip: 1072788 bytes, checksum: 9d01bfbd83430008e0f4961137f429db (MD5)","Made available in DSpace on 2010-05-19T18:34:42Z (GMT). No. of bitstreams: 21 Chen_Jonathan.pdf: 3497296 bytes, checksum: cc073f42b710a8b71c33a05e6b74a2ac (MD5) thesis.doc: 621568 bytes, checksum: 3a69ffd01c3b9d46f2e0f41d36a5d657 (MD5) X-algorithms.doc: 569856 bytes, checksum: 53667431db98b87eb7763638d04ffc37 (MD5) F-other_appendix.doc: 1552896 bytes, checksum: 82bf230ab12bf71bcc80e97c6d6a4829 (MD5) E-bohm2_appendix.doc: 1492992 bytes, checksum: c583a31d684f66dca7b047e364b8f9bd (MD5) D-bohm1imag_appendix.doc: 837632 bytes, checksum: 76fbbae636056df4215644f3c5418f2d (MD5) C-bohm1_appendix.doc: 1356800 bytes, checksum: 080b31284a87781cffb17d2599166c09 (MD5) B-fbsd_appendix.doc: 1393152 bytes, checksum: f30f40e27c9393272105364beaf8078a (MD5) A-background_appendix.doc: 1235968 bytes, checksum: 21f7a4a0b70a2c0d8ce2046e5784ec54 (MD5) 6-other.doc: 13521920 bytes, checksum: 01bb39d38944d6febe40c1ff64243a0d (MD5) 5-bohm2.doc: 2737152 bytes, checksum: 34926bbb02cda44d722e6ceed225a4f8 (MD5) 4-bohm1imag.doc: 1423360 bytes, checksum: 1cedfcf934fadde2269049db8d21f24f (MD5) 3-bohm1.doc: 2382848 bytes, checksum: 7be91f17beb5b238ad480df2e4c73c03 (MD5) 2-fbsd.doc: 2568192 bytes, checksum: 16a2759fdfffc74411ee8b1dd229220d (MD5) 1-background.doc: 784896 bytes, checksum: db3d710b2ba6d29e654f8a0012913155 (MD5) 0c-Front Matter.doc: 251392 bytes, checksum: bb7bc08cee087a18486c86eff742f267 (MD5) 0b-Abstract.doc: 247296 bytes, checksum: c58727169be6850d498a6cba37aa823a (MD5) 0a-Title.doc: 199168 bytes, checksum: 4337515b7d716d897bcad858941fa6f2 (MD5) 1_Chen_Jonathan.pdf: 3301625 bytes, checksum: 67203cd40f1f4209aaef4c97eccc1b73 (MD5) source.zip: 1072788 bytes, checksum: 9d01bfbd83430008e0f4961137f429db (MD5) license.txt: 4062 bytes, checksum: 5784258eb32e563874a2feb3193de02c (MD5)"]},{"key":"dc:title","label":"Title","values":["Theoretical methods for the study of quantum dynamics"]}]}],"canonical_facts":{"dc:contributor":["Makri, Nancy","Luthey-Schulten, Zaida A.","Bond, Stephen","Vishveshwara, Smitha"],"dc:creator":["Chen, Jonathan E."],"dc:date":["2010-05-19T18:34:42Z","2010-5"],"dc:description":["Several theoretical methods for the computation of quantum dynamical quantities are formulated, implemented, and applied, in the overall context of overcoming the exponential scaling property of quantum mechanics. The convergence of the approximate forward-backward semiclassical dynamics (FBSD) method has been accelerated by working with only the imaginary part of the real-time position and momentum time correlation functions. Simple manipulations allow the computationally favorable limit of a single factorization (“bead”) of the Boltzmann operator to yield greatly improved results. Numerical examples for a one-dimensional anharmonic oscillator and Lennard-Jones fluids are presented. Bohm's trajectory formulation of quantum mechanics is an exact mapping of the time-dependent Schrödinger equation onto classical fluid dynamics, plus one extra term responsible for all non-classical effects, the dreaded quantum potential. A computational procedure has been introduced to stably solve Bohm’s hydrodynamic equations of motion in the forward-backward quantum dynamics (FBQD) formulation of time correlation functions, and applied to one-dimensional bound systems at zero and low temperature. A key step in the formulation of this procedure was the use of Hamilton's law of varying action, a generalization of Hamilton’s principle of stationary action applicable to initial-value problems. This has resulted in the first reported synthetic computation of non-stationary quantum trajectories for a fully anharmonic oscillator. Success in one dimension has laid the groundwork for future extension to a rigorous quantum-classical scheme, which is briefly discussed. Other unpublished methods for obtaining time correlation functions and propagators in quantum dynamics are also discussed.","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2010-04-16T21:17:47Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 19 0a-Title.doc: 199168 bytes, checksum: 4337515b7d716d897bcad858941fa6f2 (MD5) 0b-Abstract.doc: 247296 bytes, checksum: c58727169be6850d498a6cba37aa823a (MD5) 0c-Front Matter.doc: 251392 bytes, checksum: bb7bc08cee087a18486c86eff742f267 (MD5) 1-background.doc: 784896 bytes, checksum: db3d710b2ba6d29e654f8a0012913155 (MD5) 2-fbsd.doc: 2568192 bytes, checksum: 16a2759fdfffc74411ee8b1dd229220d (MD5) 3-bohm1.doc: 2382848 bytes, checksum: 7be91f17beb5b238ad480df2e4c73c03 (MD5) 4-bohm1imag.doc: 1423360 bytes, checksum: 1cedfcf934fadde2269049db8d21f24f (MD5) 5-bohm2.doc: 2737152 bytes, checksum: 34926bbb02cda44d722e6ceed225a4f8 (MD5) C-bohm1_appendix.doc: 1356800 bytes, checksum: 080b31284a87781cffb17d2599166c09 (MD5) D-bohm1imag_appendix.doc: 837632 bytes, checksum: 76fbbae636056df4215644f3c5418f2d (MD5) E-bohm2_appendix.doc: 1492992 bytes, checksum: c583a31d684f66dca7b047e364b8f9bd (MD5) F-other_appendix.doc: 1552896 bytes, checksum: 82bf230ab12bf71bcc80e97c6d6a4829 (MD5) X-algorithms.doc: 569856 bytes, checksum: 53667431db98b87eb7763638d04ffc37 (MD5) thesis.doc: 621568 bytes, checksum: 3a69ffd01c3b9d46f2e0f41d36a5d657 (MD5) 6-other.doc: 13521920 bytes, checksum: 01bb39d38944d6febe40c1ff64243a0d (MD5) A-background_appendix.doc: 1235968 bytes, checksum: 21f7a4a0b70a2c0d8ce2046e5784ec54 (MD5) B-fbsd_appendix.doc: 1393152 bytes, checksum: f30f40e27c9393272105364beaf8078a (MD5) Chen_Jonathan.pdf: 3497296 bytes, checksum: cc073f42b710a8b71c33a05e6b74a2ac (MD5) source.zip: 1072788 bytes, checksum: 9d01bfbd83430008e0f4961137f429db (MD5)","Made available in DSpace on 2010-05-19T18:34:42Z (GMT). No. of bitstreams: 21 Chen_Jonathan.pdf: 3497296 bytes, checksum: cc073f42b710a8b71c33a05e6b74a2ac (MD5) thesis.doc: 621568 bytes, checksum: 3a69ffd01c3b9d46f2e0f41d36a5d657 (MD5) X-algorithms.doc: 569856 bytes, checksum: 53667431db98b87eb7763638d04ffc37 (MD5) F-other_appendix.doc: 1552896 bytes, checksum: 82bf230ab12bf71bcc80e97c6d6a4829 (MD5) E-bohm2_appendix.doc: 1492992 bytes, checksum: c583a31d684f66dca7b047e364b8f9bd (MD5) D-bohm1imag_appendix.doc: 837632 bytes, checksum: 76fbbae636056df4215644f3c5418f2d (MD5) C-bohm1_appendix.doc: 1356800 bytes, checksum: 080b31284a87781cffb17d2599166c09 (MD5) B-fbsd_appendix.doc: 1393152 bytes, checksum: f30f40e27c9393272105364beaf8078a (MD5) A-background_appendix.doc: 1235968 bytes, checksum: 21f7a4a0b70a2c0d8ce2046e5784ec54 (MD5) 6-other.doc: 13521920 bytes, checksum: 01bb39d38944d6febe40c1ff64243a0d (MD5) 5-bohm2.doc: 2737152 bytes, checksum: 34926bbb02cda44d722e6ceed225a4f8 (MD5) 4-bohm1imag.doc: 1423360 bytes, checksum: 1cedfcf934fadde2269049db8d21f24f (MD5) 3-bohm1.doc: 2382848 bytes, checksum: 7be91f17beb5b238ad480df2e4c73c03 (MD5) 2-fbsd.doc: 2568192 bytes, checksum: 16a2759fdfffc74411ee8b1dd229220d (MD5) 1-background.doc: 784896 bytes, checksum: db3d710b2ba6d29e654f8a0012913155 (MD5) 0c-Front Matter.doc: 251392 bytes, checksum: bb7bc08cee087a18486c86eff742f267 (MD5) 0b-Abstract.doc: 247296 bytes, checksum: c58727169be6850d498a6cba37aa823a (MD5) 0a-Title.doc: 199168 bytes, checksum: 4337515b7d716d897bcad858941fa6f2 (MD5) 1_Chen_Jonathan.pdf: 3301625 bytes, checksum: 67203cd40f1f4209aaef4c97eccc1b73 (MD5) source.zip: 1072788 bytes, checksum: 9d01bfbd83430008e0f4961137f429db (MD5) license.txt: 4062 bytes, checksum: 5784258eb32e563874a2feb3193de02c (MD5)"],"dc:identifier":["http://hdl.handle.net/2142/16094"],"dc:language":["en"],"dc:rights":["Copyright 2010 Jonathan E. Chen"],"dc:subject":["quantum dynamics","correlation functions","semiclassical approximation","quantum trajectories","Bohmian trajectories","Monte Carlo","forward-backward semiclassical dynamics","forward-backward quantum dynamics","sign problem","Hamilton's law of varying action"],"dc:title":["Theoretical methods for the study of quantum dynamics"],"thesis:degree_discipline":["Chemical Physics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:08Z"}