{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/33761"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/33761","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Quantum monte carlo with a stochastic potential solver","abstract":"\"Quantum Monte Carlo (QMC) is an extremely powerful method to treat many-body systems. Usually QMC has been applied in cases where the interaction potential has a simple analytic form, like the 1=r Coulomb potential. However, in a complicated environment as in a semiconductor heterostructure, the evaluation of the interaction itself becomes a non-trivial problem. Obtaining the potential from any grid-based finite-difference method, for every walker and every step is unfeasible. We demonstrate an alternative approach of solving the Poisson equation by a classical Monte Carlo within the overall QMC scheme. We have developed a modi ed \\Walk On Spheres\"\"(WOS) algorithm using Green's function techniques, which can effciently account for the interaction energy of walker configurations, typical of QMC algorithms. This stochastically obtained potential can be easily incorporated within popular QMC techniques like variational Monte Carlo (VMC) or diffusion Monte Carlo (DMC). We demonstrate the validity of this method by studying a simple problem, the polarization of a helium atom in the electric field of an infinite capacitor. Then we apply this method to calculate the singlet-triplet splitting in a realistic heterostructure device. We also outline some other prospective applications for spherical quantum dots where the dielectric mismatch becomes an important issue for the addition energy spectrum.\"","abstract_html":""Quantum Monte Carlo (QMC) is an extremely powerful method to treat many-body systems. Usually QMC has been applied in cases where the interaction potential has a simple analytic form, like the 1=r Coulomb potential. However, in a complicated environment as in a semiconductor heterostructure, the evaluation of the interaction itself becomes a non-trivial problem. Obtaining the potential from any grid-based finite-difference method, for every walker and every step is unfeasible. We demonstrate an alternative approach of solving the Poisson equation by a classical Monte Carlo within the overall QMC scheme. We have developed a modi ed \\Walk On Spheres""(WOS) algorithm using Green's function techniques, which can effciently account for the interaction energy of walker configurations, typical of QMC algorithms. This stochastically obtained potential can be easily incorporated within popular QMC techniques like variational Monte Carlo (VMC) or diffusion Monte Carlo (DMC). We demonstrate the validity of this method by studying a simple problem, the polarization of a helium atom in the electric field of an infinite capacitor. Then we apply this method to calculate the singlet-triplet splitting in a realistic heterostructure device. We also outline some other prospective applications for spherical quantum dots where the dielectric mismatch becomes an important issue for the addition energy spectrum."","abstract_has_math":false,"creators":["Das, Dyutiman"],"institution":null,"degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Martin, Richard M."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-07-30T22:14:26Z","date_published":"2012-07-30T22:14:26Z","updated_at":"2026-07-22T22:25:30Z","subjects":["Quantum Monte Carlo (QMC)","potential","Algorithm"],"languages":["en"],"rights":["© 2005 Dyutiman Das"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["5188926"],"render_values":[{"text":"5188926","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/33761","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Martin, Richard M."]},{"key":"dc:creator","label":"Author","values":["Das, Dyutiman"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2012-07-30T22:14:26Z","10000-01-01","2005"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation / Thesis","text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Physics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Quantum Monte Carlo (QMC)","potential","Algorithm"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["© 2005 Dyutiman Das"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["5188926","http://hdl.handle.net/2142/33761"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["\"Quantum Monte Carlo (QMC) is an extremely powerful method to treat many-body systems. Usually QMC has been applied in cases where the interaction potential has a simple analytic form, like the 1=r Coulomb potential. However, in a complicated environment as in a semiconductor heterostructure, the evaluation of the interaction itself becomes a non-trivial problem. Obtaining the potential from any grid-based finite-difference method, for every walker and every step is unfeasible. We demonstrate an alternative approach of solving the Poisson equation by a classical Monte Carlo within the overall QMC scheme. We have developed a modi ed \\Walk On Spheres\"\"(WOS) algorithm using Green's function techniques, which can effciently account for the interaction energy of walker configurations, typical of QMC algorithms. This stochastically obtained potential can be easily incorporated within popular QMC techniques like variational Monte Carlo (VMC) or diffusion Monte Carlo (DMC). We demonstrate the validity of this method by studying a simple problem, the polarization of a helium atom in the electric field of an infinite capacitor. Then we apply this method to calculate the singlet-triplet splitting in a realistic heterostructure device. We also outline some other prospective applications for spherical quantum dots where the dielectric mismatch becomes an important issue for the addition energy spectrum.\"","Submitted by Megan O'Donnell (mnodonn2@illinois.edu) on 2012-07-30T22:14:26Z No. of bitstreams: 1 2005_Das_Dyutiman.pdf: 767664 bytes, checksum: 2af5f2246730939f607c0348dc5c5e0e (MD5)","Made available in DSpace on 2012-07-30T22:14:26Z (GMT). No. of bitstreams: 1 2005_Das_Dyutiman.pdf: 767664 bytes, checksum: 2af5f2246730939f607c0348dc5c5e0e (MD5) Previous issue date: 2005","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Megan O'Donnell (mnodonn2@illinois.edu) on 2012-07-30T22:14:26Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:35:01-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: dissertation/thesis","dissertation/thesis","U of I Only"]},{"key":"dc:title","label":"Title","values":["Quantum monte carlo with a stochastic potential solver"]}]}],"canonical_facts":{"dc:contributor":["Martin, Richard M."],"dc:creator":["Das, Dyutiman"],"dc:date":["2012-07-30T22:14:26Z","10000-01-01","2005"],"dc:description":["\"Quantum Monte Carlo (QMC) is an extremely powerful method to treat many-body systems. Usually QMC has been applied in cases where the interaction potential has a simple analytic form, like the 1=r Coulomb potential. However, in a complicated environment as in a semiconductor heterostructure, the evaluation of the interaction itself becomes a non-trivial problem. Obtaining the potential from any grid-based finite-difference method, for every walker and every step is unfeasible. We demonstrate an alternative approach of solving the Poisson equation by a classical Monte Carlo within the overall QMC scheme. We have developed a modi ed \\Walk On Spheres\"\"(WOS) algorithm using Green's function techniques, which can effciently account for the interaction energy of walker configurations, typical of QMC algorithms. This stochastically obtained potential can be easily incorporated within popular QMC techniques like variational Monte Carlo (VMC) or diffusion Monte Carlo (DMC). We demonstrate the validity of this method by studying a simple problem, the polarization of a helium atom in the electric field of an infinite capacitor. Then we apply this method to calculate the singlet-triplet splitting in a realistic heterostructure device. We also outline some other prospective applications for spherical quantum dots where the dielectric mismatch becomes an important issue for the addition energy spectrum.\"","Submitted by Megan O'Donnell (mnodonn2@illinois.edu) on 2012-07-30T22:14:26Z No. of bitstreams: 1 2005_Das_Dyutiman.pdf: 767664 bytes, checksum: 2af5f2246730939f607c0348dc5c5e0e (MD5)","Made available in DSpace on 2012-07-30T22:14:26Z (GMT). No. of bitstreams: 1 2005_Das_Dyutiman.pdf: 767664 bytes, checksum: 2af5f2246730939f607c0348dc5c5e0e (MD5) Previous issue date: 2005","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Megan O'Donnell (mnodonn2@illinois.edu) on 2012-07-30T22:14:26Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:35:01-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: dissertation/thesis","dissertation/thesis","U of I Only"],"dc:identifier":["5188926","http://hdl.handle.net/2142/33761"],"dc:language":["en"],"dc:rights":["© 2005 Dyutiman Das"],"dc:subject":["Quantum Monte Carlo (QMC)","potential","Algorithm"],"dc:title":["Quantum monte carlo with a stochastic potential solver"],"dc:type":["Dissertation / Thesis","text"],"thesis:degree_discipline":["Physics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."]},"updated_at":"2026-07-22T22:25:30Z"}