{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/88132"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/88132","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"A continuum path integral approach to the simulation of a unitary gas","abstract":"This thesis presents an investigation by simulation of a unpolarized fermionic unitary gas system composed of two interacting fermionic species. While these species do not interact amongst themselves, they interact with each other using a pairwise zero-range delta function potential that has been tuned to unitarity i.e.the scattering length $a_{s}=-\\infty$. A path integral Monte Carlo simulation of such a system is performed using an exact novel zero-range, delta function pair propagator which has been tuned to the unitary limit so that essentially all interactions amongst the interacting particles are comprised of s-wave interactions. This tuning in some sense yields the simplest imaginable interacting fermionic system which out to display features that would apply universally to interacting fermionic particles with particular interest within this field of study being in understanding the unitary BCS-BEC crossover. Numerical and ergodic challenges to sampling a divergent approximate path integral are discussed and solutions are proposed, implemented and explored. This thesis represents a step closer to this understanding by investigating this system with this novel propagator in a fixed-node path integral Monte Carlo framework and comparing to earlier work.","abstract_html":"This thesis presents an investigation by simulation of a unpolarized fermionic unitary gas system composed of two interacting fermionic species. While these species do not interact amongst themselves, they interact with each other using a pairwise zero-range delta function potential that has been tuned to unitarity i.e.the scattering length <span class=\"etd-inline-math\">a<sub>s</sub>=-\\infty</span>. A path integral Monte Carlo simulation of such a system is performed using an exact novel zero-range, delta function pair propagator which has been tuned to the unitary limit so that essentially all interactions amongst the interacting particles are comprised of s-wave interactions. This tuning in some sense yields the simplest imaginable interacting fermionic system which out to display features that would apply universally to interacting fermionic particles with particular interest within this field of study being in understanding the unitary BCS-BEC crossover. Numerical and ergodic challenges to sampling a divergent approximate path integral are discussed and solutions are proposed, implemented and explored. This thesis represents a step closer to this understanding by investigating this system with this novel propagator in a fixed-node path integral Monte Carlo framework and comparing to earlier work.","abstract_has_math":true,"creators":["Knapp, Adam Christopher"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Chemical Physics","degree_department":null,"school":null,"contributors":["Ceperley, David M.","Clark, Bryan K","Gruebele, Martin","Phillips, Philip W."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-29T20:49:23Z","date_published":"2015-09-29T20:49:23Z","updated_at":"2026-07-22T22:26:31Z","subjects":["Unitary Fermi Gas","Computational Simulation of Cold Atoms"],"languages":["en"],"rights":["Copyright 2015 Adam Christopher Knapp"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/88132","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Ceperley, David M.","Clark, Bryan K","Gruebele, Martin","Phillips, Philip W."]},{"key":"dc:creator","label":"Author","values":["Knapp, Adam Christopher"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-29T20:49:23Z","2017-09-30T09:15:22Z","2015-08","2015-04-29","2015-8"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"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":["Unitary Fermi Gas","Computational Simulation of Cold Atoms"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2015 Adam Christopher Knapp"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/88132"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["This thesis presents an investigation by simulation of a unpolarized fermionic unitary gas system composed of two interacting fermionic species. While these species do not interact amongst themselves, they interact with each other using a pairwise zero-range delta function potential that has been tuned to unitarity i.e.the scattering length $a_{s}=-\\infty$. A path integral Monte Carlo simulation of such a system is performed using an exact novel zero-range, delta function pair propagator which has been tuned to the unitary limit so that essentially all interactions amongst the interacting particles are comprised of s-wave interactions. This tuning in some sense yields the simplest imaginable interacting fermionic system which out to display features that would apply universally to interacting fermionic particles with particular interest within this field of study being in understanding the unitary BCS-BEC crossover. Numerical and ergodic challenges to sampling a divergent approximate path integral are discussed and solutions are proposed, implemented and explored. This thesis represents a step closer to this understanding by investigating this system with this novel propagator in a fixed-node path integral Monte Carlo framework and comparing to earlier work.","Submission published under a 24 month embargo labeled 'U of I only', the embargo will last until 2017-08-01","The student, Adam Knapp, accepted the attached license on 2015-04-28 at 22:24.","The student, Adam Knapp, submitted this Dissertation for approval on 2015-04-28 at 22:30.","This Dissertation was approved for publication on 2015-04-29 at 16:12.","DSpace SAF Submission Ingestion Package generated from Vireo submission #8172 on 2015-09-29 at 14:58:24","Made available in DSpace on 2015-09-29T20:49:23Z (GMT). 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While these species do not interact amongst themselves, they interact with each other using a pairwise zero-range delta function potential that has been tuned to unitarity i.e.the scattering length $a_{s}=-\\infty$. A path integral Monte Carlo simulation of such a system is performed using an exact novel zero-range, delta function pair propagator which has been tuned to the unitary limit so that essentially all interactions amongst the interacting particles are comprised of s-wave interactions. This tuning in some sense yields the simplest imaginable interacting fermionic system which out to display features that would apply universally to interacting fermionic particles with particular interest within this field of study being in understanding the unitary BCS-BEC crossover. Numerical and ergodic challenges to sampling a divergent approximate path integral are discussed and solutions are proposed, implemented and explored. This thesis represents a step closer to this understanding by investigating this system with this novel propagator in a fixed-node path integral Monte Carlo framework and comparing to earlier work.","Submission published under a 24 month embargo labeled 'U of I only', the embargo will last until 2017-08-01","The student, Adam Knapp, accepted the attached license on 2015-04-28 at 22:24.","The student, Adam Knapp, submitted this Dissertation for approval on 2015-04-28 at 22:30.","This Dissertation was approved for publication on 2015-04-29 at 16:12.","DSpace SAF Submission Ingestion Package generated from Vireo submission #8172 on 2015-09-29 at 14:58:24","Made available in DSpace on 2015-09-29T20:49:23Z (GMT). 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