{"id":{"repo_id":"buffalo","oai_identifier":"oai:ubir.buffalo.edu:10477/80921"},"canonical_url":"https://search.dev.ndltd.org/etd/buffalo/oai:ubir.buffalo.edu:10477/80921","repository":{"repo_id":"buffalo","name":"Buffalo","base_url":"https://ubir.buffalo.edu/oai/request"},"display":{"title":"Pairing Phenomena from Low-Density Fermi Gases to Neutron Star Matter","abstract":"Ph.D.","abstract_html":"Ph.D.","abstract_has_math":false,"creators":["Fan, Hsuan-Hao; 0000-0002-7428-1349"],"institution":"State University of New York at Buffalo","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Krotscheck, Eckhard","Physics"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2019,"date_issued":"2019-10-29T16:48:10Z","date_published":"2019-10-29T16:48:10Z","updated_at":"2026-07-27T19:05:25Z","subjects":["physics","condensed matter physics"],"languages":["eng"],"rights":["Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions.","Copyright retained by author."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10477/80921","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Krotscheck, Eckhard","Physics"]},{"key":"dc:creator","label":"Author","values":["Fan, Hsuan-Hao; 0000-0002-7428-1349"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2019-10-29T16:48:10Z","2019","2019-08-08 14:48:20"]},{"key":"dc:publisher","label":"Institution","values":["State University of New York at Buffalo"]},{"key":"dc:type","label":"Dc Type","values":["Text","Dissertation"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["physics","condensed matter physics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions.","Copyright retained by author."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/10477/80921"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Ph.D.","We develop the variational theory, called Fermi-Hypernetted Chain-Euler Lagrange (FHNC-EL), for strongly interacting superfluid systems. At the beginning, we review well-developed FHNC-EL theory for normal systems. Then we introduce FHNC-EL theory for superfluids we have developed by considering correlated BCS state. We will then implement this method with weak-coupling approximation and apply it to neutron matter and low density Fermi gases. In neutron matter, we adopt the Reid V6 and the Argonne V4 potentials; in Fermi gases, we consider the Lennard-Jones model interaction and the square-well interaction. In neutron matter, ground-state calculations have been carried out by using the central part of the operator-basis representation of these interactions to determine optimal Jastrow-Feenberg correlations and corresponding effective pairing interactions within the correlated-basis formalism (CBF), the required matrix elements in the correlated basis being evaluated by Fermi hypernetted-chain techniques. Different implementations of the FHNC-EL method agree at the percent level up to nuclear matter saturation density. For the assumed interactions, which are realistic within the low density range involved in 1S0 neutron pairing, we did not find a dimerization instability arising from divergence of the in-medium scattering length. In low-density Fermi gases, we use the optimized FHNC integral equation method which has been proved to provide, in the density regimes of interest here, an accuracy better than one percent. We first examine the low-density expansion of the energy and compare with the exact answer by Huang and Yang (H. Huang and C. N. Yang, Phys. Rev. 105, 767 (1957)). It is shown that a locally correlated wave function of the Jastrow-Feenberg type does not recover the quadratic term in the expansion of the energy in powers of a0kF, where a0 is the vacuum s-wave scattering length and kF the Fermi wave number. The problem is cured by adding second-order perturbation corrections in a correlated basis. Going to higher densities and/or more strongly coupled systems, we encounter an instability of the normal state of the system which is characterized by a divergence of the in-medium scattering length. We interpret this divergence as a phonon-exchange driven dimerization of the system, similar to what one has at zero density when the vacuum scattering length a0 diverges. We then study, in the stable regime, the superfluid gap and its dependence on the density and the interaction strength.","**To request an accessible version of the file(s) associated with this item, contact library@buffalo.edu. Please include the item's persistent URL [http://hdl.handle.net/. . .] in your request.**"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Pairing Phenomena from Low-Density Fermi Gases to Neutron Star Matter"]}]}],"canonical_facts":{"dc:contributor":["Krotscheck, Eckhard","Physics"],"dc:creator":["Fan, Hsuan-Hao; 0000-0002-7428-1349"],"dc:date":["2019-10-29T16:48:10Z","2019","2019-08-08 14:48:20"],"dc:description":["Ph.D.","We develop the variational theory, called Fermi-Hypernetted Chain-Euler Lagrange (FHNC-EL), for strongly interacting superfluid systems. At the beginning, we review well-developed FHNC-EL theory for normal systems. Then we introduce FHNC-EL theory for superfluids we have developed by considering correlated BCS state. We will then implement this method with weak-coupling approximation and apply it to neutron matter and low density Fermi gases. In neutron matter, we adopt the Reid V6 and the Argonne V4 potentials; in Fermi gases, we consider the Lennard-Jones model interaction and the square-well interaction. In neutron matter, ground-state calculations have been carried out by using the central part of the operator-basis representation of these interactions to determine optimal Jastrow-Feenberg correlations and corresponding effective pairing interactions within the correlated-basis formalism (CBF), the required matrix elements in the correlated basis being evaluated by Fermi hypernetted-chain techniques. Different implementations of the FHNC-EL method agree at the percent level up to nuclear matter saturation density. For the assumed interactions, which are realistic within the low density range involved in 1S0 neutron pairing, we did not find a dimerization instability arising from divergence of the in-medium scattering length. In low-density Fermi gases, we use the optimized FHNC integral equation method which has been proved to provide, in the density regimes of interest here, an accuracy better than one percent. We first examine the low-density expansion of the energy and compare with the exact answer by Huang and Yang (H. Huang and C. N. Yang, Phys. Rev. 105, 767 (1957)). It is shown that a locally correlated wave function of the Jastrow-Feenberg type does not recover the quadratic term in the expansion of the energy in powers of a0kF, where a0 is the vacuum s-wave scattering length and kF the Fermi wave number. The problem is cured by adding second-order perturbation corrections in a correlated basis. Going to higher densities and/or more strongly coupled systems, we encounter an instability of the normal state of the system which is characterized by a divergence of the in-medium scattering length. We interpret this divergence as a phonon-exchange driven dimerization of the system, similar to what one has at zero density when the vacuum scattering length a0 diverges. We then study, in the stable regime, the superfluid gap and its dependence on the density and the interaction strength.","**To request an accessible version of the file(s) associated with this item, contact library@buffalo.edu. Please include the item's persistent URL [http://hdl.handle.net/. . .] in your request.**"],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/10477/80921"],"dc:language":["eng"],"dc:publisher":["State University of New York at Buffalo"],"dc:rights":["Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions.","Copyright retained by author."],"dc:subject":["physics","condensed matter physics"],"dc:title":["Pairing Phenomena from Low-Density Fermi Gases to Neutron Star Matter"],"dc:type":["Text","Dissertation"]},"updated_at":"2026-07-27T19:05:25Z"}