Critical temperature and energy gap for the BCS equation
We derive upper and lower bounds on the critical temperature T{sub c} and the energy gap {xi} (at zero temperature) for the BCS gap equation, describing spin-(1/2) fermions interacting via a local two-body interaction potential {lambda}V(x). At weak coupling {lambda}
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| Veröffentlicht in: | Physical review. B, Condensed matter and materials physics Condensed matter and materials physics, 2008-05, Vol.77 (18), Article 184517 |
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| container_title | Physical review. B, Condensed matter and materials physics |
| container_volume | 77 |
| creator | Hainzl, Christian Seiringer, Robert |
| description | We derive upper and lower bounds on the critical temperature T{sub c} and the energy gap {xi} (at zero temperature) for the BCS gap equation, describing spin-(1/2) fermions interacting via a local two-body interaction potential {lambda}V(x). At weak coupling {lambda} |
| doi_str_mv | 10.1103/PhysRevB.77.184517 |
| format | Article |
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At weak coupling {lambda}<<1 and under appropriate assumptions on V(x), our bounds show that T{sub c}{approx}A exp(-B/{lambda}) and {xi}{approx}C exp(-B/{lambda}) for some explicit coefficients A, B, and C depending on the interaction V(x) and the chemical potential {mu}. The ratio A/C turns out to be a universal constant, independent of both V(x) and {mu}. 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B, Condensed matter and materials physics</title><description>We derive upper and lower bounds on the critical temperature T{sub c} and the energy gap {xi} (at zero temperature) for the BCS gap equation, describing spin-(1/2) fermions interacting via a local two-body interaction potential {lambda}V(x). At weak coupling {lambda}<<1 and under appropriate assumptions on V(x), our bounds show that T{sub c}{approx}A exp(-B/{lambda}) and {xi}{approx}C exp(-B/{lambda}) for some explicit coefficients A, B, and C depending on the interaction V(x) and the chemical potential {mu}. The ratio A/C turns out to be a universal constant, independent of both V(x) and {mu}. Our analysis is valid for any {mu}; for small {mu}, or low density, our formulas reduce to well-known expressions involving the scattering length of V(x)</description><subject>BCS THEORY</subject><subject>CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY</subject><subject>COUPLING</subject><subject>CRITICAL TEMPERATURE</subject><subject>ENERGY GAP</subject><subject>EQUATIONS</subject><subject>FERMIONS</subject><subject>INTERACTIONS</subject><subject>POTENTIALS</subject><subject>SCATTERING LENGTHS</subject><subject>SPIN</subject><subject>TEMPERATURE ZERO K</subject><subject>TWO-BODY PROBLEM</subject><issn>1098-0121</issn><issn>1550-235X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2008</creationdate><recordtype>article</recordtype><recordid>eNo1kE1LxDAYhIMouK7-AU8Bz13z5qNpj27xCxYUP8BbSNO328puW5Os0H9vpXqZmcMwDA8hl8BWAExcPzdjeMHv9UrrFWRSgT4iC1CKJVyoj-MpszxLGHA4JWchfDIGMpd8QbLCt7F1dkcj7gf0Nh48UttVFDv025Fu7UDr3tPYIF0XrxS_Dja2fXdOTmq7C3jx50vyfnf7Vjwkm6f7x-JmkzgpZEx4iQq4EqCsxkrzkpWgSy3tpDm3LE3zEm3mKq0lk3UGylV1PZ1OQfJcKrEkV_NuH2Jrgmsjusb1XYcuGg4ghZJ8avG55XwfgsfaDL7dWz8aYOaXkPknZLQ2MyHxA3JuWY8</recordid><startdate>20080501</startdate><enddate>20080501</enddate><creator>Hainzl, Christian</creator><creator>Seiringer, Robert</creator><scope>AAYXX</scope><scope>CITATION</scope><scope>OTOTI</scope></search><sort><creationdate>20080501</creationdate><title>Critical temperature and energy gap for the BCS equation</title><author>Hainzl, Christian ; Seiringer, Robert</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c434t-2be5125315a7ed72b0b17b74a17b92a0669bea8cd77404f815cdff23561429453</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2008</creationdate><topic>BCS THEORY</topic><topic>CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY</topic><topic>COUPLING</topic><topic>CRITICAL TEMPERATURE</topic><topic>ENERGY GAP</topic><topic>EQUATIONS</topic><topic>FERMIONS</topic><topic>INTERACTIONS</topic><topic>POTENTIALS</topic><topic>SCATTERING LENGTHS</topic><topic>SPIN</topic><topic>TEMPERATURE ZERO K</topic><topic>TWO-BODY PROBLEM</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Hainzl, Christian</creatorcontrib><creatorcontrib>Seiringer, Robert</creatorcontrib><collection>CrossRef</collection><collection>OSTI.GOV</collection><jtitle>Physical review. B, Condensed matter and materials physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Hainzl, Christian</au><au>Seiringer, Robert</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Critical temperature and energy gap for the BCS equation</atitle><jtitle>Physical review. B, Condensed matter and materials physics</jtitle><date>2008-05-01</date><risdate>2008</risdate><volume>77</volume><issue>18</issue><artnum>184517</artnum><issn>1098-0121</issn><eissn>1550-235X</eissn><abstract>We derive upper and lower bounds on the critical temperature T{sub c} and the energy gap {xi} (at zero temperature) for the BCS gap equation, describing spin-(1/2) fermions interacting via a local two-body interaction potential {lambda}V(x). At weak coupling {lambda}<<1 and under appropriate assumptions on V(x), our bounds show that T{sub c}{approx}A exp(-B/{lambda}) and {xi}{approx}C exp(-B/{lambda}) for some explicit coefficients A, B, and C depending on the interaction V(x) and the chemical potential {mu}. The ratio A/C turns out to be a universal constant, independent of both V(x) and {mu}. Our analysis is valid for any {mu}; for small {mu}, or low density, our formulas reduce to well-known expressions involving the scattering length of V(x)</abstract><cop>United States</cop><doi>10.1103/PhysRevB.77.184517</doi><oa>free_for_read</oa></addata></record> |
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| language | eng |
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| source | American Physical Society Journals |
| subjects | BCS THEORY CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY COUPLING CRITICAL TEMPERATURE ENERGY GAP EQUATIONS FERMIONS INTERACTIONS POTENTIALS SCATTERING LENGTHS SPIN TEMPERATURE ZERO K TWO-BODY PROBLEM |
| title | Critical temperature and energy gap for the BCS equation |
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