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[{"key": "dc.contributor.advisor", "value": "Heikkil\u00e4, Tero", "language": "", "element": "contributor", "qualifier": "advisor", "schema": "dc"}, {"key": "dc.contributor.advisor", "value": "Hyart, Timo", "language": "", "element": "contributor", "qualifier": "advisor", "schema": "dc"}, {"key": "dc.contributor.author", "value": "Kuusela, Petri", "language": null, "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2017-11-13T16:21:04Z", "language": "", "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2017-11-13T16:21:04Z", "language": "", "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2017", "language": null, "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.other", "value": "oai:jykdok.linneanet.fi:1738558", "language": null, "element": "identifier", "qualifier": "other", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/55853", "language": "", "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "Suprajohtavuuden Richardsonin ja BCS mallien vertailu perustilojen laskettujen energioiden perusteella. \r\n\r\nSuprajohtavuus on edelleen aktiivinen tutkimuksen alue, koska sen tarjoamista mahdollisuuksista huolimatta sit\u00e4 ei viel\u00e4 ymm\u00e4rret\u00e4 kokonaisvaltaisesti. T\u00e4ss\u00e4 pro gradu -tutkielmassa k\u00e4yn l\u00e4pi perusteet kahdelle suprajohtavuuden mallille, Richardsonin ja BCS malleille. BCS teoria on ensimm\u00e4inen ja k\u00e4ytetyin mikroskooppinen suprajohtavuuden teoria. Richardsonin malli on harvemmin k\u00e4ytetty malli, josta saadaan redusoidun BCS Hamiltonin operaattorin tarkat ominaistilat. Lasken molempien mallien perustilojen energiat sek\u00e4 redusoidulle ett\u00e4 t\u00e4ydelle BCS Hamiltonin operaattorille.\r\nSama lasketaan my\u00f6s yleiselle tarkan m\u00e4\u00e4r\u00e4n vain pariutuneita elektroneja\r\nsis\u00e4lt\u00e4v\u00e4lle tilalle. T\u00e4lle eri Hamiltonin operaattorien energioiden erotus riippuu\r\nainoastaan hiukkasm\u00e4\u00e4r\u00e4st\u00e4, ja siten ei ole merkityst\u00e4, kumpaa Hamiltonin operaattoria\r\nsellaisten tilojen energioiden vertailuissa k\u00e4ytet\u00e4\u00e4n. Energioiden vertailuista\r\nhuomaan, ett\u00e4 tasav\u00e4listen energiatilojen systeemill\u00e4 ja kolmiulotteisella vapaiden\r\nelektronien systeemill\u00e4 Richardsonin ja BCS mallien perustilojen energiat ovat l\u00e4hell\u00e4\r\ntoisiaan, Richardsonin mallin antaessa matalamman perustilan energian. T\u00e4st\u00e4 p\u00e4\u00e4ttelen,\r\nett\u00e4 BCS malli kuvaa hyvin n\u00e4it\u00e4 systeemej\u00e4. Kaksitilasysteemill\u00e4 energioiden\r\nerotus on huomattava, Richardsonin mallin antaessa merkitt\u00e4v\u00e4sti matalamman perustilan\r\nenergian. T\u00e4m\u00e4 on merkki siit\u00e4, ett\u00e4 BCS malli ei kuvaa t\u00e4llaista systeemi\u00e4\r\nhyvin.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.abstract", "value": "Superconductivity remains an active area of research because there still is no comprehensive\r\nunderstanding of the phenomenon despite all the possibilities it offers. In this\r\nthesis I go through the basics of two models for superconductivity, the BCS model\r\nand the Richardson model. The BCS theory is the first and most used successful\r\nmicroscopic theory of superconductivity. Richardson model is a less used model\r\nwhich gives the exact eigenstates of the reduced BCS Hamiltonian. I calculate the\r\nground state energies for both the reduced and the full BCS Hamiltonian for both\r\nmodels. This is done for a general paired state with fixed number of electrons as well.\r\nFor this state I find that the difference between the full and reduced Hamiltonian\r\nenergies depends only on the number of electrons, and thus conclude that it does not\r\nmatter for comparison between such states which Hamiltonian is used. I find that\r\nin a system with equally spaced energies and in the free-electron three-dimensional\r\nsystem the ground state energies are very close to each other, with the Richardson\r\nmodel ground state energy being lower. From this I infer that the BCS model is a\r\ngood description of these systems. The ground state energies of a two-level system\r\nhowever differs considerably, with the Richardson model ground state energy being\r\nsignificantly lower. This is an indication that the BCS model is not suitable for\r\ndescribing this system.", "language": "en", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted using Plone Publishing form by Petri Kuusela (pekakuus) on 2017-11-13 16:21:03.977688. Form: Pro gradu -lomake (https://kirjasto.jyu.fi/julkaisut/julkaisulomakkeet/pro-gradu-lomake). JyX data: [jyx_publishing-allowed (fi) =True]", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by jyx lomake-julkaisija (jyx-julkaisija.group@korppi.jyu.fi) on 2017-11-13T16:21:04Z\r\nNo. of bitstreams: 2\r\nURN:NBN:fi:jyu-201711134240.pdf: 530939 bytes, checksum: 1116daae38db22c1ff5e2537713f72f2 (MD5)\r\nlicense.html: 4868 bytes, checksum: 4a847069c860232808ce816e0cb64a7e (MD5)", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2017-11-13T16:21:04Z (GMT). No. of bitstreams: 2\r\nURN:NBN:fi:jyu-201711134240.pdf: 530939 bytes, checksum: 1116daae38db22c1ff5e2537713f72f2 (MD5)\r\nlicense.html: 4868 bytes, checksum: 4a847069c860232808ce816e0cb64a7e (MD5)\r\n Previous issue date: 2017", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "1 verkkoaineisto (50 sivua)", "language": null, "element": "format", "qualifier": "extent", "schema": "dc"}, {"key": "dc.format.mimetype", "value": "application/pdf", "language": null, "element": "format", "qualifier": "mimetype", "schema": "dc"}, {"key": "dc.language.iso", "value": "eng", "language": null, "element": "language", "qualifier": "iso", "schema": "dc"}, {"key": "dc.rights", "value": "In Copyright", "language": "en", "element": "rights", "qualifier": null, "schema": "dc"}, {"key": "dc.subject.other", "value": "Richardsonin malli", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "superconductivity", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "Richardson model", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "ground state energy", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.title", "value": "Comparison of the Richardson and BCS models of superconductivity based on calculations of ground state energies", "language": null, "element": "title", "qualifier": null, "schema": "dc"}, {"key": "dc.type", "value": "master thesis", "language": null, "element": "type", "qualifier": null, "schema": "dc"}, {"key": "dc.identifier.urn", "value": "URN:NBN:fi:jyu-201711134240", "language": null, "element": "identifier", "qualifier": "urn", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Pro gradu -tutkielma", "language": "fi", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Master\u2019s thesis", "language": "en", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Matemaattis-luonnontieteellinen tiedekunta", "language": "fi", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Faculty of Sciences", "language": "en", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Fysiikan laitos", "language": "fi", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Department of Physics", "language": "en", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "University of Jyv\u00e4skyl\u00e4", "language": "en", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "Jyv\u00e4skyl\u00e4n yliopisto", "language": "fi", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Teoreettinen fysiikka", "language": "fi", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Theoretical Physics", "language": "en", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.date.updated", "value": "2017-11-13T16:21:04Z", "language": "", "element": "date", "qualifier": "updated", "schema": "dc"}, {"key": "yvv.contractresearch.funding", "value": "0", "language": "", "element": "contractresearch", "qualifier": "funding", "schema": "yvv"}, {"key": "dc.type.coar", "value": "http://purl.org/coar/resource_type/c_bdcc", "language": null, "element": "type", "qualifier": "coar", "schema": "dc"}, {"key": "dc.rights.accesslevel", "value": "openAccess", "language": "fi", "element": "rights", "qualifier": "accesslevel", "schema": "dc"}, {"key": "dc.type.publication", "value": "masterThesis", "language": null, "element": "type", "qualifier": "publication", "schema": "dc"}, {"key": "dc.subject.oppiainekoodi", "value": "4024", "language": null, "element": "subject", "qualifier": "oppiainekoodi", "schema": "dc"}, {"key": "dc.subject.yso", "value": "suprajohtavuus", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.format.content", "value": "fulltext", "language": null, "element": "format", "qualifier": "content", "schema": "dc"}, {"key": "dc.rights.url", "value": "https://rightsstatements.org/page/InC/1.0/", "language": null, "element": "rights", "qualifier": "url", "schema": "dc"}, {"key": "dc.type.okm", "value": "G2", "language": null, "element": "type", "qualifier": "okm", "schema": "dc"}]
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