{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/25250"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/25250","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Quantum dynamics of small Josephson junctions: an application to superconductivity in granular films","abstract":"This thesis is devoted to a study of the quantum dynamics of small Josephson junctions. Of interest are those features of the junction's behavior which depend explicitly on the quantum mechanical nature of the phase difference <1> between the superconductors. In Chapters I and IT several calculations are described which focus on the junction's DC resistance. A fully quantum mechanical Hamiltonian is employed which incorporates the dissipative effects due to the unpaired electrons by coupling to a bath of harmonic oscillators. It is shown that the model exhibits a novel zero temperature phase transition as a function of the strength of the dissipation. In the low dissipation regime the phase is free to tunnel quantum mechanically and the junction's resistance is finite; in response to an external current, tunnelling induces successive 21t phase slips leading to a finite voltage state. In contrast, in the high dissipation regime, tunnelling is suppressed and the junction behaves as a superconductor carrying current with no resistive losses. In Chapters m and N these results are applied in an attempt to explain the recent observation that in ultra-thin Sn films there is apparently a universal normal state sheet resistance above which superconductivity cannot be established. The ftlms are modelled as a random array of superconducting islands linked together by small Josephson junctions. By combining this picture with the calculations for the single junction behavior, a natural explanation for the observed data is presented. Specifically, it is demonstrated that when the sheet resistance is larger than the quantum of resistance, Rq=h/4e2 , quantum tunnelling of the phase between neighboring islands drives the film normal. This value of the universal resistance· agrees quantitatively with the experiment","abstract_html":"This thesis is devoted to a study of the quantum dynamics of small Josephson junctions. Of interest are those features of the junction&#x27;s behavior which depend explicitly on the quantum mechanical nature of the phase difference &lt;1&gt; between the superconductors. In Chapters I and IT several calculations are described which focus on the junction&#x27;s DC resistance. A fully quantum mechanical Hamiltonian is employed which incorporates the dissipative effects due to the unpaired electrons by coupling to a bath of harmonic oscillators. It is shown that the model exhibits a novel zero temperature phase transition as a function of the strength of the dissipation. In the low dissipation regime the phase is free to tunnel quantum mechanically and the junction&#x27;s resistance is finite; in response to an external current, tunnelling induces successive 21t phase slips leading to a finite voltage state. In contrast, in the high dissipation regime, tunnelling is suppressed and the junction behaves as a superconductor carrying current with no resistive losses. In Chapters m and N these results are applied in an attempt to explain the recent observation that in ultra-thin Sn films there is apparently a universal normal state sheet resistance above which superconductivity cannot be established. The ftlms are modelled as a random array of superconducting islands linked together by small Josephson junctions. By combining this picture with the calculations for the single junction behavior, a natural explanation for the observed data is presented. Specifically, it is demonstrated that when the sheet resistance is larger than the quantum of resistance, Rq=h/4e2 , quantum tunnelling of the phase between neighboring islands drives the film normal. This value of the universal resistance· agrees quantitatively with the experiment","abstract_has_math":false,"creators":["Fisher, Matthew Paul Alejandro"],"institution":null,"degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Leggett, Anthony J."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-06-03T15:05:02Z","date_published":"2011-06-03T15:05:02Z","updated_at":"2026-07-22T22:25:24Z","subjects":["quantum dynamics","small Josephson functions","superconductors"],"languages":["en"],"rights":["1986 Matthew Paul Alejandro Fisher"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["978711"],"render_values":[{"text":"978711","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/25250","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Leggett, Anthony J."]},{"key":"dc:creator","label":"Author","values":["Fisher, Matthew Paul Alejandro"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-06-03T15:05:02Z","10000-01-01","1986"]},{"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 dynamics","small Josephson functions","superconductors"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["1986 Matthew Paul Alejandro Fisher"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["978711","http://hdl.handle.net/2142/25250"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["This thesis is devoted to a study of the quantum dynamics of small Josephson junctions. Of interest are those features of the junction's behavior which depend explicitly on the quantum mechanical nature of the phase difference <1> between the superconductors. In Chapters I and IT several calculations are described which focus on the junction's DC resistance. A fully quantum mechanical Hamiltonian is employed which incorporates the dissipative effects due to the unpaired electrons by coupling to a bath of harmonic oscillators. It is shown that the model exhibits a novel zero temperature phase transition as a function of the strength of the dissipation. In the low dissipation regime the phase is free to tunnel quantum mechanically and the junction's resistance is finite; in response to an external current, tunnelling induces successive 21t phase slips leading to a finite voltage state. In contrast, in the high dissipation regime, tunnelling is suppressed and the junction behaves as a superconductor carrying current with no resistive losses. In Chapters m and N these results are applied in an attempt to explain the recent observation that in ultra-thin Sn films there is apparently a universal normal state sheet resistance above which superconductivity cannot be established. The ftlms are modelled as a random array of superconducting islands linked together by small Josephson junctions. By combining this picture with the calculations for the single junction behavior, a natural explanation for the observed data is presented. Specifically, it is demonstrated that when the sheet resistance is larger than the quantum of resistance, Rq=h/4e2 , quantum tunnelling of the phase between neighboring islands drives the film normal. This value of the universal resistance· agrees quantitatively with the experiment","Submitted by Carolyn Mead (cmead2@illinois.edu) on 2011-06-03T15:05:02Z No. of bitstreams: 1 1986_fisher.pdf: 7981111 bytes, checksum: f8c34b2020d99c495dbaa7bb4da7403f (MD5)","Made available in DSpace on 2011-06-03T15:05:02Z (GMT). No. of bitstreams: 1 1986_fisher.pdf: 7981111 bytes, checksum: f8c34b2020d99c495dbaa7bb4da7403f (MD5) Previous issue date: 1986","Restriction data tranferred 2014-07-01T11:12:40-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: Thesis","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Carolyn Mead (cmead2@illinois.edu) on 2011-06-03T15:05:02Z Item is restricted indefinitely.","Thesis","U of I Only"]},{"key":"dc:title","label":"Title","values":["Quantum dynamics of small Josephson junctions: an application to superconductivity in granular films"]}]}],"canonical_facts":{"dc:contributor":["Leggett, Anthony J."],"dc:creator":["Fisher, Matthew Paul Alejandro"],"dc:date":["2011-06-03T15:05:02Z","10000-01-01","1986"],"dc:description":["This thesis is devoted to a study of the quantum dynamics of small Josephson junctions. Of interest are those features of the junction's behavior which depend explicitly on the quantum mechanical nature of the phase difference <1> between the superconductors. In Chapters I and IT several calculations are described which focus on the junction's DC resistance. A fully quantum mechanical Hamiltonian is employed which incorporates the dissipative effects due to the unpaired electrons by coupling to a bath of harmonic oscillators. It is shown that the model exhibits a novel zero temperature phase transition as a function of the strength of the dissipation. In the low dissipation regime the phase is free to tunnel quantum mechanically and the junction's resistance is finite; in response to an external current, tunnelling induces successive 21t phase slips leading to a finite voltage state. In contrast, in the high dissipation regime, tunnelling is suppressed and the junction behaves as a superconductor carrying current with no resistive losses. In Chapters m and N these results are applied in an attempt to explain the recent observation that in ultra-thin Sn films there is apparently a universal normal state sheet resistance above which superconductivity cannot be established. The ftlms are modelled as a random array of superconducting islands linked together by small Josephson junctions. By combining this picture with the calculations for the single junction behavior, a natural explanation for the observed data is presented. Specifically, it is demonstrated that when the sheet resistance is larger than the quantum of resistance, Rq=h/4e2 , quantum tunnelling of the phase between neighboring islands drives the film normal. This value of the universal resistance· agrees quantitatively with the experiment","Submitted by Carolyn Mead (cmead2@illinois.edu) on 2011-06-03T15:05:02Z No. of bitstreams: 1 1986_fisher.pdf: 7981111 bytes, checksum: f8c34b2020d99c495dbaa7bb4da7403f (MD5)","Made available in DSpace on 2011-06-03T15:05:02Z (GMT). No. of bitstreams: 1 1986_fisher.pdf: 7981111 bytes, checksum: f8c34b2020d99c495dbaa7bb4da7403f (MD5) Previous issue date: 1986","Restriction data tranferred 2014-07-01T11:12:40-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: Thesis","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Carolyn Mead (cmead2@illinois.edu) on 2011-06-03T15:05:02Z Item is restricted indefinitely.","Thesis","U of I Only"],"dc:identifier":["978711","http://hdl.handle.net/2142/25250"],"dc:language":["en"],"dc:rights":["1986 Matthew Paul Alejandro Fisher"],"dc:subject":["quantum dynamics","small Josephson functions","superconductors"],"dc:title":["Quantum dynamics of small Josephson junctions: an application to superconductivity in granular films"],"dc:type":["Dissertation / Thesis","text"],"thesis:degree_discipline":["Physics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."]},"updated_at":"2026-07-22T22:25:24Z"}