{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/104841"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/104841","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Holography for the practical person","abstract":"\"This article opens with a pedagogical discussion of holography aimed at calculating the thermodynamics and transport coefficients in condensed matter systems. Therein, we will discuss the duality of thermodynamics to classical field theory, construct the associated dual action at the field theory's boundary, and divulge the numerical techniques of the Einstein-DeTurck equations. The latter allows a numerical treatment of linear response theory in highly nontrivial gravitational backgrounds. We will use these techniques in the analysis of two major problems. In the first, we will discuss the specific implementation of the numerical methodology in the exploration of holographic lattices. Particularly, we construct generalizations of AdS-Reissner-Nordstr\\\"\"om that interpolate between those used in two previous studies --- one that reports power-law scaling for the mid-frequency regime of the optical conductivity and one that does not. We find no evidence for power-law scaling of the conductivity, thereby corroborating the previous negative result that gravitational crystals are insufficient to generate the power-law mid-infrared conductivity observed in cuprate superconductors. In the second problem, we present the full charge and energy diffusion coefficients for the Einstein-Maxwell dilaton (EMD) action for Lifshitz spacetime characterized by a dynamical critical exponent $z$. We compute the fully renormalized static Lifshitz thermodynamic potential explicitly, which confirms the forms of all thermodynamic quantities including the Bekenstein-Hawking and Smarr-like relationships. For transport, we target our analysis at finite chemical potential and include axion fields to generate momentum dissipation. Beyond analysis of the bounds, we find deviation from universal transport obtains when either the chemical potential or momentum dissipation are large relative to temperature, an echo of strong thermoelectric interactions. We also find that regardless of what is diffusing, energy or charge, the diffusion constant is independent of matter content when $z=2$. This state of affairs obtains because the diffusion equation is scale invariant when $z=2$.\"","abstract_html":""This article opens with a pedagogical discussion of holography aimed at calculating the thermodynamics and transport coefficients in condensed matter systems. Therein, we will discuss the duality of thermodynamics to classical field theory, construct the associated dual action at the field theory's boundary, and divulge the numerical techniques of the Einstein-DeTurck equations. The latter allows a numerical treatment of linear response theory in highly nontrivial gravitational backgrounds. We will use these techniques in the analysis of two major problems. In the first, we will discuss the specific implementation of the numerical methodology in the exploration of holographic lattices. Particularly, we construct generalizations of AdS-Reissner-Nordstr\\""om that interpolate between those used in two previous studies --- one that reports power-law scaling for the mid-frequency regime of the optical conductivity and one that does not. We find no evidence for power-law scaling of the conductivity, thereby corroborating the previous negative result that gravitational crystals are insufficient to generate the power-law mid-infrared conductivity observed in cuprate superconductors. In the second problem, we present the full charge and energy diffusion coefficients for the Einstein-Maxwell dilaton (EMD) action for Lifshitz spacetime characterized by a dynamical critical exponent $z$. We compute the fully renormalized static Lifshitz thermodynamic potential explicitly, which confirms the forms of all thermodynamic quantities including the Bekenstein-Hawking and Smarr-like relationships. For transport, we target our analysis at finite chemical potential and include axion fields to generate momentum dissipation. Beyond analysis of the bounds, we find deviation from universal transport obtains when either the chemical potential or momentum dissipation are large relative to temperature, an echo of strong thermoelectric interactions. We also find that regardless of what is diffusing, energy or charge, the diffusion constant is independent of matter content when $z=2$. This state of affairs obtains because the diffusion equation is scale invariant when $z=2$."","abstract_has_math":true,"creators":["Langley, Brandon W."],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Phillips, Philip W.","Faulkner, Thomas","Abbamonte, Peter","Cooper, Lance"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2019,"date_issued":"2019-08-23T19:51:56Z","date_published":"2019-08-23T19:51:56Z","updated_at":"2026-07-22T22:24:42Z","subjects":["holography","condensed matter","AdS/CFT","gauge/gravity","Lifshitz","diffusion","transport","conductivity","general relativity","duality"],"languages":["en"],"rights":["Copyright 2019 by Brandon W. Langley. All rights reserved."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/104841","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Phillips, Philip W.","Faulkner, Thomas","Abbamonte, Peter","Cooper, Lance"]},{"key":"dc:creator","label":"Author","values":["Langley, Brandon W."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2019-08-23T19:51:56Z","2019-04-17","2019-05"]},{"key":"dc:type","label":"Dc Type","values":["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."]},{"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":["holography","condensed matter","AdS/CFT","gauge/gravity","Lifshitz","diffusion","transport","conductivity","general relativity","duality"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2019 by Brandon W. Langley. All rights reserved."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/104841"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["\"This article opens with a pedagogical discussion of holography aimed at calculating the thermodynamics and transport coefficients in condensed matter systems. Therein, we will discuss the duality of thermodynamics to classical field theory, construct the associated dual action at the field theory's boundary, and divulge the numerical techniques of the Einstein-DeTurck equations. The latter allows a numerical treatment of linear response theory in highly nontrivial gravitational backgrounds. We will use these techniques in the analysis of two major problems. In the first, we will discuss the specific implementation of the numerical methodology in the exploration of holographic lattices. Particularly, we construct generalizations of AdS-Reissner-Nordstr\\\"\"om that interpolate between those used in two previous studies --- one that reports power-law scaling for the mid-frequency regime of the optical conductivity and one that does not. We find no evidence for power-law scaling of the conductivity, thereby corroborating the previous negative result that gravitational crystals are insufficient to generate the power-law mid-infrared conductivity observed in cuprate superconductors. In the second problem, we present the full charge and energy diffusion coefficients for the Einstein-Maxwell dilaton (EMD) action for Lifshitz spacetime characterized by a dynamical critical exponent $z$. We compute the fully renormalized static Lifshitz thermodynamic potential explicitly, which confirms the forms of all thermodynamic quantities including the Bekenstein-Hawking and Smarr-like relationships. For transport, we target our analysis at finite chemical potential and include axion fields to generate momentum dissipation. Beyond analysis of the bounds, we find deviation from universal transport obtains when either the chemical potential or momentum dissipation are large relative to temperature, an echo of strong thermoelectric interactions. We also find that regardless of what is diffusing, energy or charge, the diffusion constant is independent of matter content when $z=2$. This state of affairs obtains because the diffusion equation is scale invariant when $z=2$.\"","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2019-08-22 without embargo terms","The student, Brandon Langley, accepted the attached license on 2019-04-16 at 04:48.","The student, Brandon Langley, submitted this Dissertation for approval on 2019-04-16 at 05:09.","This Dissertation was approved for publication on 2019-04-17 at 15:59.","DSpace SAF Submission Ingestion Package generated from Vireo submission #13661 on 2019-08-22 at 14:43:55","Made available in DSpace on 2019-08-23T19:51:56Z (GMT). No. of bitstreams: 3 LANGLEY-DISSERTATION-2019.pdf: 2372952 bytes, checksum: c0b3263762e68ddebba1c48d0a05ea5c (MD5) Thesis.zip: 51612147 bytes, checksum: 6137d19fb0fc75ff618ccdc5d45ddd0b (MD5) LICENSE.txt: 4212 bytes, checksum: 5897cc6520b7e71a3d1c1cc82e72f450 (MD5) Previous issue date: 2019-04-17"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Holography for the practical person"]}]}],"canonical_facts":{"dc:contributor":["Phillips, Philip W.","Faulkner, Thomas","Abbamonte, Peter","Cooper, Lance"],"dc:creator":["Langley, Brandon W."],"dc:date":["2019-08-23T19:51:56Z","2019-04-17","2019-05"],"dc:description":["\"This article opens with a pedagogical discussion of holography aimed at calculating the thermodynamics and transport coefficients in condensed matter systems. Therein, we will discuss the duality of thermodynamics to classical field theory, construct the associated dual action at the field theory's boundary, and divulge the numerical techniques of the Einstein-DeTurck equations. The latter allows a numerical treatment of linear response theory in highly nontrivial gravitational backgrounds. We will use these techniques in the analysis of two major problems. In the first, we will discuss the specific implementation of the numerical methodology in the exploration of holographic lattices. Particularly, we construct generalizations of AdS-Reissner-Nordstr\\\"\"om that interpolate between those used in two previous studies --- one that reports power-law scaling for the mid-frequency regime of the optical conductivity and one that does not. We find no evidence for power-law scaling of the conductivity, thereby corroborating the previous negative result that gravitational crystals are insufficient to generate the power-law mid-infrared conductivity observed in cuprate superconductors. In the second problem, we present the full charge and energy diffusion coefficients for the Einstein-Maxwell dilaton (EMD) action for Lifshitz spacetime characterized by a dynamical critical exponent $z$. We compute the fully renormalized static Lifshitz thermodynamic potential explicitly, which confirms the forms of all thermodynamic quantities including the Bekenstein-Hawking and Smarr-like relationships. For transport, we target our analysis at finite chemical potential and include axion fields to generate momentum dissipation. Beyond analysis of the bounds, we find deviation from universal transport obtains when either the chemical potential or momentum dissipation are large relative to temperature, an echo of strong thermoelectric interactions. We also find that regardless of what is diffusing, energy or charge, the diffusion constant is independent of matter content when $z=2$. This state of affairs obtains because the diffusion equation is scale invariant when $z=2$.\"","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2019-08-22 without embargo terms","The student, Brandon Langley, accepted the attached license on 2019-04-16 at 04:48.","The student, Brandon Langley, submitted this Dissertation for approval on 2019-04-16 at 05:09.","This Dissertation was approved for publication on 2019-04-17 at 15:59.","DSpace SAF Submission Ingestion Package generated from Vireo submission #13661 on 2019-08-22 at 14:43:55","Made available in DSpace on 2019-08-23T19:51:56Z (GMT). No. of bitstreams: 3 LANGLEY-DISSERTATION-2019.pdf: 2372952 bytes, checksum: c0b3263762e68ddebba1c48d0a05ea5c (MD5) Thesis.zip: 51612147 bytes, checksum: 6137d19fb0fc75ff618ccdc5d45ddd0b (MD5) LICENSE.txt: 4212 bytes, checksum: 5897cc6520b7e71a3d1c1cc82e72f450 (MD5) Previous issue date: 2019-04-17"],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/104841"],"dc:language":["en"],"dc:rights":["Copyright 2019 by Brandon W. Langley. All rights reserved."],"dc:subject":["holography","condensed matter","AdS/CFT","gauge/gravity","Lifshitz","diffusion","transport","conductivity","general relativity","duality"],"dc:title":["Holography for the practical person"],"dc:type":["text"],"thesis:degree_discipline":["Physics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:42Z"}