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 Title: Holography for the practical person Author(s): Langley, Brandon W. Director of Research: Phillips, Philip W. Doctoral Committee Chair(s): Faulkner, Thomas Doctoral Committee Member(s): Abbamonte, Peter; Cooper, Lance Department / Program: Physics Discipline: Physics Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): holography condensed matter AdS/CFT gauge/gravity Lifshitz diffusion transport conductivity general relativity duality 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 $z=2$. Issue Date: 2019-04-17 Type: Text URI: http://hdl.handle.net/2142/104841 Rights Information: Copyright 2019 by Brandon W. Langley. All rights reserved. Date Available in IDEALS: 2019-08-23 Date Deposited: 2019-05
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