We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.

Durham e-Theses
You are in:

Aspects of hydrodynamics in AdS/CMT

BRATTAN, DANIEL,KEITH (2013) Aspects of hydrodynamics in AdS/CMT. Doctoral thesis, Durham University.

PDF - Accepted Version


Condensed matter theory is the study of systems at finite density. In this thesis we will attempt to argue that gauge-gravity dualities can give deep and meaningful insights into the behaviour of strongly coupled condensed matter systems. The first three chapters will be a review of material already available in literature. Chapter 1 will introduce holography and the AdS-CFT correspondence.
Particularly, in this chapter, the technique for the extraction of diffusion constants for charge and shear stress-energy-momentum fluctuations in a field theory with a holographic dual will be demonstrated. Chapter 2 will summarise relevant literature on the relativistic fluid-gravity correspondence. In the first half of the chapter it will be shown how to calculate the transport coefficients and Navier-Stokes equations for a suitable thermal field theory. The second half of chapter 2 will then be dedicated to extracting the transport coefficients for a strongly coupled field theory dual to a Reissner-Nordstrøm AdS spacetime. In chapter 3 a scaling of the metric and gauge field found in chapter 2 will be taken such that the boundary field theory admits Galilean, as opposed to relativistic, symmetry. Consequently, the governing hydrodynamic equations will be the non-relativistic, incompressible Navier-Stokes. Chapters 4 and 5 represent novel work. In chapter 4 the transport coefficients for a particular strongly coupled thermal field theory with underlying Schrodinger symmetry will be extracted from a charged, asymptotically Schrodinger spacetime. The governing hydrodynamic equations will be compressible with non-relativistic symmetry as opposed to those found via the scaling limit of chapter 3. In chapter 5 we show how knowledge of the transport coefficients of a thermal
field theory can be used as a test-bed for numerical methods to explore beyond the hydrodynamic (long wavelength and low frequency) regime. With this in mind we consider
Reissner-Nordstrøm AdS4 and determine the two point correlators at arbitrary frequency and momentum. Finally in chapter 6 we summarise the work discussed in this thesis and speculate about further applications of hydrodynamic techniques to strongly coupled condensed matter theories.

Item Type:Thesis (Doctoral)
Award:Doctor of Philosophy
Keywords:AdS/CFT, Hydrodynamics
Faculty and Department:Faculty of Science > Mathematical Sciences, Department of
Thesis Date:2013
Copyright:Copyright of this thesis is held by the author
Deposited On:18 Jan 2013 12:48

Social bookmarking: del.icio.usConnoteaBibSonomyCiteULikeFacebookTwitter