Transport in strongly interacting quantum field theories
Abstract/Contents
- Abstract
- Weakly perturbing a system by an external force and measuring its response provides us with rich information about the underlying physics of the system. Linear response theory relates experimental quantities such as electrical conductivity and thermal conductivity to two-point correlation functions of microscopic electric and heat current operators. There is a wealth of experimental data on conductivities. However, on the theoretical front, our knowledge away from the limit of small inter-particle forces is poor. In this work, we present some new ideas and calculations that further our theoretical understanding of electric and heat transport when the inter-particle forces are strong. In chapter 1, we set up our notation, define various two-point correlation functions and derive the Kubo formula, paying special attention to subtleties that are often glossed over in many texts. In chapter 2, we derive an upper bound on diffusion that follows via an interplay of microscopic speed limits and local equilibration physics. In chapter 3, we analytically compute the electrical resistance in a special three- dimensional system of gauge fields and matter. We are able to do the computation at arbitrary values of the coupling constant and frequency of the external driving electric field, albeit in the large-N limit. In chapter 4, we analyze the breakdown of the Wiedemann-Franz law at strong- coupling and analyze various kinematic scenarios. We show that the Wiedemann- Franz ratio should become extremely small if the momentum is approximately conserved (and there is no particle-hole symmetry). In chapter 5, we use the memory-matrix formalism to compute the contribution of weak random fields to the transport near the Ising-nematic quantum critical point. In chapter 6, we generalize our scope slightly to the general problem of computing time-dependent quantities in quantum systems and present a new state-of-the-art matrix product algorithm that allows us to numerically compute expectation values of observables at larger values of time than previously possible.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2017 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Mahajan, Raghu |
|---|---|
| Associated with | Stanford University, Department of Physics. |
| Primary advisor | Hartnoll, Sean |
| Thesis advisor | Hartnoll, Sean |
| Thesis advisor | Hayden, Patrick (Patrick M.) |
| Thesis advisor | Shenker, Stephen Hart, 1953- |
| Advisor | Hayden, Patrick (Patrick M.) |
| Advisor | Shenker, Stephen Hart, 1953- |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Raghu Mahajan. |
|---|---|
| Note | Submitted to the Department of Physics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2017. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2017 by Raghu Mahajan
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
Also listed in
Loading usage metrics...