Abstract
The goal of this thesis is to obtain the statistics of transported quantities in non-equilibrium steady states of both classical and quantum systems. This transport is considered over a long time period where the large deviation principle is satisfied. Thus, the statistics of transported quantities will be described via the Scaled Cumulant Generating Functional (SCGF).Initially I introduce a simple approach for obtaining the SCGF dubbed ‘boot-strapping’. This is limited to systems that display a chiral separation and satisfy the Gallavotti-Cohen fluctuation relation which is expressed as a symmetry on the SCGF.
I then present the primary result of this work, the Ballistic Fluctuation Formalism(BFF). This approach allows for the derivation of the SCGF for ballistically transported quantities in a maximal entropy state that has arisen in the long-time limit of a system governed by Euler hydrodynamics. The BFF represents an important new organisational principle for non-equilibrium states in both classical and quantum systems.
The remainder of this thesis is the application of the BFF to three different systems.The first is a generalised Totally Asymmetric Exclusion Process, a classical system,where the SCGF for current transport is obtained. The second is a d-dimensional Con-formal Field Theory, a quantum system, where the first known expression for the SCGF of energy transport is obtained. Finally, the BFF is applied to integrable models that can be described by generalized hydrodynamics via the Thermodynamic Bethe Ansatz, where these can be either classical or quantum systems. The BFF is used to obtain a general expression for the SCGF applicable to any transported conserved quantity of any such system. These results are applied to the classical hard rod gas and the quantum Lieb-Liniger gas.
| Date of Award | 1 Feb 2020 |
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| Original language | English |
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| Supervisor | Benjamin Doyon (Supervisor), Rosemary Harris (Supervisor) & Joe Bhaseen (Supervisor) |