Dynamics of many-body open quantum systems with structured environments

Abstract

In condensed matter theory the many-body problem holds centre stage and in equilibrium a large number of techniques have been developed. These include path integration, mean-field theory and renormalisation group and have explained a wide variety of phenomena like phase transitions and transport effects such as superconductivity.

There are not nearly as many methods for out-of-equilibrium many-body systems as there are for equilibrium problems. There are a number of reasons for this. Analytically, there is no non-equilibrium analogue of the free energy which is minimised in equilibrium, rather, non-equilibrium steady states are determined dynamically. In terms of numerical approaches there are two main issues. One is the exponential scaling of the size of the Hilbert space making simulation of collective quantum particles intractable. The other is that one needs to derive the proper dissipation operators, which requires knowledge of the eigenstates. This is made even more important when the environment itself has a non-trivial density of states, said to be structured.

In this Thesis we use Redfield theory to derive microscopic dissipation processes in two prominent multi-particle models. Redfield theory gives a recipe for deriving the correct dissipative master equation from first principles by expressing the system-bath interaction in terms of the collective modes of the many-body system. First we study a model of two coupled bosonic particles and show that the true Rabi splitting deviates from the standard textbook formula. Instead we find a strong dependence on Lamb shifts, which are important in structured environ- ments. Then we study the dynamics of the driven transverse-field anisotropic XY model and investigate its non-equilibrium properties when structured dissipation is present. We discuss how structure can lead to heating or cooling depending on the detuning of the spectral peak of the density of states relative to the system eigenfrequencies.

Date of Award	28 Jun 2021
Original language	English
Awarding Institution	University of St Andrews
Supervisor	Jonathan Mark James Keeling (Supervisor) & Brendon William Lovett (Supervisor)