Quantum dynamics in strong interacting many-particle systems

This project falls within the EPSRC research areas "Mathematical Physics" and "Cold Atom and Molecules".

The aim of the project is to understand properties related to the finite-time dynamics in strongly-interacting many-particle quantum systems. These continue to attract significant theoretical attention in a variety of quantum simulation platforms including cold atoms, ion traps and NISQ devices. The project involves several lines of research:

(i) Characterise the relaxational behaviour of local operators in the non-equilibrium dynamics in homogeneous integrable many-particle systems. Here the aim is to ascertain whether local observables in an integrable model relax to their steady-state values after a quantum quench from a given initial state in an exponential or power-law behaviour. This is expected to be related to whether the observable has a non-vanishing projection to a "hydrodynamic mode" arising from one of the conservation laws.

(i) Determine robust signatures in nonlinear response functions describing pump-probe experiments in one-dimensional quantum gases on atom chips. Luttinger liquid methods fail to describe nonlinear density response functions in Bose gases. Here the aim is to apply non-linear Luttinger liquid techniques to overcome these limitations and derive explicit expressions for nonlinear dynamical susceptibilities in one-dimensional Bose gases, and make predictions for experiments.

(ii) Clarify the role of quantum integrability in Lindblad equations (and classical master equations). Many-particle quantum systems coupled to Markovian environments can be described by Lindblad equations. In recent years it has been shown that some of these are related to solutions of Yang-Baxter equations, and concomitantly quantum integrable models.

The latter posess extensively many conservation laws, but their role in Lindbladian dynamics is fundamentally different from that in closed systems. The aim of the project is to ascertain whether these Yang-Baxter conservation laws lead to specific signatures in (non-equal time) correlation functions of local operators or other measurable quantities