Quantum dynamics in closed and open many-particle systems

This project falls within the Physical Sciences Theme and the Physics grand challenge area "Emergence and Physics Far From Equilibrium". The first line of work is concerned with analysing novel non-equilibrium steady states that are realizable in cold atom experiments. It is well known that the attractive Lieb-Liniger model (bosons with attractive delta-function interaction) is thermodynamically unstable in equilibrium, but due to the existence of conservation laws can support stable non-equilibrium steady states after quantum quenches. In cold atom systems that are approximately described by the Lieb-Liniger model these correspond to metastable states. In particular, quenching the interaction strength from very strong repulsion to very strong attraction realizes the so-called super-Tonks-Girardeau gas [E. Haller et al, Science 325, 1224 (2009)]. Quenching to less strongly attractive interactions is expected to generate more exotic highly correlated steady states with an intricate hierarchical structure of many-boson bound states [L. Piroli et al, Phys. Rev. Lett. 116 (7), 070408 (2016)]. The aim of this part of the project is to characterize the physical properties of this class of states by using the recently developed framework of Generalized Hydrodynamics to determine linear response functions and by considering the dynamics under expansion. The next step will be to develop a full theory for an interaction quench from the ground state of the infinitely repulsive to the attractive Lieb-Linger model by means of the quench action approach.
The second line of work is concerned with the description of open quantum systems by Lindblad equations. The aim is to describe the short-time dynamics of Lindblad equations for many-particle systems using bosonization methods. In the first instance the bath coupling will be taken to be dephasing noise, while the Hamiltonian part allows a description in terms of a free boson (plus perturbations). The first goal is to establish the time window over which linear Luttinger liquid theory provides a good description of the Hamiltonian part. This will be done by considering exactly solvable models and by comparing to numerical matrix product state computations. The second goal is to go beyond the linear Luttinger liquid description and consider the role played by different kinds of perturbations by using equation of motion techniques. The ultimate goal is to develop a readily useable extension of Luttinger liquid theory to open quantum systems.