Dynamically driven-dissipative phases of matter

This thesis is a theoretical study of low dimensional non-equilibrium quantum many-body systems undergoing dynamical drive and dissipation. Thus, the models in this thesis host explicit time-dependent parameters while in thermal contact with an environment. The formal description of these models is approximated using a time-dependent Lindblad equation. Multiple methods are employed, such as numerical simulations, by means of exact diagonalization and direct differential equation solving, mean-field approximations, algebraic disentanglement of time-ordered exponents and integrability.
Three different dissipative models are investigated: (I) a system of free, translationally invariant fermions with dissipation, (II) driven-dissipative bosons in with a Kerr non-linearity (III) and finally noisy, driven-dissipative spins whose correlation functions are described by a non-Hermitian Richardson-Gaudin Hamiltonian. This thesis reports among others an exact solution for the wave functions of the free fermions in terms of coupled Riccati equations obtained through algebraic disentanglement. Furthermore, time-crystalline phases and chaos are identified in in the bosons.
The noisy spins cannot be investigated directly, rather requiring an in-depth study of the formal solution to the time-dependent Richardson-Gaudin Hamiltonian. This study revealed a connection between integrable (hyperbolic) Landau-Zener models and the Richardson-Gaudin Hamiltonian and its solutions. Long-time expressions for specific wavefunctions of the time-dependent Richardson-Gaudin Hamiltonian are found. A time-dependent phase transition can subsequently be observed in the spins’ correlation functions where the transient behavior of the system ultimately reduces to a power law. Furthermore, using exact results for two-point correlation functions a temporal phase transition is identified.