Condensed Matter Theory

Abstract:

We study the time evolution operator in a family of local quantum circuits with random elds in a xed direction. We argue that the presence of quantum chaos implies that at large times the time evolution operator becomes e ectively a random matrix in the many-body Hilbert space. To quantify this phenomenon we compute analytically the squared magnitude of the trace of the evolution operator the generalised spectral form factor and compare it with the prediction of Random Matrix Theory (RMT). We show that for the systems under consideration the generalised spectral form factor can be expressed in terms of dynamical correlation functions of local observables in the in nite temperature state, linking chaotic and ergodic properties of the systems. This also provides a connection between the many-body Thouless time τth the time at which the generalised spectral form factor starts following the random matrix theory prediction and the conservation laws of the system. Moreover, we explain di erent scalings of τth with the system size, observed for systems with and without the conservation laws.

Abstract:

We consider the non-equilibrium dynamics of a weakly interacting Bose gas tightly confined to a highly elongated double well potential. We use a self-consistent time-dependent Hartree–Fock approximation in combination with a projection of the full three-dimensional theory to several coupled one-dimensional channels. This allows us to model the time-dependent splitting and phase imprinting of a gas initially confined to a single quasi one-dimensional potential well and obtain a microscopic description of the ensuing damped Josephson oscillations.

Abstract:

We study the out-of-equilibrium dynamics of the quantum cellular automaton known as “Rule 54.” For a class of low-entangled initial states, we provide an analytic description of the effect of the global evolution on finite subsystems in terms of simple quantum channels, which gives access to the full thermalization dynamics at the microscopic level. As an example, we provide analytic formulas for the evolution of local observables and Rényi entropies. We show that, in contrast to other known examples of exactly solvable quantum circuits, Rule 54 does not behave as a simple Markovian bath on its own parts, and displays typical nonequilibrium features of interacting integrable many-body quantum systems such as finite relaxation rate and interaction-induced dressing effects. Our study provides a rare example where the full thermalization dynamics can be solved exactly at the microscopic level.