Thermalization dynamics and spectral statistics of extended systems with thermalizing boundaries
Pavel Kos, Tomaž Prosen, Bruno Bertini
Abstract
Quantitatively understanding the role of chaos and ergodicity in the thermalization process is crucial in our quest to decipher out-of-equilibrium quantum matter. Here, the authors address this question for a finite time-periodic quantum circuit coupled to an extended dual-unitary circuit acting as a perfect Markovian bath. The system's dynamics can thus be described by a simple quantum channel, the ergodicity of which is completely characterized. A class of gates is identified for which the channel is preserving the memory of the initial condition, while for generic gates the channel is ergodic. Moreover, the authors provide a quantitative characterization of the thermalization rate for nearly dual-unitary gates.