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We identify several distinct phases of thermalization that describe regimes of behavior in isolated, periodically driven (Floquet), mesoscopic quantum chaotic systems. In doing so, we also identify a Floquet thermal ensemble, the “ladder ensemble,” that is qualitatively distinct from the “featureless infinite-temperature” state that has long been assumed to be the appropriate maximum-entropy equilibrium ensemble for driven systems. The phases we find can be coarsely classified by (i) whether or not the system irreversibly exchanges energy of order ω with the drive, i.e., Floquet thermalizes, and (ii) the Floquet thermal ensemble describing the final equilibrium in systems that do Floquet thermalize. These phases are representative of regimes of behavior in mesoscopic systems, but they are sharply defined in a particular large-system limit where the drive frequency ω scales up with system size N as the N → ∞ limit is taken: we examine frequency scalings ranging from a weakly N-dependent ω(N)∼logN, to stronger scalings ranging from ω(N)∼√N to ω(N)∼N. We show that the transition where Floquet thermalization breaks down happens at an extensive drive frequency and, beyond that, systems that do not Floquet thermalize are distinguished based on the presence or absence of rare resonances across Floquet zones. We produce a thermalization phase diagram that is relevant for numerical studies of Floquet systems and experimental studies on small-scale quantum simulators, both of which lack a clean separation of scales between N and ω. A striking prediction of our work is that, under the assumption of perfect isolation, certain realistic quench protocols from simple pure initial states can show Floquet thermalization to a type of Schrodinger-cat state that is a global superposition of states at distinct temperatures. Our work extends and organizes the theory of Floquet thermalization, heating, and equilibrium into the setting of mesoscopic quantum systems. 

Many-body localized (MBL) systems fail to reach thermal equilibrium under their own dynamics, even though they are interacting, nonintegrable, and in an extensively excited state. One instability toward thermalization of MBL systems is the so-called “avalanche,” where a locally thermalizing rare region is able to spread thermalization through the full system. The spreading of the avalanche may be modeled and numerically studied in finite one-dimensional MBL systems by weakly coupling an infinite-temperature bath to one end of the system. We find that the avalanche spreads primarily via strong many-body resonances between rare near-resonant eigenstates of the closed system. Thus we find and explore a detailed connection between many-body resonances and avalanches in MBL systems.