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The prominent collective character of long-range interacting quantum systems makes them promising candidates for quantum technological applications. Yet, lack of additivity overthrows the traditional picture for entanglement scaling and…
We consider a class of open quantum many-body systems that evolves in a Markovian fashion, the dynamical generator being in GKS-Lindblad form. Here, the Hamiltonian contribution is characterized by an all-to-all coupling, and the…
Isolated quantum systems follow the reversible unitary evolution; if we focus on the dynamics of local states and observables, they exhibit the irreversible relaxation behaviors. Here we study the local relaxation process in an isolated…
Floquet topological insulators are noninteracting quantum systems that, when driven by a time-periodic field, are described by effective Hamiltonians whose bands carry nontrivial topological invariants. A longstanding question concerns the…
We describe our recent results on the resonant perturbation theory of decoherence and relaxation for quantum system with many qubits. The approach represents a rigorous analysis of the phenomenon of decoherence and relaxation for general…
Prethermalization, by introducing emergent quasiconserved observables, plays a crucial role in protecting Floquet many-body phases over exponentially long time, while the ultimate fate of such quasiconserved operators can signal…
We prove that quantum many-body systems on a one-dimensional lattice locally relax to Gaussian states under non-equilibrium dynamics generated by a bosonic quadratic Hamiltonian. This is true for a large class of initial states - pure or…
The assumption that quantum systems relax to a stationary state in the long-time limit underpins statistical physics and much of our intuitive understanding of scientific phenomena. For isolated systems this follows from the eigenstate…
It has recently been shown that small quantum subsystems generically equilibrate, in the sense that they spend most of the time close to a fixed equilibrium state. This relies on just two assumptions: that the state is spread over many…
We review the recent progress in the understanding of the relaxation of isolated near-integrable quantum many-body systems. Focusing on prethermalization and universal dynamics following a quench, we describe the experiments with ultracold…
We develop a perturbation theory of quantum (and classical) master equations with slowly varying parameters, applicable to systems which are externally controlled on a time scale much longer than their characteristic relaxation time. We…
We address the nature of phase transitions in periodically driven systems coupled to a bath. The latter enables a synchronized non-equilibrium Floquet steady state at finite entropy, which we analyse for rapid drives within a…
We investigate one-dimensional systems with both energy conservation and a continuous symmetry, focusing on the impact of a boundary perturbation that breaks the continuous symmetry. Our study reveals two distinct dynamical phases: one in…
Near-resonant periodic driving of quantum systems promises the implementation of a large variety of novel effective Hamiltonians. The challenge of Floquet engineering lies in the preparation and measurement of the desired quantum state. We…
Controlling the decoherence induced by the interaction of quantum system with its environment is a fundamental challenge in quantum technology. Utilizing Floquet theory, we explore the constructive role of temporal periodic driving in…
Quantum systems can be dynamically controlled using time-periodic external fields, leading to the concept of Floquet engineering, with promising technological applications. Computing Floquet energy spectra is harder than only computing…
Numerous pivotal concepts have been introduced to clarify the puzzle of relaxation and/or equilibration in closed quantum systems. All of these concepts rely in some way on specific conditions on Hamiltonians $H$, observables $A$, and…
A quantum mechanical explanation of the relaxation to equilibrium is shown for macroscopic systems for nonintegrable cases and numerically verified. The macroscopic system is initially in an equilibrium state, subsequently externally…
Quantum systems can show qualitatively new forms of behavior when they are driven by fast time-periodic modulations. In the limit of large driving frequency, the long-time dynamics of such systems can often be described by a…
We present a theory of periodically driven, many-body localized (MBL) systems. We argue that MBL persists under periodic driving at high enough driving frequency: The Floquet operator (evolution operator over one driving period) can be…