Related papers: Ergodic properties of quantum conservative systems
Quantum interference can terminate energy growth in a continually kicked system, via a single-particle ergodicity-breaking mechanism known as dynamical localization. The effect of many-body interactions on dynamically localized states,…
We give examples of rank-one transformations that are (weak) doubly ergodic and rigid (so all their cartesian products are conservative), but with non-ergodic $2$-fold cartesian product. We give conditions for rank-one infinite…
We present an introductory review of nonergodic dynamics in interacting many-body quantum systems, focusing on the phenomenon of many-body localization (MBL). We describe aspects of MBL and summarize the evidence for a crossover from the…
Two generically different but universal dynamical quantum many-body behaviors are discovered by probing the stability of trapped fragmented bosonic systems with strong repulsive finite/long range inter-particle interactions. We use…
The theoretical cornerstone of statistical mechanics is the ergodic assumption that all accessible configurations of a physical system are equally likely. Here we show how such property arises when an open quantum system is continuously…
We show that the magnetization of a single `qubit' spin weakly coupled to an otherwise isolated disordered spin chain exhibits periodic revivals in the localized regime, and retains an imprint of its initial magnetization at infinite time.…
This note discusses dynamical systems-systems that evolve through time. We start with two contemporary examples illustrating the qualitative and the quantitative behavior of dynamical systems. These are two broad categories, usually called…
Hamiltonian theory of hybrid quantum-classical systems is used to study dynamics of the classical subsystem coupled to different types of quantum systems. It is shown that the qualitative properties of orbits of the classical subsystem…
We present a theoretical and numerical study of the competition between two opposite interference effects, namely interference-induced ballistic transport on one hand, and strong (Anderson) localization on the other. While the former effect…
We study equivariant projective compactifications of reductive groups obtained by closing the image of a group in the space of operators of a projective representation. We describe the structure and the mutual position of their orbits under…
We analytically study the time evolution of the expectation values of observables in periodically kicked many-body quantum systems. Starting from an initial state, we compute both the transient and the long-time properties of the…
We study localization properties of continuously monitored dynamics and associated measurement-induced phase transitions in disordered quantum many-body systems on the basis of the quantum trajectory approach. By calculating the fidelity…
We present a quantum localization phenomenon that exists in periodically kicked 3D rotors, but is absent in the commonly studied 2D ones: edge localization. We show that under the condition of a fractional quantum resonance there are states…
We deal with the general structure of (noncommutative) stochastic processes by using the standard techniques of Operator Algebras. Any stochastic process is associated to a state on a universal object, i.e. the free product $C^*$-algebra in…
I employ random-matrix methods to set up and solve statistical models of noisy nonunitary dynamics that appear in the context of monitored quantum systems. The models cover a range of scenarios combining random dynamics and measurements of…
We discuss the condition for the validity of equilibrium quantum statistical mechanics in the light of recent developments in the understanding of classical and quantum chaotic motion. In particular, the ergodicity parameter is shown to…
We establish quantum thermodynamics for open quantum systems weakly coupled to their reservoirs when the system exhibits degeneracies. The first and second law of thermodynamics are derived, as well as a finite-time fluctuation theorem for…
In this paper we study ergodicity and mixing property of some measure preserving transformations on the Wiener space (W,H,\mu) which are generated by some random unitary operators defined on the Cameron-Martin space H.
We study the kick dynamics of periodically driven quantum systems, and provide a timeindependent effective Hamiltonian with the analytical form to reasonably describe the effective dynamics in a long timescale. It is shown that the…
This is the first of a series of two papers. We discuss some basic problems of the quantum kicked rotator (QKR) and review some important results in the literature. We point out the flaws in the inverse Cayley transform method to prove…