Related papers: Ergodicity and Mixing in Quantum Dynamics
Ergodicity breaking is observed in the blockade regime of Rydberg atoms arrays, in the form of low entanglement eigenstates known as scars, which fail to thermalize. The signature of these states persists in periodically driven systems,…
We study the dynamics of compositions of a sequence of holomorphic mappings in projective space. We define ergodicity and mixing for non-autonomous dynamical systems, and we construct totally invariant measures for which our sequence…
This work presents a general unifying theoretical framework for quantum non-equilibrium systems. It is based on a re-statement of the dynamical problem as one of inferring the distribution of collision events that move a system toward…
Avoided level crossings, commonly associated with quantum chaos, are typically interpreted as signatures of eigenstate hybridization and spatial delocalization, often viewed as ergodic spreading. We show that, contrary to this expectation,…
A short historical overview is given on the development of our knowledge of complex dynamical systems with special emphasis on ergodicity and chaos, and on the semiclassical quantization of integrable and chaotic systems. The general trace…
We study quantum chaos for systems with more than one degree of freedom, for which we present an analysis of the dynamics of entanglement. Our analysis explains the main features of entanglement dynamics and identifies entanglement-based…
The generic behavior of quantum systems has long been of theoretical and practical interest. Any quantum process is represented by a sequence of quantum channels. We consider general ergodic sequences of stochastic channels with arbitrary…
We present an extensive numerical study of spectral statistics and eigenfunctions of quantized triangular billiards. We compute two million consecutive eigenvalues for six representative cases of triangular billiards, three with generic…
A unified view on macroscopic thermodynamics and quantum transport is presented. Thermodynamic processes with an exchange of energy between two systems necessarily involve the flow of other balanceable quantities. These flows are first…
We study the semiclassical behaviour of eigenfunctions of quantum systems with ergodic classical limit. By the quantum ergodicity theorem almost all of these eigenfunctions become equidistributed in a weak sense. We give a simple derivation…
We introduce a class of quantum Markov semigroups describing the evolution of interacting quantum lattice systems, specified either as generic qudits or as fermions. The corresponding generators, which include both conservative and…
We introduce a variant of the asymmetric random average process with continuous state variables where the maximal transport is restricted by a cutoff. For periodic boundary conditions, we show the existence of a phase transition between a…
A relationship between a recently introduced multipartite entanglement measure, state mixedness, and spin-flip symmetry is established for any finite number of qubits. It is also shown that, within those classes of states invariant under…
Progress in the creation of large scale, artificial quantum coherent structures demands the investigation of their nonequilibrium dynamics when strong interactions, even between remote parts, are non-perturbative. Analysis of multiparticle…
Since the 1970s there has been a rich theory of equilibrium states over shift spaces associated to H\"older-continuous real-valued potentials. The construction of equilibrium states associated to matrix-valued potentials is much more…
We investigate beyond-mean-field dynamics in a fully connected $\mathrm{SU}(3)$ spin-exchange model, focusing on the interplay between chaotic dynamics and quantum fluctuations. Using the two-particle irreducible (2PI) effective action…
The issue of relaxation has been addressed in terms of ergodic theory in the past. However, the application of that theory to models of physical interest is problematic, especially when dealing with relaxation to nonequilibrium steady…
We investigate a quantum dynamical entropy of one-dimesional quantum spin systems. We show that the dynamical entropy is bounded from above by a quantity which is related with group velocity determined by the interaction and mean entropy of…
The thermodynamical entropy of a system which consists of different kinds of ideal gases is known to be defined successfully in the case when the differences are described by classical or quantum theory. Since these theories are special…
We examine quantum normal typicality and ergodicity properties for quantum systems whose dynamics are generated by Hamiltonians which have residual degeneracy in their spectrum and resonance in their energy gaps. Such systems can be…