Related papers: Ergodic and Mixing Quantum Channels in Finite Dime…

The development of classical ergodic theory has had a significant impact in the areas of mathematics, physics, and, in general, applied sciences. The quantum ergodic theory of Hamiltonian dynamics has its motivations to understand…

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…

Quantum channels, pivotal in information processing, describe transformations within quantum systems and enable secure communication and error correction. Ergodic and mixing properties elucidate their behavior. In this paper, we establish a…

We study measurement-induced nonlinear dynamics generated by an iterated quantum protocol combining an entangling gate, a single-qubit rotation, and post-selection. For pure single-qubit inputs, a particular choice of the single-qubit…

We analyze the ergodic properties of quantum channels that are covariant with respect to diagonal orthogonal transformations. We prove that the ergodic behaviour of a channel in this class is essentially governed by a classical stochastic…

After a brief historical review of ergodicity and mixing in dynamics, particularly in quantum dynamics, we introduce definitions of quantum ergodicity and mixing using the structure of the system's energy levels and spacings. Our…

This work develops a rigorous framework for analysing ergodicity and mixing in time-inhomogeneous quantum dynamics. It considers quantum evolutions generated by sequences of quantum channels and examines in detail the relationship between…

We provide a framework for studying randomly coloured point sets in a locally compact, second-countable space on which a metrisable unimodular group acts continuously and properly. We first construct and describe an appropriate dynamical…

For affine processes on finite-dimensional cones, we give criteria for geometric ergodicity - that is exponentially fast convergence to a unique stationary distribution. Ergodic results include both the existence of exponential moments of…

We give through pseudodifferential operator calculus a proof that the quantum dynamics of a class of infinite harmonic crystals becomes ergodic and mixing with respect to the quantum Gibbs measure if the classical infinite dynamics is…

It is well known that stationary geometrically ergodic Markov chains are $\beta$-mixing (absolutely regular) with geometrically decaying mixing coefficients. Furthermore, for initial distributions other than the stationary one, geometric…

Any discrete quantum process is represented by a sequence of quantum channels. We consider ergodic quantum processes obtained by a map that takes the points along the trajectory of a discrete ergodic dynamical system to the space of quantum…

This paper is a physicist's review of the major conceptual issues concerning the problem of spectral universality in quantum systems. Here we present a unified, graph-based view of all archetypical models of such universality (billiards,…

Statistical mechanics is founded on the assumption that all accessible configurations of a system are equally likely. This requires dynamics that explore all states over time, known as ergodic dynamics. In isolated quantum systems, however,…

In this work we obtain a new criterion to establish ergodicity and non-uniform hyperbolicity of smooth measures of diffeomorphisms. This method allows us to give a more accurate description of certain ergodic components. The use of this…

We give a simple and physically intuitive necessary and sufficient condition for a map acting on a compact metric space to be mixing (i.e. infinitely many applications of the map transfer any input into a fixed convergency point). This is a…

We study two properties of nonsingular and infinite measure-preserving ergodic systems: weak double ergodicity, and ergodicity with isometric coefficients. We show that there exist infinite measure-preserving transformations that are…

Motivated by a model presented by S. Gudder, we study a quantum generalization of Markov chains and discuss the relation between these maps and open quantum random walks, a class of quantum channels described by S. Attal et al. We consider…

Ergodic theory provides a rigorous mathematical description of chaos in classical dynamical systems, including a formal definition of the ergodic hierarchy. How ergodic dynamics is reflected in the energy levels and eigenstates of a quantum…

This paper is concerned with the ergodic subspaces of the state spaces of isolated quantum systems. We prove a new ergodic theorem for closed quantum systems which shows that the equilibrium state of the system takes the form of a grand…