Related papers: Theory of Ergodic Quantum Processes
The amplification of radiation by superradiance is a universal phenomenon observed in numerous physical systems. We demonstrate that superradiant scattering generates entanglement for different input states, including coherent states,…
In the framework of statistical mechanics the properties of macroscopic systems are deduced starting from the laws of their microscopic dynamics. One of the key assumptions in this procedure is the ergodic property, namely the equivalence…
We present a review of recent research on quantum entanglement, with special emphasis on entanglement between single atoms, processing of an encoded entanglement and its temporary evolution. Analysis based on the density matrix formalism…
Quantum channels, also called quantum operations, are linear, trace preserving and completely positive transformations in the space of quantum states. Such operations describe discrete time evolution of an open quantum system interacting…
General relation is derived which expresses the fidelity of quantum dynamics, measuring the stability of time evolution to small static variation in the hamiltonian, in terms of ergodicity of an observable generating the perturbation as…
The evolution of entanglement entropy in quantum circuits composed of Haar-random gates and projective measurements shows versatile behavior, with connections to phase transitions and complexity theory. We reformulate the problem in terms…
Ergodicity is a fundamental principle of statistical mechanics underlying the behavior of generic quantum many-body systems. However, how this universal many-body quantum chaotic regime emerges due to interactions remains largely a puzzle.…
A dynamical signature of localization in quantum systems is the absence of transport which is governed by the amount of coherence that configuration space states possess with respect to the Hamiltonian eigenbasis. To make this observation…
Let $(M,\tau)$ be a tracial von Neumann algebra with a separable predual and let $(\Omega, \mathbb{P})$ be a probability space. A bounded positive random linear operator on $L^1(M,\tau)$ is a map $\gamma : \Omega \times L^1(M,\tau) \to…
Quantum coherence quantifies the amount of superposition a quantum state can have in a given basis. Since there is a difference in the structure of eigenstates of the ergodic and many-body localized systems, we expect them also to differ in…
This paper is concerned with a translation invariant network of identical quantum stochastic systems subjected to external quantum noise. Each node of the network is directly coupled to a finite number of its neighbours. This network is…
We investigate toy dynamical models of energy-level repulsion in quantum eigenvalue sequences. We focus on parametric (with respect to a running coupling or "complexity" parameter) stochastic processes that are capable of relaxing towards a…
The thermodynamic limit of the internal energy and the entropy of the system of quantum interacting particles in random medium is shown to exist under the crucial requirements of stability and temperedness of interactions. The energy turns…
Entanglement is one of the most striking features of quantum mechanics, and yet it is not specifically quantum. More specific to quantum mechanics is the connection between entanglement and thermodynamics, which leads to an identification…
We develop a martingale theory to describe fluctuations of entropy production for open quantum systems in nonequilbrium steady states. Using the formalism of quantum jump trajectories, we identify a decomposition of entropy production into…
In this paper we study Spectral Decomposition Theorem [1] and translate it to quantum language by means of the Wigner transform. We obtain a quantum version of Spectral Decomposition Theorem (QSDT) which enables us to achieve three distinct…
It is an established fact that quantum coherences have thermodynamic value. The natural question arises, whether other genuine quantum properties such as entanglement can also be exploited to extract thermodynamic work. In the present…
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…
In ergodic physical systems, time-averaged quantities converge (for large times) to their ensemble-averaged values. Large deviation theory describes rare events where these time averages differ significantly from the corresponding ensemble…
The diagonal ensemble is the infinite time average of a quantum state following unitary dynamics. In analogy to the time average of a classical phase space dynamics, it is intimately related to the ergodic properties of the quantum system…