Related papers: An Ergodic Theorem for Quantum Counting Processes
A quantum-mechanical framework is set up to describe the full counting statistics of particles flowing between reservoirs in an open system under time-dependent driving. A symmetry relation is obtained which is the consequence of…
It is well known that quantum feedback can alter the dynamics of open quantum systems dramatically. In this paper, we show that non-ergodicity may be induced through quantum feedback and resultantly create system dynamics that have lasting…
We extend the Nonconventional Ergodic Theorem for generic measures by Furstenberg, to several situations of interest arising from quantum dynamical systems. We deal with the diagonal state canonically associated to the product state (i.e.…
Given pseudo-random binary sequence of length $L$, assuming it consists of $k$ sub-sequences of length $N$. We estimate how $k$ scales with growing $N$ to obtain a {\it limiting} ergodic behaviour, to fulfill the basic definition of…
In this paper I propose a new way for counting the microstates of a system out of equilibrium. As, according to quantum mechanics, things happen as if a given particle can be found in more than one state at once, I extend this concept to…
We give a generalization of the ergodic theorem for semi-Markov linear-type processes. This generalization is proved for the case when a common support of distributions defining this process is not arithmetic. Also we give an uniform…
The work distribution is a fundamental quantity in nonequilibrium thermodynamics mainly due to its connection with fluctuations theorems. Here we develop a semiclassical approximation to the work distribution for a quench process in chaotic…
Our knowledge of quantum mechanics can satisfactorily describe simple, microscopic systems, but is yet to explain the macroscopic everyday phenomena we observe. Here we aim to shed some light on the quantum-to-classical transition as seen…
We derive the first two moments of generic positive stochastic functionals in terms of the one- and two-time probability density functions of the underlying random walk, and we prove ergodicity of observables in stationary random walks.…
Quantum electrodynamics under conditions of distinguishability of interacting matter entities, and of controlled actions and back-actions between them, is considered. Such "mesoscopic quantum electrodynamics" is shown to share its dynamical…
We discuss Shnirelman's Quantum Ergodicity Theorem, giving an outline of a proof and an overview of some of the recent developments in mathematical Quantum Chaos.
This paper contains a very simple and general proof that eigenfunctions of quantizations of classically ergodic systems become uniformly distributed in phase space. This ergodicity property of eigenfunctions f is shown to follow from a…
If an experimentalist observes a sequence of emitted quantum states via either projective or positive-operator-valued measurements, the outcomes form a time series. Individual time series are realizations of a stochastic process over the…
We show that quantum computation can be performed in a system at thermal equilibrium if a spontaneous symmetry breaking occurs. The computing process is associated to the time evolution of the statistical average of the qubit coherence…
Conventionally the total correlations within a quantum system are quantified through distance-based expressions such as the relative entropy or the square-norm. Those expressions imply that a quantum state can contain both classical and…
We show how the concept of quantum open system and the methods in non-equilibrium statistical mechanics can be usefully applied to studies of quantum statistical processes in the early universe. We first sketch how noise, fluctuation,…
Performance of quantum process estimation is naturally limited to fundamental, random, and systematic imperfections in preparations and measurements. These imperfections may lead to considerable errors in the process reconstruction due to…
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 description of an open quantum system's decay almost always requires several approximations as to remain tractable. Here, we first revisit the meaning, domain and seeming contradictions of a few of the most widely used of such…
Dynamical ensembles have been introduced to study constrained stochastic processes. In the microcanonical ensemble, the value of a dynamical observable is constrained to a given value. In the canonical ensemble a bias is introduced in the…