相关论文: Ergodicity of Kusuoka measures on quantum trajecto…

In the analysis on self-similar fractal sets, the Kusuoka measure plays an important role (cf. \cite{kusuoka2}, \cite{kajino}, \cite{str3}). Here we investigate the Kusuoka measure from an ergodic theoretic viewpoint, seen as an invariant…

The experimental realization of successive non-demolition measurements on single microscopic systems brings up the question of ergodicity in Quantum Mechanics (QM). We investigate whether time averages over one realization of a single…

This paper contains two parts. In the first part, we study the ergodicity of periodic measures of random dynamical systems on a separable Banach space. We obtain that the periodic measure of the continuous time skew-product dynamical system…

Quantum trajectories are Markov processes describing the evolution of a quantum system subject to indirect measurements. They can be viewed as place dependent iterated function systems or the result of products of dependent and non…

This paper addresses law invariant coherent risk measures and their Kusuoka representations. By elaborating the existence of a minimal representation we show that every Kusuoka representation can be reduced to its minimal representation.…

Ergodicity of random dynamical systems with a periodic measure is obtained on a Polish space. In the Markovian case, the idea of Poincar\'e sections is introduced. It is proved that if the periodic measure is PS-ergodic, then it is ergodic.…

We give a sufficient condition for the ergodicity of the Lebesgue measure for an iterated function system of diffeomorphisms. This is done via the induced iterated function system on the space of continuum (which is called hyper-space). We…

This paper is concerned with ergodic properties of inhomogeneous Markov processes. Since the transition probabilities depend on initial times, the existing methods to obtain invariant measures for homogeneous Markov processes are not…

We consider the problem of ergodicity for the $P(\Phi)_2$ measure of quantum field theory under the flow of the singular stochastic (damped) wave equation $u_{tt} + u_t + (1-\Delta) u + {:}\,p(u)\mspace{2mu}{:} = \sqrt 2 \xi$, posed on the…

Quantum trajectories are Markov chains modeling quantum systems subjected to repeated indirect measurements. Their stationary regime depends on what observables are measured on the probes used to indirectly measure the system. In this…

In this paper we discuss how the notion of subgeometric ergodicity in Markov chain theory can be exploited to study stationarity and ergodicity of nonlinear time series models. Subgeometric ergodicity means that the transition probability…

The onset of quantum ergodicity is often quantified by the average ratio of consecutive level spacings. The reference values for ergodic quantum systems have been obtained numerically from the spectra of large but finite-dimensional random…

We study quantum measurement retrodiction using the principle of minimum change. For quantum-to-classical measurement channels, we show that all standard quantum divergences select the same retrodictive update, yielding a unique and…

We study a class of dynamical systems generated by random substitutions, which contains both intrinsically ergodic systems and instances with several measures of maximal entropy. In this class, we show that the measures of maximal entropy…

Measurements are able to fundamentally affect quantum dynamics. We here show that a continuously measured quantum many-body system can undergo a spontaneous transition from asynchronous stochastic dynamics to noise-free stable…

We investigate a tight binding quantum walk on a graph. Repeated stroboscopic measurements of the position of the particle yield a measured "trajectory", and a combination of classical and quantum mechanical properties for the walk are…

The problem of measurement in quantum mechanics is reanalyzed within a general, strictly probabilistic framework (without reduction postulate). Based on a novel comprehensive definition of measurement the natural emergence of objective…

Projective measurement is a commonly used assumption in quantum mechanics. However, advances in quantum measurement techniques allow for partial measurements, which accurately estimate state information while keeping the wavefunction…

The use of higher-order stochastic processes such as nonlinear Markov chains or vertex-reinforced random walks is significantly growing in recent years as they are much better at modeling high dimensional data and nonlinear dynamics in…

For a dynamical system satisfying the approximate product property and asymptotically entropy expansiveness, we characterize a delicate structrue of the space of invariant measures: The ergodic measures of intermediate entropies and…