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We combine earlier investigations of linear systems with Lévy fluc-We give a complete construction of the Ornstein-Uhlenbeck-Cauchy process as a fully computable model of an anomalous transport and a paradigm example of Doob's stable noise-supported Ornstein-Uhlenbeck process. Despite the nonexistence of all moments, we determine local characteristics… (More)

- Ph Blanchard, A Jadczyk, R Olkiewicz
- 2001

Departing from classical concepts of ergodic theory, formulated in terms of probability densities, measures describing the chaotic behavior and the loss of information in quantum open systems are proposed. As application we discuss the chaotic outcomes of continuous measurement processes in the EEQT framework. Simultaneous measurement of four noncommuting… (More)

- R. Olkiewicz
- 2000

A subclass of dynamical semigroups induced by the interaction of a quantum system with an environment is introduced. Such semigroups lead to the selection of a stable subalgebra of effective observables. The structure of this subalgebra is completely determined.

- Marek Miller, Robert Olkiewicz
- Open Syst. Inform. Dynam.
- 2015

We analyze the unforced and deterministically forced Burgers equation in the framework of the (diffusive) interpolating dynamics that solves the so-called Schrödinger boundary data problem for the random matter transport. This entails an exploration of the consistency conditions that allow to interpret dispersion of passive contaminants in the Burgers flow… (More)

We discuss a connection (and a proper place in this framework) of the un-forced and deterministically forced Burgers equation for local velocity fields of certain flows, with probabilistic solutions of the so-called Schrödinger interpolation problem. The latter allows to reconstruct the microscopic dynamics of the system from the available probability… (More)

We explore a connection of the deterministically forced Burgers equation for local velocity fields with probabilistic solutions of the Schrödinger boundary data problem. An issue of deducing the most likely interpolating dynamics from the given initial and terminal probability density data is here investigated to give account of the perturbation by external… (More)

- Marek Miller, Robert Olkiewicz
- Open Syst. Inform. Dynam.
- 2016

- Ph Blanchard, R Olkiewicz
- 2008

Notions of robust and " classical " states for an open quantum system are introduced and discussed in the framework of the isometric-sweeping decomposition of trace class operators. Using the predictability sieve proposed by Zurek, " quasi-classical " states are defined. A number of examples illustrating how the " quasi-classical " states correspond to… (More)

In the paper with the above title, D. (1994)] claims that the theory of Markov stochastic processes cannot provide an adequate mathematical framework for quantum mechanics. In conjunction with the specific quantum dynamics considered there, we give a general analysis of the associated dichotomic jump processes. If we assume that Gillespie's " measurement… (More)