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- 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)

We combine earlier investigations of linear systems with Lévy fluctuations [Physica 113A, 203, (1982)] with recent discussions of Lévy flights in external force fields [Phys.Rev. E 59,2736, (1999)]. 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… (More)

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

- 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. ∗Supported by the KBN research grant No 2 P03B 086 16

We analyze the unforced and deterministically forced Burgers equation in the framework of the (diffusive) interpolating dynamics that solves the socalled 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)

- R Gielerak, L Jakóbczyk, R Olkiewicz
- 1997

We consider quasi-free stochastically positive ground and thermal states on Weyl algebras in Euclidean time formulation. In particular, we obtain a new derivation of a general form of thermal quasi-free state and give conditions when such state is stochastically positive i.e. when it defines periodic stochastic process with respect to Euclidean time, so… (More)

- 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 isometricsweeping 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 classical… (More)

In the paper with the above title, D. T. Gillespie [Phys. Rev. A 49, 1607, (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… (More)

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

- Ph Blanchard, R Olkiewicz
- Physical review letters
- 2003

We investigate the reduced dynamics in the Markovian approximation of an infinite quantum spin system linearly coupled to a phonon field at positive temperature. The achieved diagonalization leads to a selection of the continuous family of pointer states corresponding to a configuration space of the one-dimensional Ising model. Such a family provides a… (More)