Decoherence induced continuous pointer states

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 mathematical description of an apparatus with continuous readings.Comment: 8 page

Nonnegative Feynman-Kac Kernels in Schr\"{o}dinger's Interpolation Problem

The existing formulations of the Schr\"{o}dinger interpolating dynamics, which is constrained by the prescribed input-output statistics data, utilize strictly positive Feynman-Kac kernels. This implies that the related Markov diffusion processes admit vanishing probability densities only at the boundaries of the spatial volume confining the process. We extend the framework to encompass singular potentials and associated nonnegative Feynman-Kac-type kernels. It allows to deal with general nonnegative solutions of the Schr\"{o}dinger boundary data problem. The resulting stochastic processes are capable of both developing and destroying nodes (zeros) of probability densities in the course of their evolution.Comment: Latex file, 25 p

Structure of the Algebra of Effective Observables in Quantum Mechanics

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

Stochastically positive structures on Weyl algebras. The case of quasi-free states

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 called thermal process. Then we show that thermal process completely determines modular structure canonically associated with quasi-free state on Weyl algebra. We discuss a variety of examples connected with free field theories on globally hyperbolic stationary space-times and models of quantum statistical mechanics.Comment: 46 pages, amste

Diffractive energy spreading and its semiclassical limit

We consider driven systems where the driving induces jumps in energy space: (1) particles pulsed by a step potential; (2) particles in a box with a moving wall; (3) particles in a ring driven by an electro-motive-force. In all these cases the route towards quantum-classical correspondence is highly non-trivial. Some insight is gained by observing that the dynamics in energy space, where $n$ is the level index, is essentially the same as that of Bloch electrons in a tight binding model, where $n$ is the site index. The mean level spacing is like a constant electric field and the driving induces long range hopping 1/(n-m).Comment: 19 pages, 11 figs, published version with some improved figure

Unitarity as preservation of entropy and entanglement in quantum systems

The logical structure of Quantum Mechanics (QM) and its relation to other fundamental principles of Nature has been for decades a subject of intensive research. In particular, the question whether the dynamical axiom of QM can be derived from other principles has been often considered. In this contribution, we show that unitary evolutions arise as a consequences of demanding preservation of entropy in the evolution of a single pure quantum system, and preservation of entanglement in the evolution of composite quantum systems.Comment: To be submitted to the special issue of Foundations of Physics on the occassion of the seventieth birthday of Emilio Santos. v2: 10 pages, no figures, RevTeX4; Corrected and extended version, containing new results on consequences of entanglement preservatio

Completely Mixing Quantum Open Systems and Quantum Fractals

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 spin components is shown to lead to a chaotic jump on quantum spin sphere and to generate specific fractal images - nonlinear ifs (iterated function system). The model is purely theoretical at this stage, and experimental confirmation of the chaotic behavior of measuring instruments during simultaneous continuous measurement of several noncommuting quantum observables would constitute a quantitative verification of Event Enhanced Quantum Theory.Comment: Latex format, 20 pages, 6 figures in jpg format. New replacement has two more references (including one to a paper by G. Casati et al on quantum fractal eigenstates), adds example and comments concerning mixing properties of of a two-level atom driven by a laser field, and also adds a number of other remarks which should make it easier to follow mathematical argument