539 research outputs found
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
is the level index, is essentially the same as that of Bloch electrons in a
tight binding model, where 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
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