Characterizations of the automorphisms of Hilbert space effect algebras

In this paper we characterize the automorphisms of Hilbert space effect algebras by means of their preserving properties which concern certain relations and quantities appearing in quantum measurement theory.Comment: 15 pages. To appear in Commun. Math. Phy

Intrinsic time-uncertainties and decoherence: comparison of 4 models

Four models of energy decoherence are discussed from the common perspective of intrinsic time-uncertainty. The four authors -- Milburn, Adler, Penrose, and myself -- have four different approaches. The present work concentrates on their common divisors at the level of the proposed equations rather than at the level of the interpretations. General relationships between time-uncertainty and energy-decoherence are presented in both global and local sense. Global and local master equations are derived. (The local concept is favored.)Comment: 7pp, 2 figs; Talk given at International Workshop DICE2004 (Piombino, Sept 1-4, 2004); Minor changes in quotation

Non-Markovian Open Quantum Systems: Lorentzian from Markovian

As a general mission, reduced dynamics and master equations are advocated as alternative method and philosophy instead of Green functions, Kubo theory and the like. A smart reduction of the Lorentzian open system to the Markovian one (Imamoglu, 1994) is presented in simple terms.Comment: Originally in Hungarian, in "New Results in Quantum Optics and Electronics" eds. Zsuzsanna Heiner and K. Osvay (University of Szeged, Szeged, 2006) p147. This version strikes through the mistaken references to the Ohmic spectru

Essentially disjoint families, conflict free colorings and Shelah's Revised GCH

Using Shelah's revised GCH theorem we prove that if mu<beth_omega <= lambda are cardinals, then every mu-almost disjoint subfamily B of [lambda]^{beth_omega} is essentially disjoint, i.e. for each b from B there is a subset f(b) of b of size < |b| such that the family {b-f(b) b in B} is disjoint. We also show that if mu<=kappa<=lambda, and kappa is infinite, and (x) every mu-almost disjoint subfamily of [lambda]^kappa is essentially disjoint, then (xx) every mu-almost disjoint family B of subsets of lambda with |b|>=kappa for all b from B has a conflict-free colorings with kappa colors. Putting together these results we obtain that if mu<beth_omega<=lambda, then every mu-almost disjoint family B of subsets of lambda with |b|>=beth_omega for all b from B has a conflict-free colorings with beth_omega colors. To yield the above mentioned results we also need to prove a certain compactness theorem concerning singular cardinals.Comment: 10 pages, minor correction

Hybrid Quantum-Classical Master Equations

We discuss hybrid master equations of composite systems which are hybrids of classical and quantum subsystems. A fairly general form of hybrid master equations is suggested, its consistency is derived from the consistency of Lindblad quantum master equations. We emphasize that quantum measurement is a natural example of exact hybrid systems. We derive a heuristic hybrid master equation of time-continuous position measurementComment: 8pp, 2tabs, based on talk at Symp.on Quantum Theory: Advances and Problems - QTAP (V\"axj\"o, June 10-13, 2013

How to teach and think about spontaneous wave function collapse theories: not like before

A simple and natural introduction to the concept and formalism of spontaneous wave function collapse can and should be based on textbook knowledge of standard quantum state collapse and monitoring. This approach explains the origin of noise driving the paradigmatic stochastic Schr\"odinger equations of spontaneous localization of the wave function $\Psi$. It reveals, on the other hand, that these equations are empirically redundant and the master equations of the noise-averaged state $\hat\rho$ are the only empirically testable dynamics in current spontaneous collapse theories.Comment: Almost the published version p3-11 in "Collapse of the Wave Function", ed.: S Gao, Cambridge University Press, 201