Central concepts in stationary quantum theory

W. F. G. Swann

E. Wolf

In Part I of this investigation [ WolfE., J. Opt. Soc. Am.72. 343 ( 1982)] new representations were introduced for the cross-spectral density of a steady-state source of any state of coherence. The central concept in that formulation was the notion of a coherent source mode (a natural mode of oscillation). In the present paper the theory is developed further and new representations are obtained for the cross-spectral densities of all orders, both of the source and of the field that the source generates. These representations involve only the previously introduced coherent source modes and the moments of certain random coefficients that characterize the statistical properties of the source. The results provide a new mathematical framework for analyzing coherence properties of all orders of stationary sources and of stationary fields. Some potential applications of the theory are mentioned.

Piotr Garbaczewski

We analyze manifestations of so-called information entropy production and the role of information dynamics in the Schrödinger picture quantum evolution. PACS numbers: 03.65.-w, 02.50.-r In a number of recent papers, [1]-[5] c.f. also [6]-[13], various links were disclosed between the concept of Fisher information in statistical inference theory (plus related indeterminacy-type inequalities) and localization properties of Schrödinger wave functions. Except for a brief notice in Ref. [13], no attention has been paid to the full-fledged Schrödinger quantum evolution and to the fact that a central role in the formalism is in fact played not by the Fisher information, but by the (formally related) concept of (configurational) information entropy production, which appears to be inseparably tied with the dynamics of quantum probability densities and the persistence of steady (stationary) states. Information theory concepts are normally introduced in the context of equilibrium and nonequlibrium statistical mechanics as natural tools for quantifying phase-space disorder (dynamical origin of increasing entropy, irreversibility and time arrow issues). However, their range of applicability

Gerald Rosen

Frigerio, Alberto, Vittorio Gorini

雅則 大矢, Dėnes Petz

I Entropies for Finite Quantum Systems.- 1 Fundamental Concepts.- 2 Postulates for Entropy and Relative Entropy.- 3 Convex Trace Functions.- II Entropies for General Quantum Systems.- 4 Modular Theory and Auxiliaries.- 5 Relative Entropy of States of Operator Algebras.- 6 From Relative Entropy to Entropy.- 7 Functionals of Entropy Type.- III Channeling Transformation and Coarse Graining.- 8 Channels and Their Transpose.- 9 Sufficient Channels and Measurements.- 10 Dynamical Entropy.- 11 Stationary Processes.- IV Perturbation Theory.- 12 Perturbation of States.- 13 Variational Expression of Perturbational Limits.- V Miscellanea.- 14 Central Limit and Quasi-free Reduction.- 15 Thermodynamics of Quantum Spin Systems.- 16 Entropic Uncertainty Relations.- 17 Temperley-Lieb Algebras and Index.- 18 Optical Communication Processes.