Continuity of the Maximum-Entropy Inference

We study the inverse problem of inferring the state of a finite-level quantum system from expected values of a fixed set of observables, by maximizing a continuous ranking function. We have proved earlier that the maximum-entropy inference can be a discontinuous map from the convex set of expected values to the convex set of states because the image contains states of reduced support, while this map restricts to a smooth parametrization of a Gibbsian family of fully supported states. Here we prove for arbitrary ranking functions that the inference is continuous up to boundary points. This follows from a continuity condition in terms of the openness of the restricted linear map from states to their expected values. The openness condition shows also that ranking functions with a discontinuous inference are typical. Moreover it shows that the inference is continuous in the restriction to any polytope which implies that a discontinuity belongs to the quantum domain of non-commutative observables and that a geodesic closure of a Gibbsian family equals the set of maximum-entropy states. We discuss eight descriptions of the set of maximum-entropy states with proofs of accuracy and an analysis of deviations.Comment: 34 pages, 1 figur

The set of photoelectromagnetic methods for determination of recombination and diffusion parameters of p-MCT thin films

In this paper the set of photoelectromagnetic methods for determination of recombination and diffusion parameters of charge carriers in p-type mercury cadmium telluride epitaxial thin films at temperature range 77–125 K is offered. The set of methods includes the photoconductivity in magnetic field for Faraday and Voigt geometries, the photoelectromagnetic effect, the Hall effect and the measurements of magnetoconductivity. Such films parameters as concentrations and mobilities of heavy and light holes, mobility of minor electrons, electrons lifetime and ratio between holes and electrons lifetimes, surface recombination velocities can be determined with help of offered set

Stability of linear problems: joint spectral radius of sets of matrices

It is wellknown that the stability analysis of step-by-step numerical methods for differential equations often reduces to the analysis of linear difference equations with variable coefficients. This class of difference equations leads to a family F of matrices depending on some parameters and the behaviour of the solutions depends on the convergence properties of the products of the matrices of F. To date, the techniques mainly used in the literature are confined to the search for a suitable norm and for conditions on the parameters such that the matrices of F are contractive in that norm. In general, the resulting conditions are more restrictive than necessary. An alternative and more effective approach is based on the concept of joint spectral radius of the family F, r(F). It is known that all the products of matrices of F asymptotically vanish if and only if r (F) < 1. The aim of this chapter is that to discuss the main theoretical and computational aspects involved in the analysis of the joint spectral radius and in applying this tool to the stability analysis of the discretizations of differential equations as well as to other stability problems. In particular, in the last section, we present some recent heuristic techniques for the search of optimal products in finite families, which constitute a fundamental step in the algorithms which we discuss. The material we present in the final section is part of an original research which is in progress and is still unpublished