Entropy Distance: New Quantum Phenomena

We study a curve of Gibbsian families of complex 3x3-matrices and point out new features, absent in commutative finite-dimensional algebras: a discontinuous maximum-entropy inference, a discontinuous entropy distance and non-exposed faces of the mean value set. We analyze these problems from various aspects including convex geometry, topology and information geometry. This research is motivated by a theory of info-max principles, where we contribute by computing first order optimality conditions of the entropy distance.Comment: 34 pages, 5 figure

Conceptual Design Of Instrumentation To Measure The Diffraction Profile Of A Single Crystal At Bragg Angle Near π 2 By Using Synchrotron Radiation

X-ray diffraction at nearly normal incidence is becoming an increasing important tool in several applications. Because the source of synchrotron radiation, an electron beam in a magnetic field in vacuum, is transparent to X-rays back-reflected through it, one can measure X-ray profiles at normal and near-normal incidence. A back-tangent port must be provided to allow a back-reflected beam to leave the storage ring. The concept can be applied to a bending-magnet or insertion-device source. Since the back-reflected beam is a low-power monochromatic beam, the front end, beryllium window, and other components of the back-tangent port can be simplified. It may be possible to merely drill a hole through the concrete shielding wall leading into a hutch for the detector. Possible arrangements for the SPEAR and Positron-Electron Project rings at the Stanford Synchrotron Radiation Laboratory (SSRL) are presented. © 1990.2911-2132134Woodruff, Seymour, McConville, Riley, Crapper, Prince, Jones, (1987) Phys. Rev. Lett., 58, p. 1460Woodruff, Seymour, McConville, Riley, Crapper, Prince, Jones, (1988) Surf. Sci., 195, p. 237Caticha, Caticha-Ellis, (1982) Phys. Rev., 25 B, p. 971Caticha, Caticha-Ellis, Free Electron Generation of Extreme Ultraviolet Coherent Radiation (1984) AIP Conf. Proc., 118, p. 220. , J.M.J. Madey, C. Pellegrini, AIP, New YorkCaticha, Caticha, Caticha-Ellis, (1989) Appl. Phys. Lett., 54, p. 887Graeff, Materlik, (1982) Nucl. Instr. and Meth., 195, p. 97Kushnir, Suvorov, (1986) JEPT Lett., 44, p. 262Caticha-Ellis, (1983) Anais do Encontro Tecnicas e aplic\̃~aoes da Radiac\̃~ao Sincrotron, pp. 240-257. , (in Portuguese), CBPF, Rio de JaneiroHoyer, A new wiggler beam line for SSRL (1983) Nuclear Instruments and Methods in Physics Research, 208, p. 117A. Bienenstock, G. Brown, H. Wiedemann and H. Winick, Rev. Sci. Instr. to be publishe