K→2πK \to 2 \pi Decay in the Nambu-Jona-Lasinio Model

We study the $K \to 2 \pi$ decays using the $U_L(3) \times U_R(3)$ version of the Nambu-Jona-Lasinio model with the effective $\Delta S = 1$ nonleptonic weak interaction. The $\Delta I = {3/2}$ amplitude is in reasonable agreement with experimental data. On the other hand, the calculated $\Delta I = {1/2}$ amplitudes strongly depend on the mass of the low-lying scalar-isoscalar $\sigma$ meson, and therefore give a strong constraint on the parameters of the model.Comment: 10 pages, 3 Postscript figures, Talk given at YITP Workshp: From Hadronic Matter to Quark Matter: Evolving View of Hadronic Matter, Kyoto, Japan, Oct. 30-Nov. 1, 1994, to be published in Prog. Theor. Phys. Supp

Pattern-recalling processes in quantum Hopfield networks far from saturation

As a mathematical model of associative memories, the Hopfield model was now well-established and a lot of studies to reveal the pattern-recalling process have been done from various different approaches. As well-known, a single neuron is itself an uncertain, noisy unit with a finite unnegligible error in the input-output relation. To model the situation artificially, a kind of 'heat bath' that surrounds neurons is introduced. The heat bath, which is a source of noise, is specified by the 'temperature'. Several studies concerning the pattern-recalling processes of the Hopfield model governed by the Glauber-dynamics at finite temperature were already reported. However, we might extend the 'thermal noise' to the quantum-mechanical variant. In this paper, in terms of the stochastic process of quantum-mechanical Markov chain Monte Carlo method (the quantum MCMC), we analytically derive macroscopically deterministic equations of order parameters such as 'overlap' in a quantum-mechanical variant of the Hopfield neural networks (let us call "quantum Hopfield model" or "quantum Hopfield networks"). For the case in which non-extensive number $p$ of patterns are embedded via asymmetric Hebbian connections, namely, $p/N \to 0$ for the number of neuron $N \to \infty$ ('far from saturation'), we evaluate the recalling processes for one of the built-in patterns under the influence of quantum-mechanical noise.Comment: 10 pages, 3 figures, using jpconf.cls, Proc. of Statphys-Kolkata VI

Loopy belief propagation and probabilistic image processing

Estimation of hyperparameters by maximization of the marginal likelihood in probabilistic image processing is investigated by using the cluster variation method. The algorithms are substantially equivalent to generalized loopy belief propagation

Electronic structure of Ca1−x_{1-x}Srx_xVO3_3: a tale of two energy-scales

We investigate the electronic structure of Ca$_{1-x}$Sr$_x$VO$_3$ using photoemission spectroscopy. Core level spectra establish an electronic phase separation at the surface, leading to distinctly different surface electronic structure compared to the bulk. Analysis of the photoemission spectra of this system allowed us to separate the surface and bulk contributions. These results help us to understand properties related to two vastly differing energy-scales, namely the low energy-scale of thermal excitations (~$k_{B}T$) and the high-energy scale related to Coulomb and other electronic interactions.Comment: 4 pages and 3 figures. Europhysics Letters (appearing

Geometric Bremsstrahlung in the Early Universe

We discuss photon emission from particles decelerlated by the cosmic expansion. This can be interpretated as a kind of bremsstrahlung induced by the Universe geometry. In the high momentum limit its transition probability does not depend on detailed behavior of the expansion.Comment: 20 pages, No figure