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

Two-Step Electroweak Baryogenesis

We analyze electroweak baryogenesis during a two-step electroweak symmetry breaking transition, wherein the baryon asymmetry is generated during the first step and preserved during the second. Focusing on the dynamics of CP-violation required for asymmetry generation, we discuss general considerations for successful two-step baryogenesis. Using a concrete model realization, we illustrate in detail the viability of this scenario and the implications for present and future electric dipole moment (EDM) searches. We find that CP-violation associated with a partially excluded sector may yield the observed baryon asymmetry while evading present and future EDM constraints.Comment: 20 pages, 11 figure

Tunnel magnetoresistance and interfacial electronic state

We study the relation between tunnel magnetoresistance (TMR) and interfacial electronic states modified by magnetic impurities introduced at the interface of the ferromagnetic tunnel junctions, by making use of the periodic Anderson model and the linear response theory. It is indicated that the TMR ratio is strongly reduced depending on the position of the $d$-levels of impurities, based on reduction in the spin-dependent $s$-electron tunneling in the majority spin state. The results are compared with experimental results for Cr-dusted ferromagnetic tunnel junctions, and also with results for metallic multilayers for which similar reduction in giant magnetoresistance has been reported.Comment: 5 pages, 4 figures, 2 column revtex4 format, ICMFS 2002 (Kyoto

Toward an understanding of short distance repulsions among baryons in QCD -- NBS wave functions and operator product expansion --

We report on our recent attempts to determine the short distance behaviors of general 2-baryon and 3-baryon forces, which are defined from the Nambu-Bethe-Salpeter(NBS) wave function, by using the operator product expansion and a renormalization group analysis in QCD. We have found that the repulsion at short distance increases as the number of valence quarks increases or when the number of different flavors involved decreases. This global tendency suggests a Pauli suppression principle among quark fields at work.Comment: 14 pages, add two exmples in sect.3.4, a version accepted for Progress of Theoretical Physic

Non-dispersive optics using storage of light

We demonstrate the non-dispersive deflection of an optical beam in a Stern-Gerlach magnetic field. An optical pulse is initially stored as a spin-wave coherence in thermal rubidium vapour. An inhomogeneous magnetic field imprints a phase gradient onto the spin wave, which upon reacceleration of the optical pulse leads to an angular deflection of the retrieved beam. We show that the obtained beam deflection is non-dispersive, i.e. its magnitude is independent of the incident optical frequency. Compared to a Stern-Gerlach experiment carried out with propagating light under the conditions of electromagnetically induced transparency, the estimated suppression of the chromatic aberration reaches 10 orders of magnitude.Comment: 11 pages, 4 figures, accepted for publication in Physical Review