General one-loop formulas for decay h→Zγh\rightarrow Z\gamma

Radiative corrections to the $h\rightarrow Z\gamma$ are evaluated in the one-loop approximation. The unitary gauge gauge is used. The analytic result is expressed in terms of the Passarino-Veltman functions. The calculations are applicable for the Standard Model as well for a wide class of its gauge extensions. In particular, the decay width of a charged Higgs boson $H^\pm \rightarrow W^\pm\gamma$ can be derived. The consistence of our formulas and several specific earlier results is shown.Comment: 33 pages, 3 figures, a new section (V) and references were improved in the published versio

Hamilton-Jacobi Theory and Information Geometry

Recently, a method to dynamically define a divergence function $D$ for a given statistical manifold $(\mathcal{M}\,,g\,,T)$ by means of the Hamilton-Jacobi theory associated with a suitable Lagrangian function $\mathfrak{L}$ on $T\mathcal{M}$ has been proposed. Here we will review this construction and lay the basis for an inverse problem where we assume the divergence function $D$ to be known and we look for a Lagrangian function $\mathfrak{L}$ for which $D$ is a complete solution of the associated Hamilton-Jacobi theory. To apply these ideas to quantum systems, we have to replace probability distributions with probability amplitudes.Comment: 8 page

A Moving Bump in a Continuous Manifold: A Comprehensive Study of the Tracking Dynamics of Continuous Attractor Neural Networks

Understanding how the dynamics of a neural network is shaped by the network structure, and consequently how the network structure facilitates the functions implemented by the neural system, is at the core of using mathematical models to elucidate brain functions. This study investigates the tracking dynamics of continuous attractor neural networks (CANNs). Due to the translational invariance of neuronal recurrent interactions, CANNs can hold a continuous family of stationary states. They form a continuous manifold in which the neural system is neutrally stable. We systematically explore how this property facilitates the tracking performance of a CANN, which is believed to have clear correspondence with brain functions. By using the wave functions of the quantum harmonic oscillator as the basis, we demonstrate how the dynamics of a CANN is decomposed into different motion modes, corresponding to distortions in the amplitude, position, width or skewness of the network state. We then develop a perturbative approach that utilizes the dominating movement of the network's stationary states in the state space. This method allows us to approximate the network dynamics up to an arbitrary accuracy depending on the order of perturbation used. We quantify the distortions of a Gaussian bump during tracking, and study their effects on the tracking performance. Results are obtained on the maximum speed for a moving stimulus to be trackable and the reaction time for the network to catch up with an abrupt change in the stimulus.Comment: 43 pages, 10 figure

Effect of conduction electron interactions on Anderson impurities

The effect of conduction electron interactions for an Anderson impurity is investigated in one dimension using a scaling approach. The flow diagrams are obtained by solving the renormalization group equations numerically. It is found that the Anderson impurity case is different from its counterpart -- the Kondo impurity case even in the local moment region. The Kondo temperature for an Anderson impurity shows nonmonotonous behavior, increasing for weak interactions but decreasing for strong interactions. The implication of the study to other related impurity models is also discussed.Comment: 10 pages, revtex, 4 figures (the postscript file is included), to appear in Phys. Rev. B (Rapid Commun.

Effect of growth conditions on optical properties of CdSe/ZnSe single quantum dots

In this work, we have investigated the optical properties of two samples of CdSe quantum dots by using submicro-photoluminescence spectroscopy. The effect of vicinal-surface GaAs substrates on their properties has been also assessed. The thinner sample, grown on a substrate with vicinal surface, includes only dots with a diameter of less than 10 nm (type A islands). Islands of an average diameter of about 16 nm (type B islands) that are related to a phase transition via a Stranski-Krastanow growth process are also distributed in the thicker sample grown on an oriented substrate. We have studied the evolution of lineshapes of PL spectra for these two samples by improving spatial resolution that was achieved using nanoapertures or mesa structures. It was found that the use of a substrate with the vicinal surface leads to the suppression of excitonic PL emitted from a wetting layer.Comment: 2pages, 2 figures, Proceedings of International Conference On Superlattices Nano-Structures And Nano-Devices, July, Toulouse, France, to appear in the special issue of Physica