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In the spectral analysis of few one dimensional quantum particles interacting through delta potentials it is well known that one can recast the problem into the spectral analysis of an integral operator (the skeleton) living on the submanifold which supports the delta interactions. We shall present several tools which allow direct insight into the spectral structure of this skeleton. We shall illustrate the method on a model of a two dimensional quantum particle interacting with two infinitely long straight wires which cross one another at a certain angle : the quantum scissor., Comment: Submitted

We study the dynamics of a 1D Bloch electron subjected to a constant electric field. The periodic potential is supposed to be less singular than the $\delta $-like potential (Dirac comb). We give a rigorous proof of Ao's result \cite{Ao} that for a large class of initial conditions (high momentum regime) there is no localization in momentum space. The proof is based on the mathematical substantiation of the two simplifying assumptions made in physical literature: the transitions between far away bands can be neglected and the transitions at the quasi-crossing can be described by Landau-Zener like formulae. Using the connection between the above model and the driven quantum ring (DQR) shown by Avron and Nemirovski \cite{AvN}, our results imply the increase of energy for weakly singular such DQR and appropiate initial conditions., Comment: 51 pages, 1 figure

Although vaccines are among the safest of pharmaceuticals, the occasional severe adverse event or cluster of adverse events associated with their use may rapidly become a serious threat to public health. It is essential that national monitoring and reporting systems for vaccine safety are efficient and adequately coordinated with those that conventionally deal with non-vaccine pharmaceuticals. Equally important is the need for an enlightened and informed national system to be in place to deal with public concerns and rapid evaluation of the risk to public safety when adverse events occur. Described in this article is the outcome of efforts by the WHO Global Training Network to describe a simple national system for dealing with vaccine safety and with emergencies as they arise. The goals of a training programme designed to help develop such a system are also outlined.

We consider a quantum particle constrained to a curved layer of a constant width built over an infinite smooth surface. We suppose that the latter is a locally deformed plane and that the layer has the hard-wall boundary. Under this assumptions we prove that the particle Hamiltonian possesses geometrically induced bound states., Comment: LaTeX2e, 15 pages, to appear in the Ukrainian J. Phys., Bogolyubov Memorial Issue

We consider curvature-induced resonances in a planar two-dimensional Dirichlet tube of a width $ d $. It is shown that the distances of the corresponding resonance poles from the real axis are exponentially small as $ d\to 0+ $, provided the curvature of the strip axis satisfies certain analyticity and decay requirements., Comment: LaTeX2.09, 30 pages, 3 figures, to appear in Helv. Phys. Acta

We consider a perturbed Floquet Hamiltonian $-i\partial_t + H + \beta V(\omega t)$ in the Hilbert space $L^2([0,T],E,dt)$. Here $H$ is a self-adjoint operator in $E$ with a discrete spectrum obeying a growing gap condition, $V(t)$ is a symmetric bounded operator in $E$ depending on $t$ $2\pi$-periodically, $\omega = 2\pi/T$ is a frequency and $\beta$ is a coupling constant. The spectrum $Spec(-i\partial_t + H)$ of the unperturbed part is pure point and dense in $R$ for almost every $\omega$. This fact excludes application of the regular perturbation theory. Nevertheless we show, for almost all $\omega$ and provided $V(t)$ is sufficiently smooth, that the perturbation theory still makes sense, however, with two modifications. First, the coupling constant is restricted to a set $I$ which need not be an interval but 0 is still a point of density of $I$. Second, the Rayleigh-Schrodinger series are asymptotic to the perturbed eigen-value and the perturbed eigen-vector., Comment: AmsTex, 45 pages

We give a partial review of what is known so far on stability of periodically driven quantum systems versus regularity of the bounded driven force. In particular we emphasize the fact that unbounded degeneracies of the unperturbed Hamiltonian are allowed. Then we give a detailed description of an extension to some unbounded driven forces. This is done by representing the Schroedinger equation in the instantaneous basis of the time dependent Hamiltonian with a method that we call progressive diagonalization., 16 pages, Latex2e