Semiclassical quantization of the hydrogen atom in crossed electric and magnetic fields

The S-matrix theory formulation of closed-orbit theory recently proposed by Granger and Greene is extended to atoms in crossed electric and magnetic fields. We then present a semiclassical quantization of the hydrogen atom in crossed fields, which succeeds in resolving individual lines in the spectrum, but is restricted to the strongest lines of each n-manifold. By means of a detailed semiclassical analysis of the quantum spectrum, we demonstrate that it is the abundance of bifurcations of closed orbits that precludes the resolution of finer details. They necessitate the inclusion of uniform semiclassical approximations into the quantization process. Uniform approximations for the generic types of closed-orbit bifurcation are derived, and a general method for including them in a high-resolution semiclassical quantization is devised

The hydrogen atom in an electric field: Closed-orbit theory with bifurcating orbits

Closed-orbit theory provides a general approach to the semiclassical description of photo-absorption spectra of arbitrary atoms in external fields, the simplest of which is the hydrogen atom in an electric field. Yet, despite its apparent simplicity, a semiclassical quantization of this system by means of closed-orbit theory has not been achieved so far. It is the aim of this paper to close that gap. We first present a detailed analytic study of the closed classical orbits and their bifurcations. We then derive a simple form of the uniform semiclassical approximation for the bifurcations that is suitable for an inclusion into a closed-orbit summation. By means of a generalized version of the semiclassical quantization by harmonic inversion, we succeed in calculating high-quality semiclassical spectra for the hydrogen atom in an electric field

Bubble concentration on spheres for supercritical elliptic problems

We consider the supercritical Lane-Emden problem (P_\eps)\qquad -\Delta v= |v|^{p_\eps-1} v \ \hbox{in}\ \mathcal{A} ,\quad u=0\ \hbox{on}\ \partial\mathcal{A} where $\mathcal A$ is an annulus in \rr^{2m}, $m\ge2$ and p_\eps={(m+1)+2\over(m+1)-2}-\eps, \eps>0. We prove the existence of positive and sign changing solutions of (P_\eps) concentrating and blowing-up, as \eps\to0, on $(m-1)-$dimensional spheres. Using a reduction method (see Ruf-Srikanth (2010) J. Eur. Math. Soc. and Pacella-Srikanth (2012) arXiv:1210.0782)we transform problem (P_\eps) into a nonhomogeneous problem in an annulus \mathcal D\subset \rr^{m+1} which can be solved by a Ljapunov-Schmidt finite dimensional reduction

Reaction rate calculation with time-dependent invariant manifolds

The identification of trajectories that contribute to the reaction rate is the crucial dynamical ingredient in any classical chemical reactivity calculation. This problem often requires a full scale numerical simulation of the dynamics, in particular if the reactive system is exposed to the influence of a heat bath. As an efficient alternative, we propose here to compute invariant surfaces in the phase space of the reactive system that separate reactive from nonreactive trajectories. The location of these invariant manifolds depends both on time and on the realization of the driving force exerted by the bath. These manifolds allow the identification of reactive trajectories simply from their initial conditions, without the need of any further simulation. In this paper, we show how these invariant manifolds can be calculated, and used in a formally exact reaction rate calculation based on perturbation theory for any multidimensional potential coupled to a noisy environment

Constraints on B--->pi,K transition form factors from exclusive semileptonic D-meson decays

According to the heavy-quark flavour symmetry, the $B\to \pi, K$ transition form factors could be related to the corresponding ones of D-meson decays near the zero recoil point. With the recent precisely measured exclusive semileptonic decays $D \to \pi \ell \nu$ and $D\to K \ell \nu$, we perform a phenomenological study of $B \to \pi, K$ transition form factors based on this symmetry. Using BK, BZ and Series Expansion parameterizations of the form factor slope, we extrapolate $B \to \pi, K$ transition form factors from $q^{2}_{max}$ to $q^{2}=0$. It is found that, although being consistent with each other within error bars, the central values of our results for $B \to \pi, K$ form factors at $q^2=0$, $f_+^{B\to \pi, K}(0)$, are much smaller than predictions of the QCD light-cone sum rules, but are in good agreements with the ones extracted from hadronic B-meson decays within the SCET framework. Moreover, smaller form factors are also favored by the QCD factorization approach for hadronic B-meson decays.Comment: 19 pages, no figure, 5 table

Photoabsorption spectra of the diamagnetic hydrogen atom in the transition regime to chaos: Closed orbit theory with bifurcating orbits

With increasing energy the diamagnetic hydrogen atom undergoes a transition from regular to chaotic classical dynamics, and the closed orbits pass through various cascades of bifurcations. Closed orbit theory allows for the semiclassical calculation of photoabsorption spectra of the diamagnetic hydrogen atom. However, at the bifurcations the closed orbit contributions diverge. The singularities can be removed with the help of uniform semiclassical approximations which are constructed over a wide energy range for different types of codimension one and two catastrophes. Using the uniform approximations and applying the high-resolution harmonic inversion method we calculate fully resolved semiclassical photoabsorption spectra, i.e., individual eigenenergies and transition matrix elements at laboratory magnetic field strengths, and compare them with the results of exact quantum calculations.Comment: 26 pages, 9 figures, submitted to J. Phys.

Tests of silicon sensors for the CMS pixel detector

The tracking system of the CMS experiment, currently under construction at the Large Hadron Collider (LHC) at CERN (Geneva, Switzerland), will include a silicon pixel detector providing three spacial measurements in its final configuration for tracks produced in high energy pp collisions. In this paper we present the results of test beam measurements performed at CERN on irradiated silicon pixel sensors. Lorentz angle and charge collection efficiency were measured for two sensor designs and at various bias voltages.Comment: Talk presented at 6th International Conference on Large Scale Applications and Radiation Hardness of Semiconductor Detectors, September 29-October 1, 2003, Firenze, Italy. Proceedings will be published in Nuclear Instr. & Methods in Phys. Research, Section

Transient fluctuation theorem in closed quantum systems

Our point of departure are the unitary dynamics of closed quantum systems as generated from the Schr\"odinger equation. We focus on a class of quantum models that typically exhibit roughly exponential relaxation of some observable within this framework. Furthermore, we focus on pure state evolutions. An entropy in accord with Jaynes principle is defined on the basis of the quantum expectation value of the above observable. It is demonstrated that the resulting deterministic entropy dynamics are in a sense in accord with a transient fluctuation theorem. Moreover, we demonstrate that the dynamics of the expectation value are describable in terms of an Ornstein-Uhlenbeck process. These findings are demonstrated numerically and supported by analytical considerations based on quantum typicality.Comment: 5 pages, 6 figure

Chunking, boosting, or offloading? Using serial position to investigate long-term memory's enhancement of verbal working memory performance

Individuals can use information stored in episodic long-term memory (LTM) to optimize performance in a working memory (WM) task, and the WM system negotiates the exchange of information between WM and LTM depending on the current memory load. In this study, we assessed the ability of different accounts of interactions between LTM and WM to explain these findings, by investigating whether the position of pre-learnt information within a memory list encoded into WM affects the benefit it provides to immediate memory. In two experiments we varied the input position of previously learned word-word pairs within a set of four to-be-remembered pairs. We replicated previous findings of superior performance when these LTM pairs were included in the WM task and show that the position in the list in which these LTM pairs were included not seem to matter. These results are most consistent with the idea that having access to information in LTM reduces or removes the need to rely on WM for its storage, implying that people “offload” information in conditions containing LTM pairs