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.

When Does Episodic Memory Contribute to Performance in Tests of Working Memory?

Both the experimental and the psychometric investigation of the WM capacity limit depend critically on the assumption that performance in our tests of WM reflects that capacity limit to a good approximation. Most tasks to measure WM rely on testing memory after a short time during which participants are asked to maintain information in WM. In these tests, episodic long-term memory is likely to also lay down a trace of the memory set. Therefore, participants can draw on two sources of information when memory is tested, making it difficult to separate the contributions of WM and episodic LTM to the performance on immediate-memory tests. Here we use proactive interference to distinguish between these two sources of remembered information, building on the fact that episodic memory is vulnerable to proactive interference, whereas WM is protected against it. We use a release-from-PI paradigm to determine the extent to which commonly used WM tasks reflect contributions from episodic LTM. We focus on memory for serial order of verbal lists, but also include visual and spatial WM tasks. The results of five experiments demonstrate that although some tasks used to investigate WM are heavily contaminated by episodic LTM, other popular paradigms such as serial and probed recall, and the standard version of the continuous color-reproduction task, are not. Measuring proactive interference can help researchers determine the extent to which WM and episodic LTM contribute to performance in immediate-memory tasks

Delayed memory for complex visual stimuli does not benefit from distraction during encoding

The covert retrieval model (McCabe, Journal of Memory and Language 58(2), 480–494, 2008) postulates that delayed memory performance is enhanced when the encoding of memoranda in working memory (WM) is interrupted by distraction. When subjects are asked to remember stimuli for an immediate memory test, they usually remember them better when the items are presented without distraction, compared to a condition in which a distraction occurs following each item. In a delayed memory test, this effect has been shown to be reversed: Memory performance is better for items followed by distraction than without. Yet, this so-called McCabe effect has not been consistently replicated in the past. In an extensive replication attempt of a previous study showing the effect for complex visual stimuli, we investigated five potential boundary conditions of the predictions of the covert retrieval model: (1) Type of Stimuli (doors vs. faces), (2) type of distractor (pictures vs. math equations), (3) expectation about task difficulty (mixed vs. blocked lists), (4) memory load in WM (small vs. large), and (5) expectation about the long-term memory (LTM) test (intentional vs. incidental encoding). Across four experiments we failed to replicate the original findings and show that delayed memory for faces and other complex visual stimuli does not benefit from covert retrieval during encoding – as suggested as being induced by distractors. Our results indicate that the transfer of information from WM to LTM does not seem to be influenced by covert retrieval processes, but rather that a fixed proportion of information is laid down as a more permanent trace

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