Open circular billiards and the Riemann hypothesis

A comparison of escape rates from one and from two holes in an experimental container (e.g. a laser trap) can be used to obtain information about the dynamics inside the container. If this dynamics is simple enough one can hope to obtain exact formulas. Here we obtain exact formulas for escape from a circular billiard with one and with two holes. The corresponding quantities are expressed as sums over zeroes of the Riemann zeta function. Thus we demonstrate a direct connection between recent experiments and a major unsolved problem in mathematics, the Riemann hypothesis.Comment: 5 pages, 4 embedded postscript figures; v2: more explicit on how the Reimann Hypothesis arises from a comparison of one and two hole escape rate

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.

Symmetry-breaking thermally induced collapse of dipolar Bose-Einstein condensates

We investigate a Bose-Einstein condensate with additional long-range dipolar interaction in a cylindrically symmetric trap within a variational framework. Compared to the ground state of this system, little attention has as yet been payed to its unstable excited states. For thermal excitations, however, the latter is of great interest, because it forms the "activated complex" that mediates the collapse of the condensate. For a certain value of the s-wave scatting length our investigations reveal a bifurcation in the transition state, leading to the emergence of two additional and symmetry-breaking excited states. Because these are of lower energy than their symmetric counterpart, we predict the occurrence of a symmetry-breaking thermally induced collapse of dipolar condensates. We show that its occurrence crucially depends on the trap geometry and calculate the thermal decay rates of the system within leading order transition state theory with the help of a uniform rate formula near the rank-2 saddle which allows to smoothly pass the bifurcation.Comment: 6 pages, 3 figure

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

Vector competence of Aedes aegypti, Culex tarsalis, and Culex quinquefasciatus from California for Zika virus.

Zika virus (ZIKV) has emerged since 2013 as a significant global human health threat following outbreaks in the Pacific Islands and rapid spread throughout South and Central America. Severe congenital and neurological sequelae have been linked to ZIKV infections. Assessing the ability of common mosquito species to transmit ZIKV and characterizing variation in mosquito transmission of different ZIKV strains is important for estimating regional outbreak potential and for prioritizing local mosquito control strategies for Aedes and Culex species. In this study, we evaluated the laboratory vector competence of Aedes aegypti, Culex quinquefasciatus, and Culex tarsalis that originated in areas of California where ZIKV cases in travelers since 2015 were frequent. We compared infection, dissemination, and transmission rates by measuring ZIKV RNA levels in cohorts of mosquitoes that ingested blood meals from type I interferon-deficient mice infected with either a Puerto Rican ZIKV strain from 2015 (PR15), a Brazilian ZIKV strain from 2015 (BR15), or an ancestral Asian-lineage Malaysian ZIKV strain from 1966 (MA66). With PR15, Cx. quinquefasciatus was refractory to infection (0%, N = 42) and Cx. tarsalis was infected at 4% (N = 46). No ZIKV RNA was detected in saliva from either Culex species 14 or 21 days post feeding (dpf). In contrast, Ae. aegypti developed infection rates of 85% (PR15; N = 46), 90% (BR15; N = 20), and 81% (MA66; N = 85) 14 or 15 dpf. Although MA66-infected Ae. aegypti showed higher levels of ZIKV RNA in mosquito bodies and legs, transmission rates were not significantly different across virus strains (P = 0.13, Fisher's exact test). To confirm infectivity and measure the transmitted ZIKV dose, we enumerated infectious ZIKV in Ae. aegypti saliva using Vero cell plaque assays. The expectorated plaque forming units PFU varied by viral strain: MA66-infected expectorated 13±4 PFU (mean±SE, N = 13) compared to 29±6 PFU for PR15-infected (N = 13) and 35±8 PFU for BR15-infected (N = 6; ANOVA, df = 2, F = 3.8, P = 0.035). These laboratory vector competence results support an emerging consensus that Cx. tarsalis and Cx. quinquefasciatus are not vectors of ZIKV. These results also indicate that Ae. aegypti from California are efficient laboratory vectors of ancestral and contemporary Asian lineage ZIKV

Diffusion Monte Carlo calculations for the ground states of atoms and ions in neutron star magnetic fields

The diffusion quantum Monte Carlo method is extended to solve the old theoretical physics problem of many-electron atoms and ions in intense magnetic fields. The feature of our approach is the use of adiabatic approximation wave functions augmented by a Jastrow factor as guiding functions to initialize the quantum Monte Carlo prodecure. We calcula te the ground state energies of atoms and ions with nuclear charges from Z= 2, 3, 4, ..., 26 for magnetic field strengths relevant for neutron stars.Comment: 6 pages, 1 figure, proceedings of the "9th International Conference on Path Integrals - New Trends and Perspectives", Max-Planck-Institut fur Physik komplexer Systeme, Dresden, Germany, September 23 - 28, 2007, to be published as a book by World Scientific, Singapore (2008