Ray chaos in optical cavities based upon standard laser mirrors

We present a composite optical cavity made of standard laser mirrors; the cavity consists of a suitable combination of stable and unstable cavities. In spite of its very open nature the composite cavity shows ray chaos, which may be either soft or hard, depending on the cavity configuration. This opens a new, convenient route for experimental studies of the quantum aspects of a chaotic wave field.Comment: 4 pages, 3 figures, 1 tabl

Detection methods for non-Gaussian gravitational wave stochastic backgrounds

We address the issue of finding an optimal detection method for a discontinuous or intermittent gravitational wave stochastic background. Such a signal might sound something like popcorn popping. We derive an appropriate version of the maximum likelihood detection statistic, and compare its performance to that of the standard cross-correlation statistic both analytically and with Monte Carlo simulations. The maximum likelihood statistic performs better than the cross-correlation statistic when the background is sufficiently non-Gaussian. For both ground and space based detectors, this results in a gain factor, ranging roughly from 1 to 3, in the minimum gravitational-wave energy density necessary for detection, depending on the duty cycle of the background. Our analysis is exploratory, as we assume that the time structure of the events cannot be resolved, and we assume white, Gaussian noise in two collocated, aligned detectors. Before this detection method can be used in practice with real detector data, further work is required to generalize our analysis to accommodate separated, misaligned detectors with realistic, colored, non-Gaussian noise.Comment: 25 pages, 12 figures, submitted to physical review D, added revisions in response to reviewers comment

Spatial correlations in vote statistics: a diffusive field model for decision-making

We study the statistics of turnout rates and results of the French elections since 1992. We find that the distribution of turnout rates across towns is surprisingly stable over time. The spatial correlation of the turnout rates, or of the fraction of winning votes, is found to decay logarithmically with the distance between towns. Based on these empirical observations and on the analogy with a two-dimensional random diffusion equation, we propose that individual decisions can be rationalised in terms of an underlying "cultural" field, that locally biases the decision of the population of a given region, on top of an idiosyncratic, town-dependent field, with short range correlations. Using symmetry considerations and a set of plausible assumptions, we suggest that this cultural field obeys a random diffusion equation.Comment: 18 pages, 5 figures; added sociophysics references

Dark soliton states of Bose-Einstein condensates in anisotropic traps

Dark soliton states of Bose-Einstein condensates in harmonic traps are studied both analytically and computationally by the direct solution of the Gross-Pitaevskii equation in three dimensions. The ground and self-consistent excited states are found numerically by relaxation in imaginary time. The energy of a stationary soliton in a harmonic trap is shown to be independent of density and geometry for large numbers of atoms. Large amplitude field modulation at a frequency resonant with the energy of a dark soliton is found to give rise to a state with multiple vortices. The Bogoliubov excitation spectrum of the soliton state contains complex frequencies, which disappear for sufficiently small numbers of atoms or large transverse confinement. The relationship between these complex modes and the snake instability is investigated numerically by propagation in real time.Comment: 11 pages, 8 embedded figures (two in color

Spectral method for the time-dependent Gross-Pitaevskii equation with a harmonic trap

We study the numerical resolution of the time-dependent Gross-Pitaevskii equation, a non-linear Schroedinger equation used to simulate the dynamics of Bose-Einstein condensates. Considering condensates trapped in harmonic potentials, we present an efficient algorithm by making use of a spectral Galerkin method, using a basis set of harmonic oscillator functions, and the Gauss-Hermite quadrature. We apply this algorithm to the simulation of condensate breathing and scissors modes.Comment: 23 pages, 5 figure

Mean-field description of collapsing and exploding Bose-Einstein condensates

We perform numerical simulation based on the time-dependent mean-field Gross-Pitaevskii equation to understand some aspects of a recent experiment by Donley et al. on the dynamics of collapsing and exploding Bose-Einstein condensates of $^{85}$Rb atoms. They manipulated the atomic interaction by an external magnetic field via a Feshbach resonance, thus changing the repulsive condensate into an attractive one and vice versa. In the actual experiment they changed suddenly the scattering length of atomic interaction from positive to a large negative value on a pre-formed condensate in an axially symmetric trap. Consequently, the condensate collapses and ejects atoms via explosion. We find that the present mean-field analysis can explain some aspects of the dynamics of the collapsing and exploding Bose-Einstein condensates.Comment: 9 Latex pages, 10 ps and eps files, version accepted in Physical Review A, minor changes mad

Kondo effect in systems with dynamical symmetries

This paper is devoted to a systematic exposure of the Kondo physics in quantum dots for which the low energy spin excitations consist of a few different spin multiplets $|S_{i}M_{i}>$. Under certain conditions (to be explained below) some of the lowest energy levels $E_{S_{i}}$ are nearly degenerate. The dot in its ground state cannot then be regarded as a simple quantum top in the sense that beside its spin operator other dot (vector) operators ${\bf R}_{n}$ are needed (in order to fully determine its quantum states), which have non-zero matrix elements between states of different spin multiplets $\ne 0$. These "Runge-Lenz" operators do not appear in the isolated dot-Hamiltonian (so in some sense they are "hidden"). Yet, they are exposed when tunneling between dot and leads is switched on. The effective spin Hamiltonian which couples the metallic electron spin ${\bf s}$ with the operators of the dot then contains new exchange terms, $J_{n} {\bf s} \cdot {\bf R}_{n}$ beside the ubiquitous ones $J_{i} {\bf s}\cdot {\bf S}_{i}$. The operators ${\bf S}_{i}$ and ${\bf R}_{n}$ generate a dynamical group (usually SO(n)). Remarkably, the value of $n$ can be controlled by gate voltages, indicating that abstract concepts such as dynamical symmetry groups are experimentally realizable. Moreover, when an external magnetic field is applied then, under favorable circumstances, the exchange interaction involves solely the Runge-Lenz operators ${\bf R}_{n}$ and the corresponding dynamical symmetry group is SU(n). For example, the celebrated group SU(3) is realized in triple quantum dot with four electrons.Comment: 24 two-column page

Crossovers in Unitary Fermi Systems

Universality and crossover is described for attractive and repulsive interactions where, respectively, the BCS-BEC crossover takes place and a ferromagnetic phase transition is claimed. Crossovers are also described for optical lattices and multicomponent systems. The crossovers, universal parameters and phase transitions are described within the Leggett and NSR models and calculated in detail within the Jastrow-Slater approximation. The physics of ultracold Fermi atoms is applied to neutron, nuclear and quark matter, nuclei and electrons in solids whenever possible. Specifically, the differences between optical lattices and cuprates is discussed w.r.t. antiferromagnetic, d-wave superfluid phases and phase separation.Comment: 50 pages, 15 figures. Contribution to Lecture Notes in Physics "BCS-BEC crossover and the Unitary Fermi Gas" edited by W. Zwerge

Highly Charged Ions in Rare Earth Permanent Magnet Penning Traps

A newly constructed apparatus at the National Institute of Standards and Technology (NIST) is designed for the isolation, manipulation, and study of highly charged ions. Highly charged ions are produced in the NIST electron-beam ion trap (EBIT), extracted through a beamline that selects a single mass/charge species, then captured in a compact Penning trap. The magnetic field of the trap is generated by cylindrical NdFeB permanent magnets integrated into its electrodes. In a room-temperature prototype trap with a single NdFeB magnet, species including Ne10+ and N7+ were confined with storage times of order 1 second, showing the potential of this setup for manipulation and spectroscopy of highly charged ions in a controlled environment. Ion capture has since been demonstrated with similar storage times in a more-elaborate Penning trap that integrates two coaxial NdFeB magnets for improved B-field homogeneity. Ongoing experiments utilize a second-generation apparatus that incorporates this two-magnet Penning trap along with a fast time-of-flight MCP detector capable of resolving the charge-state evolution of trapped ions. Holes in the two-magnet Penning trap ring electrode allow for optical and atomic beam access. Possible applications include spectroscopic studies of one-electron ions in Rydberg states, as well as highly charged ions of interest in atomic physics, metrology, astrophysics, and plasma diagnostics.Comment: Proceedings of CDAMOP-2011, 13-16 Dec 2011, Delhi, India. To be published by Springer Verla