Properties of the stochastic Gross-Pitaevskii equation: Projected Ehrenfest relations and the optimal plane wave basis

We investigate the properties of the stochastic Gross-Pitaevskii equation describing a condensate interacting with a stationary thermal cloud derived by Gardiner and coworkers. We find the appropriate Ehrenfest relations for the SGPE, including the effect of growth noise and projector terms arising from the energy cutoff. This is carried out in the high temperature regime appropriate for the SGPE, which simplifies the action of the projectors. The validity condition for neglecting the projector terms in the Ehrenfest relations is found to be more stringent than the usual condition of validity of the truncated Wigner method or classical field method -- which is that all modes are highly occupied. In addition it is required that the overlap of the nonlinear term with the lowest energy eigenstate of the non-condensate band is small. We show how to use the Ehrenfest relations along with the corrections generated by the projector to monitor dynamical artifacts arising from the cutoff. We also investigate the effect of using different bases to describe a harmonically trapped BEC at finite temperature by comparing the condensate fraction found using the plane wave and single particle bases. We show that the equilibrium properties are strongly dependent on the choice of basis. There is thus an optimal choice of plane wave basis for a given cut-off energy and we show that this basis gives the best reproduction of the single particle spectrum, the condensate fraction and the position and momentum densities.Comment: 23 pages, 5 figure

NEW PALAEOZOIC FISH REMAINS FROM SOUTHERN AFRICA

The fossil fish record of southern Africa is both sparse and spotty and the only group with a relatively complete record is the Actinopterygii; indeed several of the major fish groups have not so far been described from the African Continent. The Palaeozoic rocks of southern Africa have yielded an even more restricted fish fauna (Gardiner 1962; 1969). However, an accumulation of new, but fragmentary, material from several localities has shown the undoubted presence of two groups, coelacanths and acanthodians, hitherto unrecorded from the Palaeozoic strata of southern Africa

Coupled dynamics of RNA folding and nanopore translocation

The translocation of structured RNA or DNA molecules through narrow pores necessitates the opening of all base pairs. Here, we study the interplay between the dynamics of translocation and base-pairing theoretically, using kinetic Monte Carlo simulations and analytical methods. We find that the transient formation of basepairs that do not occur in the ground state can significantly speed up translocation.Comment: 4 pages, 3 figures, to appear in Physical Review Letter

Witnessing Entanglement with Second-Order Interference

Second-order interference and Hanbury-Brown and Twiss type experiments can provide an operational framework for the construction of witness operators that can test classical and nonclassical properties of a Gaussian squeezed state (GSS), and provide entanglement witness operators to study the separability properties of correlated Gaussian squeezed sates.Comment: 10 pages, 12 figure

Steady state entanglement in the mechanical vibrations of two dielectric membranes

We consider two dielectric membranes suspended inside a Fabry-Perot-cavity, which are cooled to a steady state via a drive by suitable classical lasers. We show that the vibrations of the membranes can be entangled in this steady state. They thus form two mechanical, macroscopic degrees of freedom that share steady state entanglement.Comment: example for higher environment temperatures added, further explanations added to the tex

Quantifying the Drivers of Star Formation on Galactic Scales. I. The Small Magellanic Cloud

We use the star formation history of the Small Magellanic Cloud (SMC) to place quantitative limits on the effect of tidal interactions and gas infall on the star formation and chemical enrichment history of the SMC. The coincident timing of two recent (< 4 Gyr) increases in the star formation rate and SMC/Milky Way(MW) pericenter passages suggests that global star formation in the SMC is driven at least in part by tidal forces due to the MW. The Large Magellanic Cloud (LMC) is the other potential driver of star formation, but is only near the SMC during the most recent burst. The poorly constrained LMC-SMC orbit is our principal uncertainty. To explore the correspondence between bursts and MW pericenter passages further, we model star formation in the SMC using a combination of continuous and tidally-triggered star formation. The behavior of the tidally-triggered mode is a strong inverse function of the SMC-MW separation (preferred behavior ~ r^-5, resulting in a factor of ~100 difference in the rate of tidally-triggered star formation at pericenter and apocenter). Despite the success of these closed-box evolutionary models in reproducing the recent SMC star formation history and current chemical abundance, they have some systematic shortcomings that are remedied by postulating that a sizable infall event (~ 50% of the total gas mass) occured about 4 Gyr ago. Regardless of whether this infall event is included, the fraction of stars in the SMC that formed via a tidally triggered mode is > 10% and could be as large as 70%.Comment: Accepted for publication in Ap

Single photon state generation from a continuous-wave non-degenerate optical parametric oscillator

We present a theoretical treatment of conditional preparation of one-photon states from a continuous-wave non-degenerate optical parametric oscillator. We obtain an analytical expression for the output state Wigner function, and we maximize the one-photon state fidelity by varying the temporal mode function of the output state. We show that a higher production rate of high fidelity Fock states is obtained if we condition the outcome on dark intervals around trigger photo detection events.Comment: 9 pages, 9 figures, v2: published versio

A NEW DICTYOPYGID FROM THE CAVE SANDSTONE OF LESOTHO, SOUTHERN AFRICA

The Lower Triassic of South Africa has yielded an array of early dictyopygids (Brough, 1931, 1936) yet none of those advanced dictyopygids so characteristic of the Upper Triassic of North America (Schaeffer, 1967) has so far been recorded from the African continent. The geographical distribution of the dictyopygids appears to be a discontinuous one with the Lower Triassic forms coming mainly from South Africa, the Middle Triassic ones from Australia and the Upper Triassic forms from North America. It is thus surprising to find a seemingly advanced dictyopygid in the rather unfossiliferous Cave Sandstone of Lesotho

Wave function Monte Carlo method for polariton condensates

We present a quantum jump approach to describe coupled quantum and classical systems in the context of Bose-Einstein condensation in the solid state. In our formalism, the excitonic gain medium is described by classical rate equations, while the polariton modes are described fully quantum mechanically. We show the equivalence of our method with a master equation approach. As an application, we compute the linewidth of a single mode polariton condensate. Both the line broadening due to the interactions between polaritons and the interactions with the reservoir excitons is taken into account.Comment: 6 pages, 2 figure

Non-degenerate, three-wave mixing with the Josephson ring modulator

The Josephson ring modulator (JRM) is a device, based on Josephson tunnel junctions, capable of performing non-degenerate mixing in the microwave regime without losses. The generic scattering matrix of the device is calculated by solving coupled quantum Langevin equations. Its form shows that the device can achieve quantum-limited noise performance both as an amplifier and a mixer. Fundamental limitations on simultaneous optimization of performance metrics like gain, bandwidth and dynamic range (including the effect of pump depletion) are discussed. We also present three possible integrations of the JRM as the active medium in a different electromagnetic environment. The resulting circuits, named Josephson parametric converters (JPC), are discussed in detail, and experimental data on their dynamic range are found to be in good agreement with theoretical predictions. We also discuss future prospects and requisite optimization of JPC as a preamplifier for qubit readout applications.Comment: 21 pages, 16 figures, 4 table