Gaussian approximations for stochastic systems with delay: chemical Langevin equation and application to a Brusselator system

We present a heuristic derivation of Gaussian approximations for stochastic chemical reaction systems with distributed delay. In particular we derive the corresponding chemical Langevin equation. Due to the non-Markovian character of the underlying dynamics these equations are integro-differential equations, and the noise in the Gaussian approximation is coloured. Following on from the chemical Langevin equation a further reduction leads to the linear-noise approximation. We apply the formalism to a delay variant of the celebrated Brusselator model, and show how it can be used to characterise noise-driven quasi-cycles, as well as noise-triggered spiking. We find surprisingly intricate dependence of the typical frequency of quasi-cycles on the delay period.Comment: 14 pages, 9 figure

The Nonlinear Evolution of Instabilities Driven by Magnetic Buoyancy: A New Mechanism for the Formation of Coherent Magnetic Structures

Motivated by the problem of the formation of active regions from a deep-seated solar magnetic field, we consider the nonlinear three-dimensional evolution of magnetic buoyancy instabilities resulting from a smoothly stratified horizontal magnetic field. By exploring the case for which the instability is continuously driven we have identified a new mechanism for the formation of concentrations of magnetic flux.Comment: Published in ApJL. Version with colour figure

Impact and Recovery Process of Mini Flash Crashes: An Empirical Study

In an Ultrafast Extreme Event (or Mini Flash Crash), the price of a traded stock increases or decreases strongly within milliseconds. We present a detailed study of Ultrafast Extreme Events in stock market data. In contrast to popular belief, our analysis suggests that most of the Ultrafast Extreme Events are not primarily due to High Frequency Trading. In at least 60 percent of the observed Ultrafast Extreme Events, the main cause for the events are large market orders. In times of financial crisis, large market orders are more likely which can be linked to the significant increase of Ultrafast Extreme Events occurrences. Furthermore, we analyze the 100 trades following each Ultrafast Extreme Events. While we observe a tendency of the prices to partially recover, less than 40 percent recover completely. On the other hand we find 25 percent of the Ultrafast Extreme Events to be almost recovered after only one trade which differs from the usually found price impact of market orders

{\em Ab initio} Quantum Monte Carlo simulation of the warm dense electron gas in the thermodynamic limit

We perform \emph{ab initio} quantum Monte Carlo (QMC) simulations of the warm dense uniform electron gas in the thermodynamic limit. By combining QMC data with linear response theory we are able to remove finite-size errors from the potential energy over the entire warm dense regime, overcoming the deficiencies of the existing finite-size corrections by Brown \emph{et al.}~[PRL \textbf{110}, 146405 (2013)]. Extensive new QMC results for up to $N=1000$ electrons enable us to compute the potential energy $V$ and the exchange-correlation free energy $F_{xc}$ of the macroscopic electron gas with an unprecedented accuracy of $|\Delta V|/|V|, |\Delta F_{xc}|/|F|_{xc} \sim 10^{-3}$. A comparison of our new data to the recent parametrization of $F_{xc}$ by Karasiev {\em et al.} [PRL {\bf 112}, 076403 (2014)] reveals significant deviations to the latter

Tomographic readout of an opto-mechanical interferometer

The quantum state of light changes its nature when being reflected off a mechanical oscillator due to the latter's susceptibility to radiation pressure. As a result, a coherent state can transform into a squeezed state and can get entangled with the motion of the oscillator. The complete tomographic reconstruction of the state of light requires the ability to readout arbitrary quadratures. Here we demonstrate such a readout by applying a balanced homodyne detector to an interferometric position measurement of a thermally excited high-Q silicon nitride membrane in a Michelson-Sagnac interferometer. A readout noise of \unit{1.9 \cdot 10^{-16}}{\metre/\sqrt{\hertz}} around the membrane's fundamental oscillation mode at \unit{133}{\kilo\hertz} has been achieved, going below the peak value of the standard quantum limit by a factor of 8.2 (9 dB). The readout noise was entirely dominated by shot noise in a rather broad frequency range around the mechanical resonance.Comment: 7 pages, 5 figure

The formation of ultra-compact dwarf galaxies and nucleated dwarf galaxies

Ultra compact dwarf galaxies (UCDs) have similar properties as massive globular clusters or the nuclei of nucleated galaxies. Recent observations suggesting a high dark matter content and a steep spatial distribution within groups and clusters provide new clues as to their origins. We perform high-resolution N-body / smoothed particle hydrodynamics simulations designed to elucidate two possible formation mechanisms for these systems: the merging of globular clusters in the centre of a dark matter halo, or the massively stripped remnant of a nucleated galaxy. Both models produce density profiles as well as the half light radii that can fit the observational constraints. However, we show that the first scenario results to UCDs that are underluminous and contain no dark matter. This is because the sinking process ejects most of the dark matter particles from the halo centre. Stripped nuclei give a more promising explanation, especially if the nuclei form via the sinking of gas, funneled down inner galactic bars, since this process enhances the central dark matter content. Even when the entire disk is tidally stripped away, the nucleus stays intact and can remain dark matter dominated even after severe stripping. Total galaxy disruption beyond the nuclei only occurs on certain orbits and depends on the amount of dissipation during nuclei formation. By comparing the total disruption of CDM subhaloes in a cluster potential we demonstrate that this model also leads to the observed spatial distribution of UCDs which can be tested in more detail with larger data sets.Comment: 8 pages, 8 figures, final version accepted for publication in MNRA

Tuning the mobility of a driven Bose-Einstein condensate via diabatic Floquet bands

We study the response of ultracold atoms to a weak force in the presence of a temporally strongly modulated optical lattice potential. It is experimentally demonstrated that the strong ac-driving allows for a tailoring of the mobility of a dilute atomic Bose-Einstein condensate with the atoms moving ballistically either along or against the direction of the applied force. Our results are in agreement with a theoretical analysis of the Floquet spectrum of a model system, thus revealing the existence of diabatic Floquet bands in the atom's band spectra and highlighting their role in the non-equilibrium transport of the atoms

Lower bounds for nodal sets of eigenfunctions

We prove lower bounds for the Hausdorff measure of nodal sets of eigenfunctions.Comment: To appear in Communications in Mathematical Physics; revised to include two additional references and update bibliographic informatio