Shear and Mixing in Oscillatory Doubly Diffusive Convection

To investigate the mechanism of mixing in oscillatory doubly diffusive (ODD) convection, we truncate the horizontal modal expansion of the Boussinesq equations to obtain a simplified model of the process. In the astrophysically interesting case with low Prandtl number, large-scale shears are generated as in ordinary thermal convection. The interplay between the shear and the oscillatory convection produces intermittent overturning of the fluid with significant mixing. By contrast, in the parameter regime appropriate to sea water, large-scale flows are not generated by the convection. However, if such flows are imposed externally, intermittent overturning with enhanced mixing is observed.Comment: 24 pages, 16 figures, Accepted for publication in Geophysical and Astrophysical Fluid Dynamic

Nonperturbative and perturbative treatments of parametric heating in atom traps

We study the quantum description of parametric heating in harmonic potentials both nonperturbatively and perturbatively, having in mind atom traps. The first approach establishes an explicit connection between classical and quantum descriptions; it also gives analytic expressions for properties such as the width of fractional frequency parametric resonances. The second approach gives an alternative insight into the problem and can be directly extended to take into account nonlinear effects. This is specially important for shallow traps.Comment: 12 pages, 2 figure

Positive P simulations of spin squeezing in a two-component Bose condensate

The collisional interaction in a Bose condensate represents a non-linearity which in analogy with non-linear optics gives rise to unique quantum features. In this paper we apply a Monte Carlo method based on the positive P pseudo-probability distribution from quantum optics to analyze the efficiency of spin squeezing by collisions in a two-component condensate. The squeezing can be controlled by choosing appropiate collision parameters or by manipulating the motional states of the two components.Comment: 5 pages, 2 figures. Submitted to Phys. Rev.

Relaxation rates and collision integrals for Bose-Einstein condensates

Near equilibrium, the rate of relaxation to equilibrium and the transport properties of excitations (bogolons) in a dilute Bose-Einstein condensate (BEC) are determined by three collision integrals, $\mathcal{G}^{12}$, $\mathcal{G}^{22}$, and $\mathcal{G}^{31}$. All three collision integrals conserve momentum and energy during bogolon collisions, but only $\mathcal{G}^{22}$ conserves bogolon number. Previous works have considered the contribution of only two collision integrals, $\mathcal{G}^{22}$ and $\mathcal{G}^{12}$. In this work, we show that the third collision integral $\mathcal{G}^{31}$ makes a significant contribution to the bogolon number relaxation rate and needs to be retained when computing relaxation properties of the BEC. We provide values of relaxation rates in a form that can be applied to a variety of dilute Bose-Einstein condensates.Comment: 18 pages, 4 figures, accepted by Journal of Low Temperature Physics 7/201

Inflationary perturbation theory is geometrical optics in phase space

A pressing problem in comparing inflationary models with observation is the accurate calculation of correlation functions. One approach is to evolve them using ordinary differential equations ("transport equations"), analogous to the Schwinger-Dyson hierarchy of in-out quantum field theory. We extend this approach to the complete set of momentum space correlation functions. A formal solution can be obtained using raytracing techniques adapted from geometrical optics. We reformulate inflationary perturbation theory in this language, and show that raytracing reproduces the familiar "delta N" Taylor expansion. Our method produces ordinary differential equations which allow the Taylor coefficients to be computed efficiently. We use raytracing methods to express the gauge transformation between field fluctuations and the curvature perturbation, zeta, in geometrical terms. Using these results we give a compact expression for the nonlinear gauge-transform part of fNL in terms of the principal curvatures of uniform energy-density hypersurfaces in field space.Comment: 22 pages, plus bibliography and appendix. v2: minor changes, matches version published in JCA

Photon blockade and quantum dynamics in intracavity coherent photoassociation of Bose-Einstein condensates

We demonstrate that a photon blockade effect exists in the intracavity coherent photoassociation of an atomic Bose-Einstein condensate and that the dynamics of the coupled atomic and molecular condensates can only be successfully described by a quantum treatment of all the interacting fields. We show that the usual mean-field calculational approaches give answers that are qualitatively wrong, even for the mean fields. The quantization of the fields gives a degree of freedom that is not present in analogous nonlinear optical processes. The difference between the semiclassical and quantum predictions can actually increase as the three fields increase in size so that there is no obvious classical limit for this process

Innocent Frauds Meet Goodhart’s Law in Monetary Policy

This paper discusses recent UK monetary policies as instances of Galbraith’s ‘innocent frauds’, including the idea that money is a thing rather than a relationship, the fallacy of composition that what is possible for one bank is possible for all banks, and the belief that the money supply can be controlled by reserves management. The origins of the idea of QE, and its defense when it was applied in Britain, are analysed through this lens. An empirical analysis of the effect of reserves on lending is conducted; we do not find evidence that QE ‘worked’ either by a direct effect on money spending, or through an equity market effect. These findings are placed in a historical context in a comparison with earlier money control experiments in the UK

The Influence of the Degree of Heterogeneity on the Elastic Properties of Random Sphere Packings

The macroscopic mechanical properties of colloidal particle gels strongly depend on the local arrangement of the powder particles. Experiments have shown that more heterogeneous microstructures exhibit up to one order of magnitude higher elastic properties than their more homogeneous counterparts at equal volume fraction. In this paper, packings of spherical particles are used as model structures to computationally investigate the elastic properties of coagulated particle gels as a function of their degree of heterogeneity. The discrete element model comprises a linear elastic contact law, particle bonding and damping. The simulation parameters were calibrated using a homogeneous and a heterogeneous microstructure originating from earlier Brownian dynamics simulations. A systematic study of the elastic properties as a function of the degree of heterogeneity was performed using two sets of microstructures obtained from Brownian dynamics simulation and from the void expansion method. Both sets cover a broad and to a large extent overlapping range of degrees of heterogeneity. The simulations have shown that the elastic properties as a function of the degree of heterogeneity are independent of the structure generation algorithm and that the relation between the shear modulus and the degree of heterogeneity can be well described by a power law. This suggests the presence of a critical degree of heterogeneity and, therefore, a phase transition between a phase with finite and one with zero elastic properties.Comment: 8 pages, 6 figures; Granular Matter (published online: 11. February 2012

Quantum jumps induced by the center-of-mass motion of a trapped atom

We theoretically study the occurrence of quantum jumps in the resonance fluorescence of a trapped atom. Here, the atom is laser cooled in a configuration of level such that the occurrence of a quantum jump is associated to a change of the vibrational center-of-mass motion by one phonon. The statistics of the occurrence of the dark fluorescence period is studied as a function of the physical parameters and the corresponding features in the spectrum of resonance fluorescence are identified. We discuss the information which can be extracted on the atomic motion from the observation of a quantum jump in the considered setup

Raman spectroscopy of a single ion coupled to a high-finesse cavity

We describe an ion-based cavity-QED system in which the internal dynamics of an atom is coupled to the modes of an optical cavity by vacuum-stimulated Raman transitions. We observe Raman spectra for different excitation polarizations and find quantitative agreement with theoretical simulations. Residual motion of the ion introduces motional sidebands in the Raman spectrum and leads to ion delocalization. The system offers prospects for cavity-assisted resolved-sideband ground-state cooling and coherent manipulation of ions and photons.Comment: 8 pages, 6 figure