Observation of long-lived polariton states in semiconductor microcavities across the parametric threshold

The excitation spectrum around the pump-only stationary state of a polariton optical parametric oscillator (OPO) in semiconductor microcavities is investigated by time-resolved photoluminescence. The response to a weak pulsed perturbation in the vicinity of the idler mode is directly related to the lifetime of the elementary excitations. A dramatic increase of the lifetime is observed for a pump intensity approaching and exceeding the OPO threshold. The observations can be explained in terms of a critical slowing down of the dynamics upon approaching the threshold and the following onset of the soft Goldstone mode

Neural Modeling and Control of Diesel Engine with Pollution Constraints

The paper describes a neural approach for modelling and control of a turbocharged Diesel engine. A neural model, whose structure is mainly based on some physical equations describing the engine behaviour, is built for the rotation speed and the exhaust gas opacity. The model is composed of three interconnected neural submodels, each of them constituting a nonlinear multi-input single-output error model. The structural identification and the parameter estimation from data gathered on a real engine are described. The neural direct model is then used to determine a neural controller of the engine, in a specialized training scheme minimising a multivariable criterion. Simulations show the effect of the pollution constraint weighting on a trajectory tracking of the engine speed. Neural networks, which are flexible and parsimonious nonlinear black-box models, with universal approximation capabilities, can accurately describe or control complex nonlinear systems, with little a priori theoretical knowledge. The presented work extends optimal neuro-control to the multivariable case and shows the flexibility of neural optimisers. Considering the preliminary results, it appears that neural networks can be used as embedded models for engine control, to satisfy the more and more restricting pollutant emission legislation. Particularly, they are able to model nonlinear dynamics and outperform during transients the control schemes based on static mappings.Comment: 15 page

Self-trapping of impurities in Bose-Einstein condensates: Strong attractive and repulsive coupling

We study the interaction-induced localization -- the so-called self-trapping -- of a neutral impurity atom immersed in a homogeneous Bose-Einstein condensate (BEC). Based on a Hartree description of the BEC we show that -- unlike repulsive impurities -- attractive impurities have a singular ground state in 3d and shrink to a point-like state in 2d as the coupling approaches a critical value. Moreover, we find that the density of the BEC increases markedly in the vicinity of attractive impurities in 1d and 2d, which strongly enhances inelastic collisions between atoms in the BEC. These collisions result in a loss of BEC atoms and possibly of the localized impurity itself.Comment: 7 pages, 5 figure

A variational problem on Stiefel manifolds

In their paper on discrete analogues of some classical systems such as the rigid body and the geodesic flow on an ellipsoid, Moser and Veselov introduced their analysis in the general context of flows on Stiefel manifolds. We consider here a general class of continuous time, quadratic cost, optimal control problems on Stiefel manifolds, which in the extreme dimensions again yield these classical physical geodesic flows. We have already shown that this optimal control setting gives a new symmetric representation of the rigid body flow and in this paper we extend this representation to the geodesic flow on the ellipsoid and the more general Stiefel manifold case. The metric we choose on the Stiefel manifolds is the same as that used in the symmetric representation of the rigid body flow and that used by Moser and Veselov. In the extreme cases of the ellipsoid and the rigid body, the geodesic flows are known to be integrable. We obtain the extremal flows using both variational and optimal control approaches and elucidate the structure of the flows on general Stiefel manifolds.Comment: 30 page

RPAE versus RPA for the Tomonaga model with quadratic energy dispersion

Recently the damping of the collective charge (and spin) modes of interacting fermions in one spatial dimension was studied. It results from the nonlinear correction to the energy dispersion in the vicinity of the Fermi points. To investigate the damping one has to replace the random phase approximation (RPA) bare bubble by a sum of more complicated diagrams. It is shown here that a better starting point than the bare RPA is to use the (conserving) linearized time dependent Hartree-Fock equations, i.e. to perform a random phase approximation (with) exchange (RPAE) calculation. It is shown that the RPAE equation can be solved analytically for the special form of the two-body interaction often used in the Luttinger liquid framework. While (bare) RPA and RPAE agree for the case of a strictly linear disperson there are qualitative differences for the case of the usual nonrelativistic quadratic dispersion.Comment: 6 pages, 3 figures, misprints corrected; to appear in PRB7

High-Contrast Interference in a Thermal Cloud of Atoms

The coherence properties of a gas of bosonic atoms above the BEC transition temperature were studied. Bragg diffraction was used to create two spatially separated wave packets, which interfere during expansion. Given sufficient expansion time, high fringe contrast could be observed in a cloud of arbitrary temperature. Fringe visibility greater than 90% was observed, which decreased with increasing temperature, in agreement with a simple model. When the sample was "filtered" in momentum space using long, velocity-selective Bragg pulses, the contrast was significantly enhanced in contrast to predictions

Nonequilibrium perturbation theory of the spinless Falicov-Kimball model

We perform a perturbative analysis for the nonequilibrium Green functions of the spinless Falicov-Kimball model in the presence of an arbitrary external time-dependent but spatially uniform electric field. The conduction electron self-energy is found from a strictly truncated second-order perturbative expansion in the local electron-electron repulsion U. We examine the current at half-filling, and compare to both the semiclassical Boltzmann equation and exact numerical solutions for the contour-ordered Green functions from a transient-response formalism (in infinite dimensions) on the Kadanoff-Baym-Keldysh contour. We find a strictly truncated perturbation theory in the two-time formalism cannot reach the long-time limit of the steady state; instead it illustrates pathological behavior for times larger than approximately 2/U

Spin Susceptibility of an Ultra-Low Density Two Dimensional Electron System

We determine the spin susceptibility in a two dimensional electron system in GaAs/AlGaAs over a wide range of low densities from 2$\times10^{9}$cm$^{-2}$ to 4$\times10^{10}$cm$^{-2}$. Our data can be fitted to an equation that describes the density dependence as well as the polarization dependence of the spin susceptibility. It can account for the anomalous g-factors reported recently in GaAs electron and hole systems. The paramagnetic spin susceptibility increases with decreasing density as expected from theoretical calculations.Comment: 5 pages, 2 eps figures, to appear in PR

On the lowest energy excitations of one-dimensional strongly correlated electrons

It is proven that the lowest excitations $E_{low}(k)$ of one-dimensional half-integer spin generalized Heisenberg models and half-filled extended Hubbard models are $\pi$-periodic functions. For Hubbard models at fractional fillings $E_{low}{(k+ 2 k_f)} = E_{low}(k)$, where $2 k_f= \pi n$, and $n$ is the number of electrons per unit cell. Moreover, if one of the ground states of the system is magnetic in the thermodynamic limit, then $E_{low}(k) = 0$ for any $k$, so the spectrum is gapless at any wave vector. The last statement is true for any integer or half-integer value of the spin.Comment: 6 Pages, Revtex, final versio

Propagators in Coulomb gauge from SU(2) lattice gauge theory

A thorough study of 4-dimensional SU(2) Yang-Mills theory in Coulomb gauge is performed using large scale lattice simulations. The (equal-time) transverse gluon propagator, the ghost form factor d(p) and the Coulomb potential V_{coul} (p) ~ d^2(p) f(p)/p^2 are calculated. For large momenta p, the gluon propagator decreases like 1/p^{1+\eta} with \eta =0.5(1). At low momentum, the propagator is weakly momentum dependent. The small momentum behavior of the Coulomb potential is consistent with linear confinement. We find that the inequality \sigma_{coul} \ge \sigma comes close to be saturated. Finally, we provide evidence that the ghost form factor d(p) and f(p) acquire IR singularities, i.e., d(p) \propto 1/\sqrt{p} and f(p) \propto 1/p, respectively. It turns out that the combination g_0^2 d_0(p) of the bare gauge coupling g_0 and the bare ghost form factor d_0(p) is finite and therefore renormalization group invariant.Comment: 10 pages, 7 figure