Dimer states in atomic mixtures

A mixture of heavy atoms in a Mott state and light spin-1/2 fermionic atoms is studied in an optical lattice. Inelastic scattering processes between both atomic species excite the heavy atoms and renormalize the tunneling rate as well as the interaction of the light atoms. An effective Hamiltonian for the latter is derived that describes tunneling of single fermions, tunneling of fermionic pairs and an exchange of fermionic spins. Low energy states of this Hamiltonian are a N\'eel state for strong effective repulsion, dimer states for moderate interaction, and a density wave of paired fermions for strong effective attraction.Comment: 10 pages, 3 figure, extended versio

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

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

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

Analytical solutions for the dynamics of two trapped interacting ultracold atoms

We discuss exact solutions of the Schroedinger equation for the system of two ultracold atoms confined in an axially symmetric harmonic potential. We investigate different geometries of the trapping potential, in particular we study the properties of eigenenergies and eigenfunctions for quasi-one- and quasi-two-dimensional traps. We show that the quasi-one- and the quasi-two-dimensional regimes for two atoms can be already realized in the traps with moderately large (or small) ratios of the trapping frequencies in the axial and the transverse directions. Finally, we apply our theory to Feshbach resonances for trapped atoms. Introducing in our description an energy-dependent scattering length we calculate analytically the eigenenergies for two trapped atoms in the presence of a Feshbach resonance.Comment: RevTeX, 15 pages, 15 figure

Tunable photonic band gaps with coherently driven atoms in optical lattices

Optical lattice loaded with cold atoms can exhibit a tunable photonic band gap for a weak probe field under the conditions of electromagnetically induced transparency. This system possesses a number of advantageous properties, including reduced relaxation of Raman coherence and the associated probe absorption, and simultaneous enhancement of the index modulation and the resulting reflectivity of the medium. This flexible system has a potential to serve as a testbed of various designs for the linear and nonlinear photonic band gap materials at a very low light level and can be employed for realizing deterministic entanglement between weak quantum fields