15,827 research outputs found
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
- …