142 research outputs found
Infinitesimal natural and gauge-natural lifts
AbstractInfinitesimal natural and gauge-natural lifts are defined as special “systems” of vector fields on a fibred manifold p:E→B. (Infinitesimally) natural and gauge-natural operators are defined via the commutativity with Lie derivatives
Generalized geometrical structures of odd dimensional manifolds
We define an almost--cosymplectic--contact structure which generalizes
cosymplectic and contact structures of an odd dimensional manifold.
Analogously, we define an almost--coPoisson--Jacobi structure which generalizes
a Jacobi structure. Moreover, we study relations between these structures and
analyse the associated algebras of functions. As examples of the above
structures, we present geometrical dynamical structures of the phase space of a
general relativistic particle, regarded as the 1st jet space of motions in a
spacetime. We describe geometric conditions by which a metric and a connection
of the phase space yield cosymplectic and dual coPoisson structures, in case of
a spacetime with absolute time (a Galilei spacetime), or
almost--cosymplectic--contact and dual almost--coPoisson--Jacobi structures, in
case of a spacetime without absolute time (an Einstein spacetime)
Smooth and F-smooth systems with applications to Covariant Quantum Mechanics
Title in English: Smooth and F-smooth systems with applications to Covariant Quantum Mechanics We review the geometric theory of smooth systems of smooth maps, of smooth systems of smooth sections of a smooth double fibred manifold and of smooth systems of smooth connections of a smooth fibred manifold. Moreover, after reviewing the concept of F-smooth space due to A. Froelicher, we discuss the F-smooth systems of smooth maps, the F-smooth systems of fibrewisely smooth sections of a smooth double fibred manifold, the F-smooth systems of fibrewisely smooth connections of a smooth fibred manifold and of F-smooth connections of an F-smooth system of fibrewisely smooth sections. Further, we discuss three applications of the general geometric theory, which are taken in the framework of Covariant Quantum Mechanics. Namely, we discuss the smooth upper quantum connection, the F-smooth sectional quantum bundle and the Schroedinger operator regarded as an F-smooth connection of the F-smoth sectional quantum bundle
Exploiting Robot Redundancy for Online Learning and Control
Accurate trajectory tracking in the task space is critical in many robotics applications. Model-based robot controllers are able to ensure very good tracking but lose effectiveness in the presence of model uncertainties. On the other hand, online learning-based control laws can handle poor dynamic modeling, as long as prediction errors are kept small and decrease over time. However, in the case of redundant robots directly controlled in the task space, this condition is not usually met. We present an online learning-based control framework that exploits robot redundancy so as to increase the overall performance and shorten the learning transient. The validity of the proposed approach is shown through a comparative study conducted in simulation on a KUKA LWR4+ robot
Direct evaporative cooling of 39K atoms to Bose-Einstein condensation
We report the realization of Bose-Einstein condensates of 39K atoms without
the aid of an additional atomic coolant. Our route to Bose-Einstein
condensation comprises Sub Doppler laser cooling of large atomic clouds with
more than 10^10 atoms and evaporative cooling in optical dipole traps where the
collisional cross section can be increased using magnetic Feshbach resonances.
Large condensates with almost 10^6 atoms can be produced in less than 15
seconds. Our achievements eliminate the need for sympathetic cooling with Rb
atoms which was the usual route implemented till date due to the unfavourable
collisional property of 39K. Our findings simplify the experimental set-up for
producing Bose-Einstein condensates of 39K atoms with tunable interactions,
which have a wide variety of promising applications including
atom-interferometry to studies on the interplay of disorder and interactions in
quantum gases.Comment: 7 pages, 6 figure
Feshbach resonances in ultracold K(39)
We discover several magnetic Feshbach resonances in collisions of ultracold
K(39) atoms, by studying atom losses and molecule formation. Accurate
determination of the magnetic-field resonance locations allows us to optimize a
quantum collision model for potassium isotopes. We employ the model to predict
the magnetic-field dependence of scattering lengths and of near-threshold
molecular levels. Our findings will be useful to plan future experiments on
ultracold potassium atoms and molecules.Comment: 7 pages, 6 figure
Accurate near-threshold model for ultracold KRb dimers from interisotope Feshbach spectroscopy
We investigate magnetic Feshbach resonances in two different ultracold K-Rb
mixtures. Information on the K(39)-Rb(87) isotopic pair is combined with novel
and pre-existing observations of resonance patterns for K(40)-Rb(87).
Interisotope resonance spectroscopy improves significantly our near-threshold
model for scattering and bound-state calculations. Our analysis determines the
number of bound states in singlet/triplet potentials and establishes precisely
near threshold parameters for all K-Rb pairs of interest for experiments with
both atoms and molecules. In addition, the model verifies the validity of the
Born-Oppenheimer approximation at the present level of accuracy.Comment: 9 pages, 7 figure
- …