618 research outputs found
Short-pulse photoassociation in rubidium below the D line
Photoassociation of two ultracold rubidium atoms and the subsequent formation
of stable molecules in the singlet ground and lowest triplet states is
investigated theoretically. The method employs laser pulses inducing
transitions via excited states correlated to the asymptote.
Weakly bound molecules in the singlet ground or lowest triplet state can be
created by a single pulse while the formation of more deeply bound molecules
requires a two-color pump-dump scenario. More deeply bound molecules in the
singlet ground or lowest triplet state can be produced only if efficient
mechanisms for both pump and dump steps exist. While long-range
-potentials allow for efficient photoassociation, stabilization is
facilitated by the resonant spin-orbit coupling of the states.
Molecules in the singlet ground state bound by a few wavenumbers can thus be
formed. This provides a promising first step toward ground state molecules
which are ultracold in both translational and vibrational degrees of freedom
Calculation of three-body resonances using slow-variable discretization coupled with complex absorbing potential
We developed a method to calculate positions and widths of three-body
resonances. The method combines the hyperspherical adiabatic approach, slow
variable discretization method (Tolstikhin et al., J. Phys. B: At. Mol. Opt.
Phys. 29, L389 (1996)), and a complex absorbing potential. The method can be
used to obtain resonances having short-range or long-range wave functions. In
particular, we applied the method to obtain very shallow three-body Efimov
resonances for a model system (Nielsen et al., Phys. Rev. A 66, 012705 (2002)).Comment: 23 pages, 10 figure
Existence, regularity and structure of confined elasticae
We consider the problem of minimizing the bending or elastic energy among
Jordan curves confined in a given open set . We prove existence,
regularity and some structural properties of minimizers. In particular, when
is convex we show that a minimizer is necessarily a convex curve. We
also provide an example of a minimizer with self-intersections
Maximum Likelihood Approach for Stochastic Volatility Models
Projecte final de MĂ ster Oficial fet en col.laboraciĂł amb Universitat de Barcelona. Departament de FĂsica FonamentalEnglish: Volatility is a measure of the amplitude of price return fluctuations. Despite it is one of the most important quantities in finance, volatility is a hidden quantity because it is not directly observable. Here we apply a known maximum likelihood process which assumes that volatility is a time-dependent diffusions coefficient of the random walk of the price return and that it is a Markov process. We use this method using the expOU, the OU and the Heston models which are previously imposed. We find an estimator of the volatility for each model and we observe that it works reasonably well for the three models. Using these estimators, we reach a way of forecasting absolute values of future returns with current volatilities. During all the process, no-correlation is introduced and at the end, we see that volatility has non-zero autocorrelation for hundreds of days and we observe a significant correlation between volatility and price return called leverage effect. We finally apply this methodology to different market indexes and we conclude that its properties are universal
- …