The three-body recombination of a condensed Bose gas near a Feshbach resonance

In this paper, we study the three-body recombination rate of a homogeneous dilute Bose gas with a Feshbach resonance at zero temperature. The ground state and excitations of this system are obtained. The three-body recombination in the ground state is due to the break-up of an atom pair in the quantum depletion and the formation of a molecule by an atom from the broken pair and an atom from the condensate. The rate of this process is in good agreement with the experiment on $^{23}$Na in a wide range of magnetic fields.Comment: 10 pages, 2 figures, to be published in Phys. Rev.

ANOVA for diffusions and It\^{o} processes

It\^{o} processes are the most common form of continuous semimartingales, and include diffusion processes. This paper is concerned with the nonparametric regression relationship between two such It\^{o} processes. We are interested in the quadratic variation (integrated volatility) of the residual in this regression, over a unit of time (such as a day). A main conceptual finding is that this quadratic variation can be estimated almost as if the residual process were observed, the difference being that there is also a bias which is of the same asymptotic order as the mixed normal error term. The proposed methodology, ``ANOVA for diffusions and It\^{o} processes,'' can be used to measure the statistical quality of a parametric model and, nonparametrically, the appropriateness of a one-regressor model in general. On the other hand, it also helps quantify and characterize the trading (hedging) error in the case of financial applications.Comment: Published at http://dx.doi.org/10.1214/009053606000000452 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Frequency domain criteria for lp-robust stability of systems with fuzzy parameters

The paper deals with the problem of determining stability margin of linear continuous-time system with fuzzy parametric uncertainty. Non-symmetric multivariate membership functions with lp -constraints describing the uncertainty of characteristic polynomial parameters are considered. An elegant solution, graphical in nature, based on generation of Tsypkin-Polyak plot is presented