Bose-Einstein Condensation in a Trap: the Case of a Dense Condensate

We consider the Bose-Einstein condensation of atoms in a trap where the density of particles is so high that the low density approach of Gross and Pitaevskii will not be applicable. For this purpose we use the slave boson representation which is valid for hard-core bosons at any density. This description leads to the same results as the Gross-Pitaevskii approach in the low density limit, but for higher densities, it predicts the depletion of the order parameter field condensate in the regions where the density of the atomic cloud is high.Comment: 6 pages RevTeX, 3 eps-figure

Dynamic Response of Suspended Underwater Systems

A method is presented for analyzing the steady-state or stationary random heave response of suspended underwater systems. The nonlinear continuous system is replaced by a discretized pseudolinear system by means of an equation difference minimization technique. The resulting pseudolinear system is solved by an iterative scheme. An example of the application of the proposed method of analysis to a suspended hydrophone system is given. The example shows that the nonlinear pressure drag forces have a very significant effect on the over-all response of the system. The nature of the response is discussed and some practical conclusions are given

Completely positive maps on modules, instruments, extremality problems, and applications to physics

Convex sets of completely positive maps and positive semidefinite kernels are considered in the most general context of modules over $C^*$-algebras and a complete charaterization of their extreme points is obtained. As a byproduct, we determine extreme quantum instruments, preparations, channels, and extreme autocorrelation functions. Various applications to quantum information and measurement theories are given. The structure of quantum instruments is analyzed thoroughly.Comment: 32 page