Aspect ratio analysis for ground states of bosons in anisotropic traps

Characteristics of the initial condensate in the recent experiment on Bose-Einstein condensation (BEC) of ${}^{87}$Rb atoms in an anisotropic magnetic trap is discussed. Given the aspect ratio $R$, the quality of BEC is estimated. A simple analytical Ansatz for the initial condensate wave function is proposed as a function of the aspect ratio which, in contrast to the Baym-Pethick trial wave function, reproduces both the weak and the strong intaraction limits and which is in better agreement with numerical results than the latter.Comment: 12 pages, latex, 3 figures added, minor corrections; to appear in J. Res. Nat. Inst. of Standards and Technolog

Gauge Physics of Finance: simple introduction

In this paper we state the fundamental principles of the gauge approach to financial economics and demonstrate the ways of its application. In particular, modelling of realistic price processes is considered for an example of S&P500 market index. Derivative pricing and portfolio theory are also briefly discussed.