Stochastic Gross-Pitaevsky Equation for BEC via Coarse-Grained Effective Action

We sketch the major steps in a functional integral derivation of a new set of Stochastic Gross-Pitaevsky equations (GPE) for a Bose-Einstein condensate (BEC) confined to a trap at zero temperature with the averaged effects of non-condensate modes incorporated as stochastic sources. The closed-time-path (CTP) coarse-grained effective action (CGEA) or the equivalent influence functional method is particularly suitable because it can account for the full back-reaction of the noncondensate modes on the condensate dynamics self-consistently. The Langevin equations derived here containing nonlocal dissipation together with colored and multiplicative noises are useful for a stochastic (as distinguished from say, a kinetic) description of the nonequilibrium dynamics of a BEC. This short paper contains original research results not yet published anywhere.Comment: 6 page

Wave Equation for Sound in Fluids with Vorticity

We use Clebsch potentials and an action principle to derive a closed system of gauge invariant equations for sound superposed on a general background flow. Our system reduces to the Unruh (1981) and Pierce (1990) wave equations when the flow is irrotational, or slowly varying. We illustrate our formalism by applying it to waves propagating in a uniformly rotating fluid where the sound modes hybridize with inertial waves.Comment: RevTeX, 27page

Diversity of free-living ciliates in the sandy sediment of a Spanish stream in winter

This study had two objectives: to determine the number of (phenotypic) ciliate species co-existing in 1 m2 of sandy river sediment at a maximum temperature of 4 "C; and to determine the ecological mechanism(s) facilitating their co-existence. The ciliate community was diverse (65 species [8 of which are new], belonging to 50 genera, from 17 orders). The sediment supported a superficial mat of diatoms (> 30 species). These served as food for at least 16 ciliate species. The size frequency distribution of ingested diatoms was almost identical to that for the diatoms in the sediment: thus the probability of a diatom being ingested appears to be a simple function of its relative abundance. Two factors were probably important for the co-existence of ciliate species : wide variation in cell size and shape enabled them to occupy most habitats; and they deployed a variety of feeding mechanisms to consume the variety of microbial food types. Taken as a whole, the ciliate community was capable of feeding on all microbes, including other protozoa, up to a size of about 80 pm. Considering the broad diversity of ciliate habitats available within 1 m2, the importance of physical transport processes in the river basin, and the known cosmopolitan distribution of many ciliate species, it is believed likely that the species richness we recorded is representative of the expanse of sandy sediment in this river, on this occasion

The Dirac equation without spinors

In the first part of the paper we give a tensor version of the Dirac equation. In the second part we formulate and analyse a simple model equation which for weak external fields appears to have properties similar to those of the 2--dimensional Dirac equation.Comment: 20 pages. Submitted for publication in the proceedings of the conference `Functional analysis, partial differential equations and applications', Rostock (Germany) 31 August--4 September 199