9614133 Leggett Within the last year the phenomena of Bose-Einstein condensation (BEC) in dilute atomic gases has been realized in three different laboratories and many more are moving into this area. The systems in question lie in a regime of parameters (density, temperature, isolation _.) many orders of magnitude different from those which characterize the only previously known laboratory system believed to exhibit BEC, namely superfluid 4He. Consequently, it should be possible to use these systems to subject to experimental test a variety of ideas which are believed to apply to superfluid Helium but have never been tested there and in particular to explore the precise relation between BEC and the complex of phenomena which go under the name of "superfluidity". Theoretical work will be carried out, both in general and in the context of dilute atomic gases, to examine the superfluid density and the condition for the phenomena of zero rotation and of persistent currents, and to make predictions about a number of interesting experiments on the subject of "quantum phase coherence" and "phase memory" which are apparently feasible in these systems. This grant has been co-reviewed with the Theoretical Physics program in the Division of Physics and is being co-funded with them. %%% This grant supports the work of a senior, distinguished PI whose many thoughtful contributions to the general area of superfluidity and other condensed state phenomena (such as macroscopic quantum tunneling) are well known. This project, motivated by recent experiments, takes him back to the questions associated with relationship between Bose- Einstein condensation and superfluidity in dilute gases. This grant has been co-reviewed with the Theoretical Physics program in the Division of Physics and is being co-funded with them. ***