We have studied the effects of a disordered optical potential on the transport and phase coherence of a Bose-Einstein condensate (BEC) of
7Li atoms. At moderate disorder strengths
(VD), we observe inhibited transport and damping of dipole excitations, while in time-of-flight images, random but reproducible interference patterns are observed. In situ images reveal that the appearance of interference is correlated with density modulation, without complete fragmentation. At higher
VD, the interference contrast diminishes as the BEC fragments into multiple pieces with little phase coherence.
This paper develops the formal first order perturbation theory of transport phenomena in an ideal Bose-Einstein gas.The perturbation relaxation time is an unknown parameter in the theory. The ratio of thermal conductivity to viscosity is independent of this relaxation time; it increases discontinuously by a factor almost 2 at the Bose-Einstein condensation temperature ${T}_{\ensuremath{\lambda}}$. The isothermal Knudsen heat of transport through a small hole, classically equal to
2kT, drops rapidly to zero as
T falls to ${T}_{\ensuremath{\lambda}}$: the Bose-Einstein gas flowing isothermally through a small hole carries no heat when its temperature is below ${T}_{\ensuremath{\lambda}}$ and it exhibits corresponding thermo-mechanical effects.The mathematical analysis is carried out in terms of an approximation in which the lowest energy states of the gas are treated discretely while above an arbitrary level they are treated by an integration approximation. The treatment is capable of generalization to models in which there are anomalies in the lowest level spacings.