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It is shown that thermal fluctuations of the normal component inducedephasing -- reversible damping of the low energy collective modes of aconfined Bose-Einstein condensate. The dephasing rate is calculated for theisotropic oscillator trap, where Landau damping is expected to be suppressed.This rate is characterized by a steep temperature dependence, and it is weaklyamplitude dependent.  In the limit of large numbers of bosons forming the condensate, the rateapproaches zero. However, for the numbers employed by the JILA group, thecalculated value of the rate is close to the experimental one. We suggest thata reversible nature of the damping caused by the thermal dephasing in theisotropic trap can be tested by the echo effect. A reversible nature of Landaudamping is also discussed, and a possibility of observing the echo effect in ananisotropic trap is considered as well. The parameters of the echo arecalculated in the weak echo limit for the isotropic trap. Results of thenumerical simulations of the echo are also presented.Comment: 12 pages, 2 figures included (RevTeX), submitted to PR

Thermal dephasing and the echo effect in a confined Bose-Einstein condensate