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The mechanism for the transition of a Bose gas to the superfluid state viathermal fluctuations is considered. It is shown that in the process of externalcooling some critical fluctuations (instantons) are formed above the criticaltemperature. The probability of the instanton formation is calculated in thethree and two-dimensional cases. It is found that this probability increases asthe system approaches the transition temperature. It is shown that theevolution of an individual instanton is impossible without the formation ofvortices in its superfluid part

Condensation and vortex formation in a Bose gas upon cooling