Abstract
This paper studies the influence of thermal fluctuations on the stability of the homogeneous state of a Bose system with condensate in lowering the roton minimum. In contrast to the case of quantum fluctuations, thermal fluctuations delay the appearance of local instability. Another difference from the case T = O with a real roton minimum is the fact that to describe the complete region of stability at T>O the single-loop approximation is inadequate. An additional metastable homogenous phase at T = O with ''complex roton minmum'' is found.
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