Geodesic
The role of thermal fluctuations in a~Bose system in lowering the roton minimum
Teoretičeskaâ i matematičeskaâ fizika, Tome 63 (1985) no. 3, pp. 428-439

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A study is made of 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, which at $T=0$ are responsible for a premature loss of stability with respect to arbitrarily small perturbations, this occurring moreover first for long-wavelength (phonon) and not roton perturbations [7, 8], thermal fluctuations delay the appearance of local instability. Another difference from the case $T=0$ with a real roton minimum is the fact that to describe the complete region of stability at $T>0$ the single-loop approximation is inadequate. An additional metastable homogeneous phase at $T=0$ with “complex roton minimum” is found. 
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     author = {Yu. A. Nepomnyashchii and V. A. Podolskii},
     title = {The role of thermal fluctuations in {a~Bose} system in lowering the roton minimum},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     volume = {63},
     number = {3},
     year = {1985},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1985_63_3_a10/}
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Yu. A. Nepomnyashchii; V. A. Podolskii. The role of thermal fluctuations in a~Bose system in lowering the roton minimum. Teoretičeskaâ i matematičeskaâ fizika, Tome 63 (1985) no. 3, pp. 428-439. http://geodesic.mathdoc.fr/item/TMF_1985_63_3_a10/