Averaging the operators for a large number of clusters: Phase transitions
Teoretičeskaâ i matematičeskaâ fizika, Tome 125 (2000) no. 2, pp. 297-314
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We develop the theory of averaging the operators in a Fock space, introduced in our previous papers. We find the algebra of mean operators. We introduce the quantum entropy and quantum free energy using the function $f(z)=z\ln(z)$ of the mean unit operator (the “measure” of mean operators). Such a “quantum thermodynamics” determines the temperature dependence of the critical speed (“the Landau criterion”) and the temperature distribution at which the speed of a superfluid system is nonzero even at zero temperature. We generalize the consideration to the case where sparsely distributed bosons form clusters.
@article{TMF_2000_125_2_a7,
author = {V. P. Maslov},
title = {Averaging the operators for a large number of clusters: {Phase} transitions},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {297--314},
publisher = {mathdoc},
volume = {125},
number = {2},
year = {2000},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2000_125_2_a7/}
}
V. P. Maslov. Averaging the operators for a large number of clusters: Phase transitions. Teoretičeskaâ i matematičeskaâ fizika, Tome 125 (2000) no. 2, pp. 297-314. http://geodesic.mathdoc.fr/item/TMF_2000_125_2_a7/