Geodesic
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. 
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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/

[1] V. P. Maslov, TMF, 121:3 (1999), 492 | DOI | MR

[2] V. P. Maslov, Funkts. analiz i ego prilozh., 33:4 (1999), 50 | DOI | MR | Zbl

[3] F. A. Berezin, Metod vtorichnogo kvantovaniya, Nauka, M., 1986 | MR | Zbl

[4] V. P. Maslov, Operatornye metody, Nauka, M., 1973 | MR

[5] V. P. Maslov, DAN SSSR, 114:5 (1957), 957 | Zbl

[6] A. E. Glassgold, A. N. Kaufman, K. M. Watson, Phys. Rev., 120 (1960), 660 | DOI | MR | Zbl

[7] T. D. Lee, C. N. Yang, Phys. Rev., 113 (1959), 1419

[8] M. Girardeau, J. Math. Phys., 3 (1962), 131 | DOI | MR

[9] V. P. Maslov, O. Yu. Shvedov, TMF, 98:2 (1994), 266 | MR | Zbl

[10] N. N. Bogolyubov, Izv. AN SSSR. Ser. fiz., 11:1 (1947), 77 | MR