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Averaging the operators for a large number of clusters: Phase transitions

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Abstract

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)=zlog(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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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    V. P. Maslov

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  1. V. P. Maslov
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 125, No. 2, pp. 297–314, November, 2000.

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Maslov, V.P. Averaging the operators for a large number of clusters: Phase transitions. Theor Math Phys 125, 1552–1567 (2000). https://doi.org/10.1007/BF02551014

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  • DOI: https://doi.org/10.1007/BF02551014

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