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Name:
Miloslav Znojil
Reviewer number:
9689
Email:
znojil@ujf.cas.cz
Item's zbl-Number:
DE 017 290 069
Author(s):
maslov, V. P.:
Shorttitle:
A new representation of the Hamiltonian operator for bosons and fermions. Quantization of free energy and dependence of Landau criterion on temperature.
Source:
Math. Notes 68, No. 6, 800-802 (2000); translation from Mat. Zametki 68, No. 6, 945-947 (2000), in Russian.
Classification:
81S99None of the above, but in this section
Primary Classification:
82D50Superfluids
Secondary Classification:
82B10Quantum equilibrium statistical mechanics general
82B26Phase transitions general
Keywords:
many particle Hamiltonians; bosonic and fermonic Fock space; creation and annihilation operators; entropy operator; free energy operator; thermodynamic limit; phase transition; condensate; Landau criterion of the loss of superfluidity;
Review:
Three pages of short notes on three subjects covered by the title
and by the three recent papers by the author (plus his two older
books). This means that the text (the majority of which are
formulae) forms an extended abstract by itself. Its main theorem
states that in terms of the (either bosonic or fermionic) creation
and annihilation operators one can introduce a density-like
functional and an ''averaged" operator H in such a way that the
projection of H on the pertaining Fock space coincides with the
usual partial differential Hamiltonian of the system. The
subsequent commentary (adding, in the similar spirit, an entropy
and free energies) is split in the weak- and strong-interaction
parts. Curiously enough, the paper was originally presented in
Russian (I was told by my Russian friends that such a practice has
also some pecuniary benefits)] but the text concerning the latter
case [including the operator representation of the free energies
(8) and related discussion] appears only in its ''translated"
English update where one misses (for compensation?) the explicit
half-page form of the equation which determines the k=1 solutions
(6) and, via the loss of reality of its eigenvalues, describes
the Landau's boundary of the domain of the superfluidity (hence,
interested people and the specialists should rather read both the
language mutations).
Remarks to the editors:

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