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Trudy Mat. Inst. Steklova, 2000, Volume 228, Pages 246–263 (Mi tm504)  

The Complex-Germ Method for Statistical Mechanics of Model Systems

V. P. Maslov, O. Yu. Shvedov

M. V. Lomonosov Moscow State University, Faculty of Physics

Abstract: We consider a special (“semiclassical”) class of Hamiltonian operators in the Fock space. This class involves the superconductivity BCS model, as well as the lattice magnetic Hamiltonians. It is shown that the commutator of two observables from this class is proportional to a small parameter. For each observable of this type, one can introduce a function on the phase space which corresponds to the observable. The Poisson bracket between two functions is defined. Two approaches are developed for investigating the Schrödinger equation with the Hamiltonian of the class under consideration. One of them is based on the Ehrenfest theorem, and another is based on the substitution of the hypothetical asymptotic solution to the equation. We construct the “semiclassical” states obeying the following property: in the “semiclassical” limit, the average values of “semiclassical” observables in such states coincide with the values of the corresponding functions at a certain point of the classical phase space. The asymptotics constructed can be interpreted in terms of the complex-germ theory.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2000, 228, 234–251

Bibliographic databases:
UDC: 531.19
Received in September 1999

Citation: V. P. Maslov, O. Yu. Shvedov, “The Complex-Germ Method for Statistical Mechanics of Model Systems”, Problems of the modern mathematical physics, Collection of papers dedicated to the 90th anniversary of academician Nikolai Nikolaevich Bogolyubov, Trudy Mat. Inst. Steklova, 228, Nauka, MAIK Nauka/Inteperiodika, M., 2000, 246–263; Proc. Steklov Inst. Math., 228 (2000), 234–251

Citation in format AMSBIB
\Bibitem{MasShv00}
\by V.~P.~Maslov, O.~Yu.~Shvedov
\paper The Complex-Germ Method for Statistical Mechanics of Model Systems
\inbook Problems of the modern mathematical physics
\bookinfo Collection of papers dedicated to the 90th anniversary of academician Nikolai Nikolaevich Bogolyubov
\serial Trudy Mat. Inst. Steklova
\yr 2000
\vol 228
\pages 246--263
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm504}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1782585}
\zmath{https://zbmath.org/?q=an:1034.82035}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2000
\vol 228
\pages 234--251


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