Koval’, G. V. Asymptotics in the number of elements of a statistical ensemble for Maslov equations in quantum thermodynamics. (English. Russian original) Zbl 1052.82005 Math. Notes 73, No. 4, 590-593 (2003); translation from Mat. Zametki 73, No. 4, 631-633 (2003). Summary: We consider a simple model problem which provides us with an example showing that not only periodic trajectories of the classical Hamiltonian system are significant for solutions of asymptotic problems, but the trajectories filling invariant tori also should be taken into consideration. For this model problem, we find the invariant tori and prove that the corresponding Maslov canonical operator gives an asymptotic solution of the problem. MSC: 82B10 Quantum equilibrium statistical mechanics (general) Keywords:Hamiltonian system; semiclassical asymptotics; Maslov canonical operator; invariant tori; periodic trajectories; Bose-Fock space PDFBibTeX XMLCite \textit{G. V. Koval'}, Math. Notes 73, No. 4, 590--593 (2003; Zbl 1052.82005); translation from Mat. Zametki 73, No. 4, 631--633 (2003) Full Text: DOI