2007/02/28 by Tatsuya Tate
Mathematics · Physics and Astronomy · #Asymptotic formula #Boson #Differential operator #Hamiltonian (control theory) #Mathematical analysis #Mathematical physics #Mathematics #Operator (biology) #Order (exchange) #Physics #Pure mathematics #Quantum chaos and dynamical systems #Quantum mechanics #Scientific Research and Discoveries #Spectral Theory in Mathematical Physics #math.FA #math.SP #msc:35P20 #msc:58J50
paper · pdf · doi:10.3233/asy-2009-0973
published as Asymptotic Analysis 67 (2010) 101-123 · Introduction has rewritten. In particular, the assumption in the main theorem has been changed. The assumption of main theorem in the old version is not suitable. Some mistakes are fixed. To appear in the journal Asymptotic Analysis
arxiv created 2009/09/28 · openalex publication_date 2010/04/01 · arxiv updated 2017/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We discuss asymptotics of the number of states of Boson gas whose Hamiltonian is given by a positive elliptic pseudo-differential operator of order one on a compact manifold. We obtain an asymptotic formula for the average of the number of states. Furthermore, when the operator has integer eigenvalues and the periodic orbits of period less than 2π of the classical mechanics form clean submanifolds of lower dimensions, we give an asymptotic formula for the number of states itself. This is regarded as an analogue of the Meinardus theorem on asymptotics of the number of partitions of a positive integer. We use the Meinardus saddle point method of obtaining the asymptotics of the number of partitions, combined with a theorem due to Duistermaat–Guillemin and other authors on the singularities of the trace of the wave operators.