Sergio Albeverio, Yuri kondratiev, Agnieszka Kozak, Yuri Kozitsky
A Hierarchical Model of Quantum Anharmonic Oscillators: Critical Point Convergence
(390K, pdf)

ABSTRACT.  A hierarchical model of interacting quantum particles performing 
 anharmonic oscillations 
is studied in the Euclidean approach, in which the local Gibbs states are constructed as measures on infinite 
dimensional spaces. The local states restricted to the subalgebra generated by fluctuations of displacements of 
particles are in the center of the study. They are described by means of the corresponding temperature Green 
(Matsubara) functions. The result of the paper is a theorem, which describes the critical point convergence of such 
Matsubara functions in the thermodynamic limit.