an:06166756
Zbl 1273.82011
Fidaleo, Francesco
Harmonic analysis on Cayley trees. II: The Bose-Einstein condensation
EN
Infin. Dimens. Anal. Quantum Probab. Relat. Top. 15, No. 4, Paper No. 1250024, 32 p. (2012).
0219-0257 1793-6306
2012
j
82B20 05C05 47N50
Bose-Einstein condensation; trees; inhomogeneous graphs; eigenvalue problems
The article is a continuation of researches presented in a previous paper of the author [J. Funct. Anal. 261, No. 3, 604--634 (2011; Zbl 1229.47020)] and its correction [ibid. 262, No. 10, 4634--4637 (2012; Zbl 1307.47012)]. Further investigations on the Bose-Einstein condensation for the pure hopping model on amenable networks obtained by perturbations on periodic graphs are to be found in the paper of \textit{F. Fidaleo, D. Guido} and \textit{T. Isola} [Infin. Dimens. Anal. Quantum Probab. Relat. Top. 14, No. 2, 149--197 (2011; Zbl 1223.82012)].
The article refers largely to the results in the above papers. In the first part, there is a presentation of the models as well as of their general statistical properties. It follows an investigation on the dynamics associated to the so-called pure hopping one-particle Hamiltonian for the perturbed Cayley trees. The article ends with a presentation of results regarding the infinite-volume behavior of finite-volume Gibbs states.
Claudia Simionescu-Badea (Wien)
1229.47020; 1223.82012; 1307.47012