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Harmonic analysis on Cayley trees. II: The Bose-Einstein condensation. (English) Zbl 1273.82011
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 F. Fidaleo, D. Guido and 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.

82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
05C05 Trees
47N50 Applications of operator theory in the physical sciences
Full Text: DOI arXiv
[1] DOI: 10.1142/S0219025704001645 · Zbl 1073.81057
[2] DOI: 10.1103/PhysRev.106.162
[3] DOI: 10.1007/BF01053795 · Zbl 0893.60094
[4] DOI: 10.1007/978-3-662-09089-3
[5] DOI: 10.1088/0953-4075/34/23/314
[6] DOI: 10.1016/j.jfa.2011.04.007 · Zbl 1229.47020
[7] DOI: 10.1016/j.jfa.2012.02.019 · Zbl 1307.47012
[8] DOI: 10.1142/S0219025711004389 · Zbl 1223.82012
[9] DOI: 10.1112/blms/21.3.209 · Zbl 0645.05048
[10] DOI: 10.1007/978-3-642-74346-7
[11] DOI: 10.1007/0-387-32792-4 · Zbl 1099.60004
[12] DOI: 10.1016/j.physleta.2007.05.119
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