Harmonic analysis on Cayley Trees II: the Bose Einstein condensation

@article{Fidaleo2012HarmonicAO,
  title={Harmonic analysis on Cayley Trees II: the Bose Einstein condensation},
  author={F. Fidaleo},
  journal={arXiv: Mathematical Physics},
  year={2012}
}
  • F. Fidaleo
  • Published 2012
  • Mathematics, Physics
  • arXiv: Mathematical Physics
We investigate the Bose-Einstein Condensation on non homogeneous non amenable networks for the model describing arrays of Josephson junctions on perturbed Cayley Trees. The resulting topological model has also a mathematical interest in itself. The present paper is then the application to the Bose-Einstein Condensation phenomena, of the harmonic analysis aspects arising from additive and density zero perturbations, previously investigated by the author in a separate work. Concerning the… Expand

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References

SHOWING 1-10 OF 13 REFERENCES
Harmonic analysis on perturbed Cayley Trees
We study the mathematical aspects of the Bose Einstein Condensation for the pure hopping model describing arrays of Josephson junctions on non homogeneous networks. The graphs under investigation areExpand
BOSE–EINSTEIN CONDENSATION ON INHOMOGENEOUS AMENABLE GRAPHS
We investigate the Bose–Einstein condensation on nonhomogeneous amenable networks for the model describing arrays of Josephson junctions. The resulting topological model, whose Hamiltonian is theExpand
Bose-Einstein condensation on inhomogeneous complex networks
The thermodynamic properties of non-interacting bosons on a complex network can be strongly affected by topological inhomogeneities. The latter give rise to anomalies in the density of states thatExpand
The boson gas on a Cayley tree
We analyze the free boson gas on a Cayley tree using two alternative methods. The spectrum of the lattice Laplacian on a finite tree is obtained using a direct iterative method for solving theExpand
Corrigendum to “Harmonic analysis on perturbed Cayley Trees” [J. Funct. Anal. 261 (3) (2011) 604–634]
Abstract Due to the boundary effects, the standard definition of the integrated density of the states (i.d.s. for short) used in [F. Fidaleo, Harmonic analysis on perturbed Cayley Trees, J. Funct.Expand
MONOTONE INDEPENDENCE, COMB GRAPHS AND BOSE EINSTEIN CONDENSATION
The adjacency matrix of a comb graph is decomposed into a sum of monotone independent random variables with respect to the vacuum state. The vacuum spectral distribution is shown to be asymptoticallyExpand
Topology-induced critical current enhancement in Josephson networks
Abstract We investigate the properties of Josephson junction networks with inhomogeneous architecture. The networks are shaped as “square comb” planar lattices on which Josephson junctions linkExpand
Spectra of Random and Almost-Periodic Operators
I. Metrically Transitive Operators.- 1 Basic Definitions and Examples.- 1.A Random Variables, Functions and Fields.- 1.B Random Vectors and Operators.- l.C Metrically Transitive Random Fields.- l.DExpand
A Survey on Spectra of infinite Graphs
Introduction. Operateurs lineaires associes a un graphe. Resultats fondamentaux. Rayon spectral, fonctions generatrices de marche et mesures spectrales. Croissance et nombre isoperimetrique d'unExpand
Non-negative Matrices and Markov Chains
Finite Non-Negative Matrices.- Fundamental Concepts and Results in the Theory of Non-negative Matrices.- Some Secondary Theory with Emphasis on Irreducible Matrices, and Applications.- InhomogeneousExpand
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