Harmonic Analysis on Inhomogeneous Amenable Networks and the Bose–Einstein Condensation

@article{Fidaleo2015HarmonicAO,
  title={Harmonic Analysis on Inhomogeneous Amenable Networks and the Bose–Einstein Condensation},
  author={F. Fidaleo},
  journal={Journal of Statistical Physics},
  year={2015},
  volume={160},
  pages={715-759}
}
  • F. Fidaleo
  • Published 2015
  • Physics, Mathematics
  • Journal of Statistical Physics
We study in detail relevant spectral properties of the adjacency matrix of inhomogeneous amenable networks, and in particular those arising by negligible additive perturbations of periodic lattices. The obtained results are deeply connected to the systematic investigation of the Bose–Einstein condensation for the so called Pure Hopping model describing the thermodynamics of Cooper pairs in arrays of Josephson junctions. After a careful investigation of the infinite volume limits of the finite… Expand

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References

SHOWING 1-10 OF 27 REFERENCES
Harmonic analysis on Cayley Trees II: the Bose Einstein condensation
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 topologicalExpand
HARMONIC ANALYSIS ON PERTURBED CAYLEY TREES AND THE BOSE EINSTEIN CONDENSATION
We study some spectral properties of the adjacency operator of non homogeneous networks. The graphs under investigation are obtained by adding density zero perturbations to the homogeneous CayleyExpand
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
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
On Bose–Einstein condensation in Josephson junctions star graph arrays
Abstract We report on the evidence of anomalous currents in graph-shaped arrays of Josephson junctions along peculiar branches of the networks. The specific case of a star-shaped array is consideredExpand
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
Graph Spectra for Complex Networks
TLDR
This self-contained book provides a concise introduction to the theory of graph spectra and its applications to the study of complex networks, and the general properties of both the adjacency and Laplacian spectrum of graphs are derived and applied to complex networks. Expand
Bose–Einstein condensation of photons in an optical microcavity
TLDR
The observation of a Bose–Einstein condensate of photons is reported, formally equivalent to a two-dimensional gas of trapped, massive bosons, in a dye-filled optical microcavity which acts as a ‘white-wall’ box. Expand
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
...
1
2
3
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