Bose-Einstein condensation in diamond hierarchical lattices.
Phys Rev E Stat Nonlin Soft Matter Phys
; 89(5): 052133, 2014 May.
Article
em En
| MEDLINE
| ID: mdl-25353765
The Bose-Einstein condensation of noninteracting particles restricted to move on the sites of hierarchical diamond lattices is investigated. Using a tight-binding single-particle Hamiltonian with properly rescaled hopping amplitudes, we are able to employ an orthogonal basis transformation to exactly map it on a set of decoupled linear chains with sizes and degeneracies written in terms of the network branching parameter q and generation number n. The integrated density of states is shown to have a fractal structure of gaps and degeneracies with a power-law decay at the band bottom. The spectral dimension d(s) coincides with the network topological dimension d(f) = ln(2q)/ln(2). We perform a finite-size scaling analysis of the fraction of condensed particles and specific heat to characterize the critical behavior of the BEC transition that occurs for q > 2 (d(s) > 2). The critical exponents are shown to follow those for lattices with a pure power-law spectral density, with non-mean-field values for q < 8 (d(s) < 4). The transition temperature is shown to grow monotonically with the branching parameter, obeying the relation 1/T(c) = a + b/(q - 2).
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Base de dados:
MEDLINE
Assunto principal:
Modelos Moleculares
/
Coloides
/
Cristalização
/
Partículas Elementares
/
Modelos Químicos
Idioma:
En
Revista:
Phys Rev E Stat Nonlin Soft Matter Phys
Assunto da revista:
BIOFISICA
/
FISIOLOGIA
Ano de publicação:
2014
Tipo de documento:
Article
País de afiliação:
Brasil
País de publicação:
Estados Unidos