title: Bose-Einstein condensation in diamond hierarchical lattices.
abstract: 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).
authors.affiliation: Instituto de Física, Universidade Federal de Alagoas, 57072-900 Maceió-AL, Brazil.
authors.forename: M L
authors.initials: ML
authors.lastname: Lyra
authors.affiliation: Instituto de Física, Universidade Federal de Alagoas, 57072-900 Maceió-AL, Brazil.
authors.forename: F A B F
authors.initials: FA
authors.lastname: de Moura
authors.affiliation: Instituto de Física, Universidade Federal de Alagoas, 57072-900 Maceió-AL, Brazil.
authors.forename: I N
authors.initials: IN
authors.lastname: de Oliveira
authors.affiliation: Departamento de Biofísica e Farmacologia, Universidade Federal do Rio Grande do Norte, 59072-970 Natal-RN, Brazil.
authors.forename: M
authors.initials: M
authors.lastname: Serva
mesh_terms: D003102:Colloids / Q000737:chemistry*; D003198:Computer Simulation; D003460:Crystallization / Q000379:methods*; D004601:Elementary Particles; D008956:Models, Chemical; D008958:Models, Molecular; D044367:Phase Transition; D013816:Thermodynamics
chemical_list: D003102:Colloids