title: Bose-Einstein condensation in the infinitely ramified star and wheel graphs.
abstract: In this work, we provide exact solutions for the ideal boson lattice gas on the infinitely ramified star and wheel graphs. Within a tight-binding description, we show that Bose-Einstein condensation (BEC) takes place at a finite temperature after a proper rescaling of the hoping integral ɛ connecting a central site to the peripheral ones. Analytical expressions for the transition temperature, the condensed gas fraction, and the specific heat are given for the star graph as a function of the density of particles n. In particular, the specific heat has a mean-field character, being null in the high-temperature noncondensed phase with a discontinuity at T(c). In the wheel graph, on which the peripheral sites form a closed chain with hopping integral t, BEC takes place only above a critical value of the ratio ɛ/t for which a gap ΔE appears between the ground state and a one-dimensional band. A detailed analysis of the BEC characteristics as a function of n and ΔE is provided. The specific heat in the high-temperature phase of the wheel graph remains finite due to correlations among the peripheral sites.
authors.affiliation: Instituto de Física, Universidade Federal de Alagoas, Maceió AL, Brazil.
authors.forename: E J G G
authors.initials: EJ
authors.lastname: Vidal
authors.forename: R P A
authors.initials: RP
authors.lastname: Lima
authors.forename: M L
authors.initials: ML
authors.lastname: Lyra