Critical temperature of non-interacting Bose gases on disordered lattices

Abstract

For a non-interacting Bose gas on a lattice we compute the shift of the critical temperature for condensation when random-bond and onsite disorder are present. We evidence that the shift depends on the space dimensionality D and the filling fraction f. For D -> infinity (infinite-range model), using results from the theory of random matrices, we show that the shift of the critical temperature is negative, depends on f, and vanishes only for large f. The connections with analogous results obtained for the spherical model are discussed. For D=3 we find that, for large f, the critical temperature Tc is enhanced by disorder and that the relative shift does not sensibly depend on f; at variance, for small f, Tc decreases in agreement with the results obtained for a Bose gas in the continuum. We also provide numerical estimates for the shift of the critical temperature due to disorder induced on a non-interacting Bose gas by a bichromatic incommensurate potential.

18 pages, 8 figures; Fig. 8 improved adding results for another value of q (q=830/1076)

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• Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
• Metastability and discrete spectrum of long-range systems
• Stochastic Mean-Field Theory: Method and Application to the Disordered Bose-Hubbard Model at Finite Temperature and Speckle Disorder
• Lattice bosons in a quasi-disordered environment: The effects of next-nearest-neighbor hopping on localization and Bose-Einstein condensation
• Effect of random on-site energies on the critical temperature of a lattice Bose gas