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We study the thermodynamics of ideal Bose gas as well as the transportproperties of non interacting bosons and fermions in a one dimensionalquasi-periodic potential, namely Aubry-Andr\'e (AA) model at finitetemperature. For bosons in finite size systems, the effect of quasi-periodicpotential on the crossover phenomena corresponding to Bose-Einsteincondensation (BEC), superfluidity and localization phenomena at finitetemperatures are investigated. From the ground state number fluctuation wecalculate the crossover temperature of BEC which exhibits a non monotonicbehavior with the strength of AA potential and vanishes at the self-dualcritical point following power law. Appropriate rescaling of the crossovertemperatures reveals universal behavior which is studied for differentquasi-periodicity of the AA model. Finally, we study the temperature and fluxdependence of the persistent current of fermions in presence of aquasi-periodic potential to identify the localization at the Fermi energy fromthe decay of the current.

A finite temperature study of ideal quantum gases in the presence of one dimensional quasi-periodic potential