Thermodynamic properties of bosons symmetric double-well potentials

We study the thermodynamic properties and the Bose-Einstein condensation (B EC) for a finite number N of identical non-interacting bosons in the field of a deep symmetric double-well potential (SDWP). The temperature dependenc e of the heat capacity C(T) at low temperatures is analyzed, and we derive several generic results which are valid when the energy difference between the first two excited states is sufficiently large. We also investigate num erically the properties of non-interacting bosons in three-dimensional supe rpositions of deep quartic SDWP's. At low temperatures, we find that C(T) d isplays microstructures which are sensitive to the value of N and the therm al variation of the condensate fraction shows a characteristic plateau. The origin of these features is discussed, and some general conclusions are dr awn.