Bose-Einstein Condensation in Multilayers

The critical BEC temperature T _c of a non interacting boson gas in a layered structure like those of cuprate superconductors is shown to have a minimum T _{c, m} , at a characteristic separation between planes a _m . It is shown that for a< a _m , T _c increases monotonically back up to the ideal Bose gas T ₀ suggesting that a reduction in the separation between planes, as happens when one increases the pressure in a cuprate, leads to an increase in the critical temperature. For finite plane separation and penetrability the specific heat as a function of temperature shows two novel crests connected by a valley in addition to the well-known BEC peak at T _c associated with the 3D behavior of the gas. For completely impenetrable planes the model reduces to many disconnected infinite slabs for which just one hump survives becoming a peak only when the slab widths are infinite.