Abstract
Thermodynamic properties of Robin quantum well with extrapolation length Λ are analyzed theoretically both for canonical and two grand canonical ensembles with special attention being paid to situation when energies of one or two lowest-lying states are split-off from rest of spectrum by large gap that is controlled by varying Λ. For single split-off level, which exists for the geometry with equal magnitudes but opposite signs of Robin distances on confining interfaces, heat capacity c_V of canonical averaging is a nonmonotonic function of temperature T with its salient maximum growing to infinity as ln²Λ for decreasing to zero extrapolation length and its position being proportional to 1/(Λ²lnΛ). Specific heat per particle c_N of Fermi-Dirac ensemble depends nonmonotonically on temperature too with its pronounced extremum being foregone on T axis by plateau whose value at dying Λ is (N-1)/(2N)k_B, with N being a number of fermions. Maximum of c_N, similar to canonical averaging, unrestrictedly increases as Λ goes to zero and is the largest for one particle. Most essential property of Bose-Einstein ensemble is a formation, for growing number of bosons, of sharp asymmetric shape on the c_N-T characteristics that is more protrusive at the smaller Robin distances. This cusp-like structure is a manifestation of the phase transition to the condensate state. For two split-off orbitals, one additional maximum emerges whose position is shifted to colder temperatures with increase of energy gap between these two states and their higher-lying counterparts and whose magnitude approaches Λ-independent value. All these physical phenomena are qualitatively and quantitatively explained by variation of energy spectrum by Robin distance.