Trap-size scaling of finite Bose systems within an exact canonical ensemble

Universal fine structure of the specific heat at the criticalλ-point for an ideal Bose gas in an arbitrary trap

“…Critical phenomena and the lack of an analytical solution to them are a cause for concern, and researchers want to see an explicit rigorous formula and its true plot instead of an incorrect, within the critical region, mean-field or grand canonical ensemble ansatz [3,4,6,9]. The problem of the influence of the boundaries and form of the confining potential on the BEC phase transition in the mesoscopic systems has been discussed by many authors (see [6,8] and [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]), but remained unsolved until recently, even for the case of an ideal gas. We refer to [1,2] for a discussion of the known theories, including the Landau meanfield [3,4,27,28] and phenomenological renormalization group [29][30][31][32][33] theories.…”

“…The latter theories are based on the grand canonical ensemble approximation and do not correctly describe critical fluctuations (see [5,6] and [34][35][36][37][38]). We need to solve the essentially more complicated, but correctly physically formulated problem of BEC in the canonical ensemble (see [3,4,6,8,16,17], [22][23][24][25][26][27][28], [35][36][37][38][39], [42][43][44][45][46][47]).…”

Efficiency at Maximum Power Output of a Quantum-Mechanical Brayton Cycle

“…where n is a positive integer quantum number, and σ is an index of the single-particle energy spectrum. Here we have used the relation ω = λL −θ , where λ is a constant for a given potential, and θ is trap exponent, [38] which is dependent on the trapping potential. The index σ is also sensitively dependent on the form of trapping potential that determines the energy spectrum.…”