2017/11/28 by J. G. Martínez-Herrera, Martínez-Herrera, J. G., J. García-Nila +3
Physics and Astronomy · #FOS: Physical sciences #Quantum Gases (cond-mat.quant-gas) #cond-mat.quant-gas
paper · pdf · doi:10.48550/arxiv.1711.10100
8 pages, 9 figures
arxiv created 2018/12/20 · arxiv updated 2018/12/21
Bose-Einstein condensation in a Bose gas is studied analytically, in any positive dimensionality (d>0) for identical bosons with any energy-momentum positive-exponent (s>0) plus an energy gap Δ between the ground state energy ε0 and the first excited state, i.e., ε=ε0 for k=0 and ε=ε0 +Δ+ csks, for k>0, where ℏ k is the particle momentum and cs a constant with dimensions of energy multiplied by a length to the power s > 0. Explicit formula with arbitrary d/s and Δ are obtained and discussed for the critical temperature and the condensed fraction, as well as for the equation of state from where we deduce a generalized Δ independent thermal de Broglie wavelength. Also the internal energy is calculated from where we obtain the isochoric specific heat and its jump at Tc. When Δ> 0, a Bose-Einstein critical temperature Tc ≠ 0 exists for any d > 0 at which the internal energy shows a peak and the specific heat shows a jump. Both the critical temperature and the specific heat jump increase as functions of the gap but they decrease as of d/s. At sufficiently high temperatures Δ- independent classical results are recovered. However, for temperatures below the critical one the gap effects are predominant. For Δ= 0 we recover previous reported results.