1207.0019 (V. P. Maslov)

Bose Condensate in the D-Dimensional Case, in Particular, for D=2    [PDF]

V. P. Maslov

This paper states that as the temperature tends to the degeneracy temperature, there are sufficiently many particles accumulating at the point of Bose condensate and a gap is being formed in the spectrum of the Schr\"odinger equation corresponding to the Bose gas. In the two-dimensional case, the spectrum is purely discrete, there is no transition to the integral formula, and the gap in the spectrum becomes more visual (Maslov). The case of finitely many particles of the order of $10^2$ is considered in the paper on the basis of heuristic considerations similar to those used by V. A. Fock to derive the Hartree--Fock equation. The paper is written in the physical language. The author's old results about the $\lambda$-point and superfluidity are given. The author's paper written in 1995 is presented in the Appendix.

View original: http://arxiv.org/abs/1207.0019