Bose-Einstein
Condensation of the D-dimensional System of the Ideal Bose-gas
with
Excitation Spectrum ep = cps in the
Presence of Trapping Potential with
an Arbitrary Profile
Bose-Einstein
Condensation of the D-dimensional System of the Ideal Bose-gas
with
Excitation Spectrum ep = cps in the
Presence of Trapping Potential with
an Arbitrary Profile
Asymptotical methods are used to derive the
criterion of BEC possibility, and the criteria determining the order of phase
transition at BEC and indicating that BEC can be a phase transition (PTn) of an arbitrary order v Î
[2,¥) with finite or infinite jumps of the k-th
(k = n - 1) derivatives of
chemical potential m(T) and total energy E(T) with
regard to T and that all this is being determined by parameter c = D/s+
+¼+
(qi - are the exponents of
calibrating functions of asymptotical behavior of
at the minimum
point). Parameter c takes on an infinite sequence of
values (ck = k/(k - 1)), setting the Dc interval in which the BEC is possible, and for each PTn Dcn subintervals of Dc and on each Dcn there are subintervals where the jumps of m(T) and E(T) are either finite or infinite. The universal
role of parameter c in systematization of infinite
variety of extended systems "external field-system of bosons" by classes of
identical nature of phase transitions at BEC is also shown.