A spinless Bose-Einstein condensate

Eric Cornell, Carl Wieman

Ajanta Bhowal, Muktish Acharyya

The density of bosonic states are calculated for spinless free massive bosons in generalised d dimensions. The number of bosons are calculated in the lowest energy state. The Bose Einstein condensation was found in generalised dimensions (on and above d = 3) and the condensation temperature was observed to drop abruptly above three dimensions and decreases monotonically as the dimensionalities of the system increases. The rate of fall of the condensation temperature decreases as the dimensionality increases. This article is aimed to the University graduate students.

Maksim Tomchenko

It is well known that a Bose–Einstein (BE) condensate of atoms exists in a system of interacting Bose atoms at T≲Tc(i), where Tc(i) is the BE condensation temperature of an ideal gas. It is also generally accepted that BE condensation is impossible at “ultrahigh” temperatures T≫Tc(i). While the latter property has been theoretically proven for an ideal gas, no such proof exists for an interacting system, to our knowledge. In this paper, we propose an approximate mathematical proof for a finite, nonrelativistic, periodic system of N spinless interacting bosons. The key point is that, at T≫Tc(i), the main contribution to the occupation number N0=1Z∑℘e−E℘/kBT⟨Ψ℘|a^0+a^0|Ψ℘⟩, corresponding to atoms with zero momentum, originates from the states containing N elementary quasiparticles. These states do not contain the BE condensate of zero-momentum atoms, implying that an ultrahigh temperature should “blur” such a condensate.

Eric Cornell, Carl Wieman

Rodrigo González Escudero, Chun-Chia Chen, Shayne Bennetts +2 more

Ajanta Bhowal Acharyya, Muktish Acharyya

The density of bosonic states are calculated for spinless free massive bosons in generalised d dimensions. The number of bosons are calculated in the lowest energy state. The Bose Einstein condensation was found in generalised d dimensions (on and above d = 3) and the condensation temperature is calculated which is observed to drop abruptly above three dimensions and decreases monotonically as the dimensionalities of the system increases. The rate of fall of the condensation temperature decreases as the dimensionality increases. Interestingly, in the limit of infinite dimensions, the condensation temperature is observed to approach a nonzero finite value.