CRC Press eBooks

Bose–Einstein condensation

Kerson Huang

Published Nov 9, 2001• 177 citations

Abstract

Consider a gas of bosons whose total number is conserved. The equation for the fugacity is nλ3 = g3/2(z) (11.1) and a qualitative plot of the function g3/2 is shown in Fig.11. 1. The function has infinite slope at z = 1, since z d dz g3/2(z) = g1/2(z) = ∞∑ =1 z√ (11.2) and the series diverges at z = 1. It is thus bounded by the value g3/2(1) = ∞∑ =1 −3/2 = ζ (3/2) = 2.612 . . . (11.3) solution to (11.1) nλ3 ≤ g3/2(1). (11.4) This condition can be violated by increasing the density, or lowering the temperature. What then would be the value of z?

DOI: 10.1201/9781482268300-13

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