Weakly Interacting Bose Gas
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چکیده
We will look at the weakly interacting system at low temperatures. Already, without interactions, we have Bose condensation 〈 b+ 0 b0 〉 = N0 = N. (2) Interactions will reduce this, but if they are weak the depletion of the condensate will be a small fraction (N −N0)/N 1, or ∑ E k ′ 〈 bE k bE k 〉 N, (3) with ∑′ denoting the sum over all E k 6= 0. With the macroscopic occupation of the zero mode we can neglect the quantum fluctuations relative to the mean (cf. the classical treatment of electromagnetism) b0 → N 0 , b+ 0 → N 0 (4)
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