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Download [tex110] Occupation number fluctuations
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Transcript
[tex110] Occupation number fluctuations Consider an ideal quantum gas specified by the grand partition function Z. Start from the expressions 2 ∞ 1 −2 ∂ 2 Z 1 −1 ∂Z 1X 2 2 hnk i − hnk i = β − , ln Z = β ln(1 + aze−βk ), Z ∂2k Z ∂k a k=1 where a = +1, 0, −1 represent the FD, MB, and BE cases, respectively, to derive the following result for the relative fluctuations in the occupation numbers: 1 hn2k i − hnk i2 = − a. 2 hnk i hnk i Note that in the BE (FD) statistics, these fluctuations are enhanced (suppressed) relative to those in the MB statistics. Solution:
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