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In Mudelung's book, Introduction to Solid-State Theory, I have a confusion about the statement.

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Here, $x$ should be $\frac{\mu}{k_B T}$.

I am cofused about his statement. Why does $x<0$ mean nondegeneracy and $x>0$ mean strong degeneracy?

I don't understand his statement, can you help me?

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2 Answers 2

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The reason is the following. If you write down the formula for Fermi-Dirac distribution, you can see that when x is negative, expanding the Fermi-Dirac distribution function using Maclaurin series, you will get the Boltzmann distribution which holds for a classical gas. So it means that your gas is nondegenerate.

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Notice that the Fermi-Dirac integral comes from the use of the Fermi-Dirac distribution. Another way to define a system degenerate or non degenerate is to compare the Fermi temperature $T_{F}$ to the actual temperature $T$ of the fermionic system under the study.

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