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I have recently heard the following statement:

A negative chemical potential means absence of particles.

However, I cannot make this consistent with e.g. a system of free bosons for which $\mu$ must be negative to ensure stability of the partition function.

Qmechanic
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S-low
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    Source for this quote? Related to your question: https://physics.stackexchange.com/q/92314/ – Tobias Fünke Jan 26 '21 at 10:38
  • See e.g. here http://qpt.physics.harvard.edu/c58.pdf at the end of pag 5.

    How should I then interpret "The ground state for μ < 0 is the vacuum with no particles"?

     – S-low Jan 26 '21 at 11:07
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    The quote "A negative chemical potential means absence of particles." is in section 2.1 of your cited notes. Section 2 is about fermions, so the necessity of negative $\mu$ for bosons is irrelevent. – mike stone Jan 27 '21 at 13:01

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Let me recapitulate to answer my own question

  1. A system of boson requires $\mu\leq 0$ to ensure stability of the theory.
  2. $\mu\leq 0$ means that the system is happy to accept new particles Ref. This is sort of intuitive for a system of bosons
  3. At $T=0$ the Bose distribution function vanishes. This means that \begin{equation} \mu\leq0 \rightarrow n_\text{B}(T=0,\epsilon)=0 \end{equation} which ultimately means absence of particles.
S-low
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