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Chemical potential of ideal solution in grand canonical ensemble

Even though I follow a bit different way compared to what you have, I will provide an answer that it end up with the same equation. First step: Derive the chemical potential formula from the Grand ...
Theodoros's user avatar
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Distinguishability in Maxwell-Boltzmann statistics

For the record, the three regimes agree in the dilute limit, i.e. when $N_i\to0$ when fugacity $z = e^{\beta\mu}$ vanishes (not when $z\to+\infty$ as you claimed, this is perhaps due to your sign ...
LPZ's user avatar
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1 vote
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The definition on vacuum-vacuum amplitude with current in chapter of External Field Method of Weinberg's QFT

$Z_0=Z[J\!=\!0]$ in eq. (9.39) is the functional determinant from the Gaussian integration of the path integral with a quadratic action. See also how P&S complete the square in eqs. (9.37)-(9.38). ...
Qmechanic's user avatar
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Calculation of canonical partition function for fermion system with degenerate energy levels

I think LPZ already gave a very good answer, so here I'll just add a comment and a general picture. In some sense, you can say that this kind of problem is exactly one of the reasons you would like to ...
Jun_Gitef17's user avatar
1 vote

Calculation of canonical partition function for fermion system with degenerate energy levels

In general it is easier to compute the canonical partition function from the grand canonical one. For a direct computation of the canonical ensemble, it is also easier to think in terms of orbitals ...
LPZ's user avatar
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The definition of the path integral

The generating of functional of a (scalar) quantum field theory with field operator $\Phi(x)$ is defined by $$Z[f]=\langle 0 |e^{i \int d^dx \, \Phi(x) f(x)} |0\rangle, \tag{1} \label{1}$$ where $f(x)$...
Hyperon's user avatar
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2 votes

The partition function of a particle in a magnetic field diverges. Why?

Making everything dimensionless so that $\hbar=1$: $$ H = \frac12(p-A)^2\\ A = \frac\omega2(-y,x) $$ with $\omega$ the cyclotron frequency, the usual theory of Landau level gives the spectrum of the ...
LPZ's user avatar
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1 vote

The partition function of a particle in a magnetic field diverges. Why?

I may have solved my issue (thanks to @By Symmetry for the hint). Indeed, the divergence appears to be related to the infinite area covered by the quantum system in 2D. We could consider the similar ...
Cham's user avatar
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