# Tag Info

### 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 ...

### 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 ...
• 11.7k
1 vote
Accepted

### 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). ...
• 203k
1 vote

### 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 ...
• 333
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 ...
• 11.7k

### 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 $f(x)$...
• 6,208
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 ...