Errata¶

This post collects various typos etc. in my publications. If you think you see something wrong that is not listed here, please let me know so I can correct it or include it.

The Unitary Fermi Gas: From Monte Carlo to Density Functionals¶

Equation numbers correspond to the preprint arXiv:1008.3933 but match the book without the prefix. Thus (9.72a) in the preprint corresponds to (72a) in the published book [Bulgac:2011].

\begin{gather} \begin{aligned} \nu(\vect{r}) &= \frac{1}{2}\sum_{n} u_n(\vect{r})v_n^*(\vect{r})\Bigl(f_\beta(E_n) - f_\beta(-E_n)\Bigr),\\ \vect{j}_a(\vect{r}) &= \frac{-\I}{2}\sum_{n} [u_n^*(\vect{r})\nabla u_n(\vect{r}) - u_n(\vect{r})\nabla u_n^*(\vect{r})]f_\beta(E_n),\\ \vect{j}_b(\vect{r}) &= \frac{-\I}{2}\sum_{n} [v_n(\vect{r})\nabla v_n^*(\vect{r}) - v_n^*(\vect{r})\nabla v_n(\vect{r})]f_\beta(-E_n), \end{aligned} \tag{9.72b} \end{gather}

The correct formula should have $g < 0$ for attractive interactions. In this case, $\Delta$ and $\nu$ have opposite signs:

\begin{gather} \Delta = g\nu = g_{\mathrm{eff}} \nu_c\tag{9.74} \end{gather}\begin{gather} \mathcal{E} = \frac{\hbar^2}{m}\left(\frac{\tau_a+\tau_b}{2}\right) + \Delta^\dagger \nu\tag{9.75} \end{gather}\begin{gather} \tau_+(k) = \tau_a(k) + \tau_b(k) \rightarrow \frac{2(m^*)^2\Delta^\dagger \Delta}{\hbar^4 k^2}, \qquad \nu(k) \rightarrow - \frac{m^*\Delta}{\hbar^2k^2}\tag{9.81} \end{gather}

and the following equation:

$$ \frac{\hbar^2 \tau_+}{2m^*} + \Delta^\dagger \nu = \frac{\hbar^2}{m}\left(\frac{\alpha_a\tau_a}{2} +\frac{\alpha_b\tau_b}{2}\right) + g\nu^\dagger\nu $$\begin{gather} \Delta = g\nu = g_{\mathrm{eff}} \nu_c\tag{9.82} \end{gather}\begin{gather} \tilde{C}(n_a, n_b) = \frac{\alpha_+ \nu}{\Delta} + \frac{1}{2}\int\frac{\d^3{\vect{k}}}{(2\pi)^3} \frac{1}{\hbar^2k^2}{2m} - \frac{\mu_+}{\alpha+} + \I 0^+ = \frac{\alpha_+}{g_{\mathrm{eff}}} + \Lambda \tag{9.84} \end{gather}

[Bulgac:2011]: http://dx.doi.org/10.1007/978-3-642-21978-8_9 'Aurel Bulgac, Michael McNeil Forbes, and Piotr Magierski, "The Unitary Fermi Gas: From Monte Carlo to Density Functionals", 836, 305 -- 373 (2012) 1008.3933'