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This commit is contained in:
Anthony Scemama 2021-02-02 17:00:49 +01:00
parent 2ee80b9bb3
commit b63191f9a7
1 changed files with 6 additions and 4 deletions
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@ -2040,6 +2040,8 @@ print(f"A = {A} +/- {deltaA}")
#+END_SRC
#+RESULTS:
: E = -0.48034171558629885 +/- 0.0005286038561061781
: A = 0.6210380000000001 +/- 0.0005457375900937905
*Fortran*
#+BEGIN_SRC f90
@ -2379,13 +2381,13 @@ gfortran hydrogen.f90 qmc_stats.f90 vmc_metropolis.f90 -o vmc_metropolis
$\exp \left( -\delta t\,( E_L(\mathbf{r}) - E_{\rm ref}) \right)$ as a
cumulative product of weights:
\[
\begin{eqnarray*}
W(\mathbf{r}_n, \tau)
= \exp \left( \int_0^\tau - (E_L(\mathbf{r}_t) - E_{\text{ref}}) dt \right)
\approx \prod_{i=1}^{n} \exp \left( -\delta t\,
& = & \exp \left( \int_0^\tau - (E_L(\mathbf{r}_t) - E_{\text{ref}}) dt \right) \\
& \approx & \prod_{i=1}^{n} \exp \left( -\delta t\,
(E_L(\mathbf{r}_i) - E_{\text{ref}}) \right) =
\prod_{i=1}^{n} w(\mathbf{r}_i)
\]
\end{eqnarray*}
where $\mathbf{r}_i$ are the coordinates along the trajectory and we introduced a time-step $\delta t$.