TREX/qmc-lttc
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Anthony Scemama 2021-02-03 17:24:21 +01:00
parent 14b35f2c2c
commit 8027106331
1 changed files with 8 additions and 10 deletions
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@ -9,7 +9,7 @@
#+OPTIONS: H:4 num:t toc:t \n:nil @:t ::t |:t ^:t -:t f:t *:t <:t
#+OPTIONS: TeX:t LaTeX:t skip:nil d:nil todo:t pri:nil tags:not-in-toc
# EXCLUDE_TAGS: solution
#+EXCLUDE_TAGS: solution
#+BEGIN_SRC elisp :output none :exports none
(setq org-latex-listings 'minted
@ -2239,7 +2239,7 @@ gfortran hydrogen.f90 qmc_stats.f90 vmc_metropolis.f90 -o vmc_metropolis
(pure Diffusion Monte Carlo):
\[
\exp \left( \int_0^\tau - (V(\mathbf{r}_t) - E_{\text{ref}}) dt \right).
\prod_i \exp \left( - (V(\mathbf{r}_i) - E_{\text{ref}}) \delta t \right).
\]
@ -2287,7 +2287,7 @@ gfortran hydrogen.f90 qmc_stats.f90 vmc_metropolis.f90 -o vmc_metropolis
when $\Psi_T$ gets closer to the exact wave function.
This term can be simulated by
\[
\exp \left( \int_0^\tau - (E_L(\mathbf{r}_t) - E_{\text{ref}}) dt \right).
\prod_i \exp \left( - (E_L(\mathbf{r}_i) - E_{\text{ref}}) \delta t \right).
\]
where $E_{\rm ref}$ is the constant we had introduced above, which is adjusted to
an estimate of the average energy to keep the weights close to one.
@ -2384,9 +2384,7 @@ gfortran hydrogen.f90 qmc_stats.f90 vmc_metropolis.f90 -o vmc_metropolis
the potential term is considered 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\,
W(\mathbf{r}_n, \tau) = \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*}
@ -2472,8 +2470,8 @@ def MonteCarlo(a, nmax, dt, Eref):
# Run simulation
a = 1.2
nmax = 100000
dt = 0.01
tau = 10.
dt = 0.05
tau = 100.
E_ref = -0.5
X0 = [ MonteCarlo(a, nmax, dt, E_ref) for i in range(30)]
@ -2516,9 +2514,9 @@ end subroutine pdmc
program qmc
implicit none
double precision, parameter :: a = 1.2d0
double precision, parameter :: dt = 0.1d0
double precision, parameter :: dt = 0.05d0
double precision, parameter :: E_ref = -0.5d0
double precision, parameter :: tau = 10.d0
double precision, parameter :: tau = 100.d0
integer*8 , parameter :: nmax = 100000
integer , parameter :: nruns = 30