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: 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 #+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 #+BEGIN_SRC elisp :output none :exports none
(setq org-latex-listings 'minted (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): (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. when $\Psi_T$ gets closer to the exact wave function.
This term can be simulated by 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 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. 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: the potential term is considered as a cumulative product of weights:
\begin{eqnarray*} \begin{eqnarray*}
W(\mathbf{r}_n, \tau) W(\mathbf{r}_n, \tau) = \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) = (E_L(\mathbf{r}_i) - E_{\text{ref}}) \right) =
\prod_{i=1}^{n} w(\mathbf{r}_i) \prod_{i=1}^{n} w(\mathbf{r}_i)
\end{eqnarray*} \end{eqnarray*}
@ -2472,8 +2470,8 @@ def MonteCarlo(a, nmax, dt, Eref):
# Run simulation # Run simulation
a = 1.2 a = 1.2
nmax = 100000 nmax = 100000
dt = 0.01 dt = 0.05
tau = 10. tau = 100.
E_ref = -0.5 E_ref = -0.5
X0 = [ MonteCarlo(a, nmax, dt, E_ref) for i in range(30)] X0 = [ MonteCarlo(a, nmax, dt, E_ref) for i in range(30)]
@ -2516,9 +2514,9 @@ end subroutine pdmc
program qmc program qmc
implicit none implicit none
double precision, parameter :: a = 1.2d0 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 :: E_ref = -0.5d0
double precision, parameter :: tau = 10.d0 double precision, parameter :: tau = 100.d0
integer*8 , parameter :: nmax = 100000 integer*8 , parameter :: nmax = 100000
integer , parameter :: nruns = 30 integer , parameter :: nruns = 30