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