Commit e2b2a7a5 authored by dmar's avatar dmar
Browse files

Exercise-9

parent aaec79ae
%% Cell type:code id: tags:
``` python
import numpy as np
import matplotlib.pyplot as plt
```
%% Cell type:markdown id: tags:
Compute correlation as:
$$ corr (t) = \int \dot{\mu}(\tau) \cdot \dot{\mu}(\tau + t) d \tau $$
$\tau$ will be an index that runs on all the simulation time. For every value of $\tau$ $t$ varies and we compute the single integrand elements and sum (~integrate) it to $corr(t - \tau)$
%% Cell type:code id: tags:
``` python
# load file reading only the columns of the derivative and skipping the first 45 rows (~ thermalization)
D_dipole = np.loadtxt('dipolemet.traj',usecols = (4,5,6),skiprows=45,comments=' DIPOLE [Non Periodic](')
Nmax = 500
N = len(D_dipole)
timestep = 0.5 #fs
c_cm_s = 29979245800
corr_time = np.zeros(Nmax)
for tau in range(N-Nmax):
for t in range(tau,tau+Nmax):
corr_time[t-tau] = corr_time[t-tau] + np.dot(D_dipole[tau], D_dipole[t])
for t in range(Nmax):
corr_time[t] /= (N*(N-t))
```
%% Cell type:code id: tags:
``` python
fig = plt.plot(timestep*np.arange(Nmax),corr_time/corr_time[0],color='crimson', lw=2)
ax = plt.gca()
ax.set_xlabel('time')
ax.set_ylabel('correlation')
plt.savefig('METtime_corr', dpi=300,transparent=True)
```
%% Cell type:code id: tags:
``` python
#Fmax up to 4000 cm^-1
Fmax = int((2e-15*np.pi*timestep*c_cm_s)*N*(4000/(2*np.pi)))
corr_freq = np.zeros([Fmax])
freq = np.zeros([Fmax])
for i in range(Fmax):
omega = i*2*np.pi/N
for j in range(Nmax):
corr_freq[i] += np.cos(omega*j)*corr_time[j]
freq[i] = omega/(2e-15*np.pi*timestep*c_cm_s)
#corr_freq
```
%% Cell type:code id: tags:
``` python
fig = plt.plot(freq,corr_freq,color='crimson', lw=2)
ax = plt.gca()
ax.set_xlabel('frequency')
ax.set_ylabel('correlation')
plt.savefig('METfreq_corr', dpi=300,transparent=True)
```
%% Cell type:code id: tags:
``` python
```
%% Cell type:code id: tags:
``` python
```
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