def gen_signal(atoms, pol_direction, k=2, nrep=1):
ttime = 20
steps = 100
tlist = np.linspace(0, ttime * 1e-6, steps)
NS = MuonNuclearInteraction(atoms)
NS.translate_rotate_sample_vec(pol_direction)
print("Computing signal...", end='', flush=True)
signal = np.zeros_like(tlist)
# Do we need more random realizations? Celio used 4 for a 8192 dim. H space.
for i in range(nrep):
signal += NS.celio(tlist, k=k)
signal /= nrep
print('done!')
del NS
return signal
r = 1.17 * angtom
atoms = [{
'Position': np.array([0., 0., 0.]),
'Label': 'F'
}, {
'Position': np.array([0., 0., r]),
'Label': 'mu'
}, {
'Position': np.array([0., 0., 2 * r]),
'Label': 'F'
}]
# Time values, in seconds
tlist = np.linspace(0, 10e-6, 100)
# Define main class
NS = MuonNuclearInteraction(atoms)
# cutoff the dipolar interaction in order to avoid F-F term,
# Rotate sample such that axis z used to define the atomic positions
# is aligned with quantization axis which also happens to be z.
# Basically the next call will do nothing
NS.translate_rotate_sample_vec([0, 0, 1])
# cutoff the dipolar interaction in order to avoid F-F term
signal_FmuF = NS.polarization(tlist, cutoff=1.2 * angtom)
NS = MuonNuclearInteraction(atoms, log_level='info')
NS.translate_rotate_sample_vec([0, 1, 0])
signal_FmuF += NS.polarization(tlist, cutoff=1.2 * angtom)
NS = MuonNuclearInteraction(atoms, log_level='info')
NS.translate_rotate_sample_vec([1, 0, 0])
])
#This is the Celio method for the polarization function with positive EFG.
print("Computing signal for positive EFGs...", end='', flush=True)
signal_positive_EFG = np.zeros(
[len(LongitudinalFields),
steps]) # Define the polarization signal with positive EFGs.
for i, B in enumerate(LongitudinalFields):
# Align the external field along z i.e. parallel to the muon spin.
B_pos = B * np.array([0., 0., 1.])
NS_positive = MuonNuclearInteraction(atoms,
external_field=B_pos,
log_level='warn')
signal_positive_EFG[i] = NS_positive.celio(tlist, k=3)
del NS_positive
print('done!')
#This is the Celio method for the polarization function with negative EFG.
print("And now for negative EFG...", end='', flush=True)
# Align the external field along z i.e. parallel to the muon spin.
B_neg = LongitudinalFields[2] * np.array([0., 0., 1.])
# change sign
#| ## Polarization function
#|
#| The muon polarization is obtained with the method introduced by Celio.
steps = 200
tlist = np.linspace(0, 16e-6, steps)
signals = np.zeros([6, steps], dtype=np.float)
# import matplotlib as mpl; mpl.style.use(['bmh', 'paper', 'paper_twocol'])
LongitudinalFields = (0.0, 0.001, 0.003, 0.007, 0.008, 0.01)
for idx, Bmod in enumerate(LongitudinalFields):
# Put field along muon polarization, that is always z
B = Bmod * np.array([0, 0., 1.])
NS = MuonNuclearInteraction(atoms, external_field=B, log_level='info')
# rotate the sample such that the muon spin is aligned with
# the 111 direction (and, just for convenience, the muon position is
# set to (0,0,0) )
NS.translate_rotate_sample_vec(np.array([1., 1., 1.]))
print("Computing signal 4 times with LF {} T...".format(Bmod),
end='',
flush=True)
signal_Cu = NS.celio(tlist, k=2)
for i in range(3):
print('{}...'.format(i + 1), end='', flush=True)
signal_Cu += NS.celio(tlist, k=2)
print('done!')
signal_Cu /= float(i + 1 + 1)
# Computation is long and when COMPUTE==False stored values are used.
if COMPUTE:
print("Computing signal for positive EFGs...", end='', flush=True)
signal = np.zeros((fields, axis, steps))
for i in range(fields):
#| Align the magnetic fields along x.
B = TF[i] * B_dir
# do not rotate aanything yet
R = np.eye(3)
rpos = np.dot(R, pos.T).T
NS = MuonNuclearInteraction(gen_atoms(rpos),
external_field=B,
log_level='info')
signal[i, 0, :] = NS.celio(tlist, k=1) + NS.celio(tlist, k=1)
del NS
# rotate 45 deg with axis=z to get [110] along B direction, which is x
R = rotation_matrix([0, 0, 1], np.pi / 4)
rpos = np.dot(R, rpos.T).T
NS = MuonNuclearInteraction(gen_atoms(rpos),
external_field=B,
log_level='info')
signal[i, 1, :] = NS.celio(tlist, k=1) + NS.celio(tlist, k=1)
del NS
# rotate 45 deg again, but this time with axis y.
R = rotation_matrix([0, 1, 0], np.pi / 4)
# Polarization function
The muon polarization is obtained with the method introduced by Celio.
"""
steps = 100
tlist = np.linspace(0, 16e-6, steps)
signals = np.zeros([6, steps], dtype=np.float)
#LongitudinalFields = (0.0, 0.001, 0.003, 0.007, 0.008, 0.01)
LongitudinalFields = (0.0, 0.0)
for idx, Bmod in enumerate(LongitudinalFields):
# Put field along muon polarization, that is always z
B = Bmod * np.array([0, 0., 1.])
NS = MuonNuclearInteraction(atoms, external_field=B, log_level='info')
# rotate the sumple such that the muon spin is aligned with
# the 111 direction (and, just for convenience, the muon position is
# set to (0,0,0) )
NS.translate_rotate_sample_vec(np.array([1., 1., 1.]))
print("Computing signal 5 times with LF {} T...".format(Bmod),
end='',
flush=True)
signal_Cu = NS.celio(tlist, k=6)
for i in range(4):
print('{}...'.format(i + 1), end='', flush=True)
signal_Cu += NS.celio(tlist, k=6)
print('done!')
signal_Cu /= float(i + 1 + 1)