def test_C2(self):
en, wf, ham = energies(1,
B20=0.3365,
B22=7.4851,
B40=0.4062,
IB42=-3.8296,
IB44=-2.3210)
self._do_test_eigensystem(en, wf, ham)
def test_C2v_ext(self):
en, wf, ham = energies(1,
B20=0.3365,
B22=7.4851,
B40=0.4062,
B42=-3.8296,
B44=-2.3210,
Bext=[1, 2, 3])
self._do_test_eigensystem(en, wf, ham)
def _calcEigensystem(self):
"""Calculate the eigensystem: energies and wavefunctions.
Also store them and the hamiltonian.
Protected method. Shouldn't be called directly by user code.
"""
if self._dirty_eigensystem:
import CrystalField.energies as energies
nre = self.ion_nre_map[self._ion]
self._eigenvalues, self._eigenvectors, self._hamiltonian = energies.energies(nre, **self._fieldParameters)
self._dirty_eigensystem = False
def _calcEigensystem(self):
"""Calculate the eigensystem: energies and wavefunctions.
Also store them and the hamiltonian.
Protected method. Shouldn't be called directly by user code.
"""
if self._dirty_eigensystem:
import CrystalField.energies as energies
nre = self.ion_nre_map[self._ion]
self._eigenvalues, self._eigenvectors, self._hamiltonian = energies.energies(
nre, **self._fieldParameters)
self._dirty_eigensystem = False
def test_upd3(self):
# Parameters are from Phys Rev B 89 235114 / arXiv:1403.4785, originally calculated using McPhase
# Ion is U4+ which is equivalent to Pr3+ (5f2 instead of 4f2)
en, wf, ham = energies(2,
B20=0.035,
B40=-0.012,
B43=-0.027,
B60=-0.00012,
B63=0.0025,
B66=0.0068)
self._do_test_eigensystem(en, wf, ham)
expectedEigenvalues = [
0, 0, 4.36, 9.64, 9.64, 20.65, 30.03, 30.03, 52.50
]
emin = np.amin(en)
for i in range(9):
self.assertAlmostEqual(expectedEigenvalues[i], en[i], 1)
# Now test the eigenvectors by computing the dipole transition matrix elements. Use the magnetic field
# terms but divide by gJ*uB (gJ=0.8 for U4+/Pr3+ and uB=0.6715)
_, _, hx = energies(2, Bext=[1, 0, 0])
_, _, hy = energies(2, Bext=[0, 1, 0])
_, _, hz = energies(2, Bext=[0, 0, 1])
ix = np.dot(np.conj(np.transpose(wf)), np.dot(hx, wf))
iy = np.dot(np.conj(np.transpose(wf)), np.dot(hy, wf))
iz = np.dot(np.conj(np.transpose(wf)), np.dot(hz, wf))
gJuB = 0.53716
trans = np.multiply(ix, np.conj(ix)) + np.multiply(
iy, np.conj(iy)) + np.multiply(iz, np.conj(iz))
# For some reason, in the paper I also divided the matrix elements by a factor of 4. (not sure why)
trans = trans / (gJuB**2) / 4
expectedDipoleTM = [
0, 0, 0.31, 1.24 / 2., 1.24 / 2., 2.04, 3.4 / 2., 3.4 / 2., 0
]
for i in range(2, 9):
self.assertAlmostEqual(expectedDipoleTM[i],
trans[i, 0] + trans[i, 1], 1)
def test_upd3(self):
# Parameters are from Phys Rev B 89 235114 / arXiv:1403.4785, originally calculated using McPhase
# Ion is U4+ which is equivalent to Pr3+ (5f2 instead of 4f2)
en, wf, ham = energies(2, B20=0.035, B40=-0.012, B43=-0.027, B60=-0.00012, B63=0.0025, B66=0.0068)
self._do_test_eigensystem(en, wf, ham)
expectedEigenvalues = [0, 0, 4.36, 9.64, 9.64, 20.65, 30.03, 30.03, 52.50]
emin = np.amin(en)
for i in range(9):
self.assertAlmostEqual(expectedEigenvalues[i], en[i], 1)
# Now test the eigenvectors by computing the dipole transition matrix elements. Use the magnetic field
# terms but divide by gJ*uB (gJ=0.8 for U4+/Pr3+ and uB=0.6715)
_, _, hx = energies(2, Bext=[1, 0, 0])
_, _, hy = energies(2, Bext=[0, 1, 0])
_, _, hz = energies(2, Bext=[0, 0, 1])
ix = np.dot(np.conj(np.transpose(wf)), np.dot(hx, wf))
iy = np.dot(np.conj(np.transpose(wf)), np.dot(hy, wf))
iz = np.dot(np.conj(np.transpose(wf)), np.dot(hz, wf))
gJuB = 0.53716
trans = np.multiply(ix, np.conj(ix)) + np.multiply(iy, np.conj(iy)) + np.multiply(iz, np.conj(iz))
# For some reason, in the paper I also divided the matrix elements by a factor of 4. (not sure why)
trans = trans / (gJuB ** 2) / 4
expectedDipoleTM = [0, 0, 0.31, 1.24 / 2., 1.24 / 2., 2.04, 3.4 / 2., 3.4 / 2., 0]
for i in range(2, 9):
self.assertAlmostEqual(expectedDipoleTM[i], trans[i, 0] + trans[i, 1], 1)
def test_C2v_ext(self):
en, wf, ham = energies(1, B20=0.3365, B22=7.4851, B40=0.4062, B42=-3.8296, B44=-2.3210, Bext=[1, 2, 3])
self._do_test_eigensystem(en, wf, ham)
def test_C2(self):
en, wf, ham = energies(1, B20=0.3365, B22=7.4851, B40=0.4062, IB42=-3.8296, IB44=-2.3210)
self._do_test_eigensystem(en, wf, ham)
