def test_no_operators():
n = 4
l = 10
dim = 3
spas = SpatialOrbitalSystem(n, RandomBasisSet(l, dim))
gos = GeneralOrbitalSystem(n, RandomBasisSet(l, dim))
assert not spas.has_one_body_time_evolution_operator
assert not gos.has_one_body_time_evolution_operator
assert not spas.has_two_body_time_evolution_operator
assert not gos.has_two_body_time_evolution_operator
np.testing.assert_allclose(spas.h_t(10), spas.h)
np.testing.assert_allclose(spas.u_t(10), spas.u)
np.testing.assert_allclose(gos.h_t(10), gos.h)
np.testing.assert_allclose(gos.u_t(10), gos.u)
spas.set_time_evolution_operator(
[],
add_h_0=False,
add_u_0=False,
)
gos.set_time_evolution_operator([], add_h_0=False, add_u_0=False)
assert not spas.has_one_body_time_evolution_operator
assert not gos.has_one_body_time_evolution_operator
assert not spas.has_two_body_time_evolution_operator
assert not gos.has_two_body_time_evolution_operator
np.testing.assert_allclose(spas.h_t(0), np.zeros_like(spas.h))
np.testing.assert_allclose(spas.u_t(0), np.zeros_like(spas.u))
np.testing.assert_allclose(gos.h_t(0), np.zeros_like(gos.h))
np.testing.assert_allclose(gos.u_t(0), np.zeros_like(gos.u))
def construct_general_orbital_system(self,
a=[1, 0],
b=[0, 1],
anti_symmetrize=True):
r"""Function constructing a ``GeneralOrbitalSystem`` by
duplicating every basis element of current system. That is,
.. math:: \psi(\mathbf{r}, t)
\to \psi(x, t) = \psi(\mathbf{r}, t) \sigma(m_2),
where :math:`x = (\mathbf{r}, m_s)` is a generalized coordinate of both
position :math:`\mathbf{r}` and spin :math:`m_s`, with
:math:`\sigma(m_s)` one of the two spin-functions.
Note that this function creates a copy of the basis set.
Parameters
----------
a : list, np.array
The :math:`\alpha` (up) spin basis vector. Default is :math:`\alpha
= (1, 0)^T`.
b : list, np.array
The :math:`\beta` (down) spin basis vector. Default is :math:`\beta
= (0, 1)^T`. Note that ``a`` and ``b`` are assumed orthonormal.
anti_symmetrize : bool
Whether or not to create the anti-symmetrized two-body elements.
Default is ``True``.
Returns
-------
GeneralOrbitalSystem
The doubly degenerate general spin-orbital system.
See Also
-------
BasisSet.change_to_general_orbital_basis
"""
gos = GeneralOrbitalSystem(
self.n * 2,
self._basis_set.copy_basis(),
a=a,
b=b,
anti_symmetrize=anti_symmetrize,
)
import copy
if not self._time_evolution_operator is None:
gos.set_time_evolution_operator(
copy.deepcopy(self._time_evolution_operator))
return gos
def test_multiple_time_evolution_operators():
n = 4
l = 10
dim = 3
spas = SpatialOrbitalSystem(n, RandomBasisSet(l, dim))
gos = GeneralOrbitalSystem(n, RandomBasisSet(l, dim))
assert not spas.has_one_body_time_evolution_operator
assert not gos.has_one_body_time_evolution_operator
assert not spas.has_two_body_time_evolution_operator
assert not gos.has_two_body_time_evolution_operator
spas.set_time_evolution_operator(
[
CustomOneBodyOperator(2, spas.h),
CustomOneBodyOperator(3, spas.s),
AdiabaticSwitching(2),
],
add_u_0=False,
)
gos.set_time_evolution_operator(
(
CustomOneBodyOperator(1, gos.h),
CustomOneBodyOperator(3, gos.s),
CustomOneBodyOperator(-2, gos.position[0]),
),
add_h_0=False,
)
assert spas.has_one_body_time_evolution_operator
assert gos.has_one_body_time_evolution_operator
assert spas.has_two_body_time_evolution_operator
assert not gos.has_two_body_time_evolution_operator
np.testing.assert_allclose(
spas.h_t(0),
spas.h + spas.h * 2 + spas.s * 3,
)
np.testing.assert_allclose(spas.u_t(0), 2 * spas.u)
np.testing.assert_allclose(
gos.h_t(0),
gos.h + gos.s * 3 - gos.position[0] * 2,
)
np.testing.assert_allclose(gos.u_t(0), gos.u)
def test_single_dipole_time_evolution_operator():
n = 4
l = 10
dim = 3
omega = 0.25
spas = SpatialOrbitalSystem(n, RandomBasisSet(l, dim))
gos = GeneralOrbitalSystem(n, RandomBasisSet(l, dim))
field = lambda t: np.sin(omega * 2)
polarization = np.zeros(dim)
polarization[0] = 1
spas.set_time_evolution_operator(
DipoleFieldInteraction(
field,
polarization,
))
gos.set_time_evolution_operator(
DipoleFieldInteraction(
field,
polarization,
))
assert spas.has_one_body_time_evolution_operator
assert gos.has_one_body_time_evolution_operator
assert not spas.has_two_body_time_evolution_operator
assert not gos.has_two_body_time_evolution_operator
for t in [0, 0.1, 0.5, 1.3]:
np.testing.assert_allclose(
spas.h_t(t),
spas.h - field(t) * spas.dipole_moment[0],
)
np.testing.assert_allclose(
gos.h_t(t),
gos.h - field(t) * gos.dipole_moment[0],
)
np.testing.assert_allclose(spas.u_t(t), spas.u)
np.testing.assert_allclose(gos.u_t(t), gos.u)
def test_single_time_evolution_operator():
n = 4
l = 10
dim = 3
spas = SpatialOrbitalSystem(n, RandomBasisSet(l, dim))
gos = GeneralOrbitalSystem(n, RandomBasisSet(l, dim))
assert not spas.has_one_body_time_evolution_operator
assert not gos.has_one_body_time_evolution_operator
assert not spas.has_two_body_time_evolution_operator
assert not gos.has_two_body_time_evolution_operator
np.testing.assert_allclose(spas.h_t(10), spas.h)
np.testing.assert_allclose(spas.u_t(10), spas.u)
np.testing.assert_allclose(gos.h_t(10), gos.h)
np.testing.assert_allclose(gos.u_t(10), gos.u)
spas.set_time_evolution_operator(CustomOneBodyOperator(2, spas.h),
add_h_0=False)
gos.set_time_evolution_operator(CustomOneBodyOperator(3, gos.h),
add_u_0=False)
assert spas.has_one_body_time_evolution_operator
assert gos.has_one_body_time_evolution_operator
assert not spas.has_two_body_time_evolution_operator
assert not gos.has_two_body_time_evolution_operator
np.testing.assert_allclose(
spas.h_t(0),
spas.h * 2,
)
np.testing.assert_allclose(spas.u_t(0), spas.u)
np.testing.assert_allclose(
gos.h_t(0),
gos.h + gos.h * 3,
)
np.testing.assert_allclose(gos.u_t(0), np.zeros_like(gos.u))