def test_wigner_seitz_radius_2d(self):
wigner_seitz_radius = 0.5
n_particles = 3
two_d_test = wigner_seitz_length_scale(wigner_seitz_radius,
n_particles, 2)**2.
self.assertAlmostEqual(
two_d_test, n_particles * numpy.pi * wigner_seitz_radius**2.)
def test_wigner_seitz_radius_1d(self):
wigner_seitz_radius = 3.17
n_particles = 20
one_d_test = wigner_seitz_length_scale(wigner_seitz_radius,
n_particles, 1)
self.assertAlmostEqual(one_d_test,
n_particles * 2. * wigner_seitz_radius)
def dual_basis_jellium_hamiltonian(grid_length, dimension=3,
wigner_seitz_radius=10., n_particles=None,
spinless=True):
"""Return the jellium Hamiltonian with the given parameters.
Args:
grid_length (int): The number of spatial orbitals per dimension.
dimension (int): The dimension of the system.
wigner_seitz_radius (float): The radius per particle in Bohr.
n_particles (int): The number of particles in the system.
Defaults to half filling if not specified.
"""
n_qubits = grid_length ** dimension
if not spinless:
n_qubits *= 2
if n_particles is None:
# Default to half filling fraction.
n_particles = n_qubits // 2
if not (0 <= n_particles <= n_qubits):
raise ValueError('n_particles must be between 0 and the number of'
' spin-orbitals.')
# Compute appropriate length scale.
length_scale = wigner_seitz_length_scale(
wigner_seitz_radius, n_particles, dimension)
grid = Grid(dimension, grid_length, length_scale)
hamiltonian = jellium_model(grid, spinless=spinless, plane_wave=False)
hamiltonian = normal_ordered(hamiltonian)
hamiltonian.compress()
return hamiltonian
def test_wigner_seitz_radius_6d(self):
wigner_seitz_radius = 5.
n_particles = 42
six_d_test = wigner_seitz_length_scale(wigner_seitz_radius,
n_particles, 6)**6
self.assertAlmostEqual(
six_d_test,
n_particles * (numpy.pi**3 / 6 * wigner_seitz_radius**6))
def test_wigner_seitz_radius_3d(self):
wigner_seitz_radius = 4.6
n_particles = 37
three_d_test = wigner_seitz_length_scale(wigner_seitz_radius,
n_particles, 3)**3.
self.assertAlmostEqual(
three_d_test,
n_particles * (4. * numpy.pi / 3. * wigner_seitz_radius**3.))
def test_wigner_seitz_radius_bad_dimension_not_positive(self):
with self.assertRaises(ValueError):
wigner_seitz_length_scale(3, 2, dimension=0)