def spin_fock(spin_state):
n = spin_state.shape[0]
j = dim_spin(n)
bases = []
for m in np.arange(-1 * j, j + 1, 1):
amp = spin_state.overlap(qt.spin_state(j, m))
bases.append(amp * spin_fockBASIS(j, m))
return sum(bases)
def tensor_clebsch(j1, j2):
J3 = possible_j3s(j1, j2)
states = []
labels = []
for j3 in J3:
substates = []
sublabels = []
for m3 in np.arange(-j3, j3 + 1):
terms = []
for m1 in np.arange(-j1, j1 + 1):
for m2 in np.arange(-j2, j2 + 1):
terms.append(\
qt.clebsch(j1, j2, j3, m1, m2, m3)*\
qt.tensor(qt.spin_state(j1, m1),\
qt.spin_state(j2, m2)))
substates.append(sum(terms))
sublabels.append((j3, m3))
states.extend(substates[::-1])
labels.append(sublabels[::-1])
return qt.Qobj(np.array([state.full().T[0] for state in states])), labels
def coupling_(a, b):
particle_types = []
for a_i in np.arange(-1 * a, a + 1, 1):
for b_j in np.arange(-1 * b, b + 1, 1):
c = abs(a_i + b_j)
c2 = abs(abs(a_i) + abs(b_j))
if c != c2:
particle_types.append(c2)
particle_types.append(c)
T = {}
for particle in particle_types:
particle_dict = {}
if particle == 0:
states = []
for a_i in np.arange(-1 * a, a + 1, 1):
for b_j in np.arange(-1 * b, b + 1, 1):
state = qt.clebsch(a, b, 0, a_i, b_j, 0)*\
qt.tensor(qt.spin_state(a, a_i), qt.spin_state(b, b_j))
states.append(state)
STATE = sum(states)
particle_dict[particle] = (qt.spin_state(0, 0), STATE)
else:
for c_m in np.arange(-1 * particle, particle + 1, 1):
states = []
for a_i in np.arange(-1 * a, a + 1, 1):
for b_j in np.arange(-1 * b, b + 1, 1):
state = qt.clebsch(a, b, particle, a_i, b_j, c_m)*\
qt.tensor(qt.spin_state(a, a_i), qt.spin_state(b, b_j))
states.append(state)
STATE = sum(states)
particle_dict[c_m] = (qt.spin_state(particle, c_m), STATE)
T[particle] = particle_dict
return T
def test_spinstate_type():
"State CSR Type: spin_state"
st = spin_state(5,3)
assert_equal(isspmatrix_csr(st.data), True)
def fock_spinBASIS(n1, n2):
j = (n1 + n2) / 2.
m = n1 - j
return qt.spin_state(j, m) #, (j, m)