def test_integrate(self):
ssys = SpinSystem(['e'])
ssys.add_linear_term(0, [1, 0, 0]) # Precession around x
H = ssys.hamiltonian
rho0 = DensityOperator.from_vectors() # Start along z
avg = H.integrate_decaying(rho0, 1.0, ssys.operator({0: 'z'}))
self.assertTrue(np.isclose(avg[0], 0.5 / (1.0 + 4 * np.pi**2)))
def test_evolve(self):
ssys = SpinSystem(['e'])
ssys.add_linear_term(0, [1, 0, 0]) # Precession around x
H = ssys.hamiltonian
rho0 = DensityOperator.from_vectors() # Start along z
t = np.linspace(0, 1, 100)
evol = H.evolve(rho0, t, ssys.operator({0: 'z'}))
self.assertTrue(
np.all(np.isclose(evol[:, 0], 0.5 * np.cos(2 * np.pi * t))))
def test_addterms(self):
ssys = SpinSystem(['mu', 'e'])
t1 = ssys.add_linear_term(0, [1, 0, 1])
self.assertEqual(t1.label, 'Single')
self.assertEqual(t1.operator, ssys.operator({0: 'x'}) +
ssys.operator({0: 'z'}))
t2 = ssys.add_bilinear_term(0, 1, np.eye(3))
self.assertEqual(t2.label, 'Double')
self.assertEqual(t2.operator, ssys.operator({0: 'x', 1: 'x'}) +
ssys.operator({0: 'y', 1: 'y'}) +
ssys.operator({0: 'z', 1: 'z'}))
H = ssys.hamiltonian
self.assertTrue(np.all(np.isclose(H.matrix,
np.array([[0.75, 0, 0.5, 0.0],
[0, 0.25, 0.5, 0.5],
[0.5, 0.5, -0.75, 0],
[0.0, 0.5, 0, -0.25]]))))
ssys.add_dissipative_term(ssys.operator({0: 'x'}), 1.0)
self.assertTrue(ssys.is_dissipative)
def test_lindbladian(self):
ssys = SpinSystem(['mu'])
ssys.add_linear_term(0, [0, 0, 1])
H = ssys.hamiltonian
L = ssys.lindbladian
L0 = -1.0j*SuperOperator.commutator(ssys.operator({0: 'z'}))
self.assertTrue(np.all(np.isclose(L.matrix, L0.matrix)))
sx = ssys.operator({0: 'x'})
d = 2.0
ssys.add_dissipative_term(sx, d)
L1 = L0 + d*(SuperOperator.bracket(sx) -
0.5*SuperOperator.anticommutator(sx*sx))
L = ssys.lindbladian
self.assertTrue(np.all(np.isclose(L.matrix, L1.matrix)))