def test_dissipation(self):
# Simple system
g = 1.0
muexp = MuonExperiment(['mu'])
muexp.set_dissipation_coupling(0, g)
times = np.linspace(0, 10)
results = muexp.run_experiment(times)
evol = results['e']
solx = np.real(0.5 * np.exp(-np.pi * g * times))
self.assertTrue(np.all(np.isclose(evol[:, 0], solx)))
# Check for temperature equilibrium
T = 0.1
muexp.set_magnetic_field(-1.0)
muexp.set_temperature(T)
beta = 1.0 / (cnst.k * T)
Z = np.exp(-cnst.h * constants.MU_GAMMA * 1e6 * beta)
# Just let it evolve, see the result at long times
Sz = muexp.spin_system.operator({0: 'z'})
rhoinf = muexp.run_experiment([20], Sz)['e']
self.assertAlmostEqual(rhoinf[0, 0], 0.5 * (1 - Z) / (1 + Z))
def test_slices(self):
gmu = constants.MU_GAMMA
muexp = MuonExperiment(['mu'])
muexp.spin_system.add_zeeman_term(0, 1.0 / gmu)
muexp.set_powder_average(100)
times = np.linspace(0, 1.0)
cos = np.cos(2 * np.pi * times)
signal = muexp.run_experiment(times)['e'][:, 0]
self.assertTrue(
np.all(
np.isclose(signal,
0.5 * (2.0 / 3.0 + 1.0 / 3.0 * cos),
atol=1e-3)))
# Now slice
signal_0 = muexp.run_experiment(times,
orient_slice=slice(0, 1))['e'][:, 0]
self.assertTrue(
np.all(
np.isclose(signal_0, 0.5 * cos * muexp.weights[0], atol=1e-3)))
def test_run(self):
# Empty system
muexp = MuonExperiment(['e', 'mu'])
times = np.linspace(0, 10)
results = muexp.run_experiment(times)
self.assertTrue(np.all(results['e'] == 0.5))
# Simple system
muexp.spin_system.add_linear_term(1, [0, 0, 1.0])
results = muexp.run_experiment(times, acquire='ei')
tau = constants.MU_TAU
self.assertTrue(
np.all(
np.isclose(results['e'][:, 0],
0.5 * np.cos(2 * np.pi * times))))
self.assertAlmostEqual(results['i'][0, 0],
0.5 / (1.0 + 4 * np.pi**2 * tau**2))