Magnetic Equivalence¶

In [2]:

from numpy import pi
import numpy as np
import matplotlib.pyplot as plt

from tins import spinsys, mesolve

from numpy import pi import numpy as np import matplotlib.pyplot as plt from tins import spinsys, mesolve

Spin System with 4 spins¶

In [3]:

I1, I2, I3, I4 = spinsys(0.5, 0.5, 0.5, 0.5)

def J(I1, I2):
    """
    Construct Full Scalar coupling hamiltonian

    """
    return I1.z @ I2.z + I1.x @ I2.x + I1.y @ I2.y

I1, I2, I3, I4 = spinsys(0.5, 0.5, 0.5, 0.5) def J(I1, I2): """ Construct Full Scalar coupling hamiltonian """ return I1.z @ I2.z + I1.x @ I2.x + I1.y @ I2.y

Case I: Magnetic Equivalence¶

In [4]:

Ω = 2 * pi * 100
J13, J23 = 2 * pi * 10, 2 * pi * 10
J14, J24 = 2 * pi * 5, 2 * pi * 5
J12 = 2 * pi * 10

meq = (
    + Ω * (I1.z + I2.z)
    + J12 * J(I1, I2)
    + J13 * J(I1, I3)
    + J14 * J(I1, I4)
    + J23 * J(I2, I3)
    + J24 * J(I2, I4)
)

start = I1.x + I2.x
detect = I1.p + I2.p
time = np.linspace(0, 5, 2000)


fid = mesolve(start=start, detect=detect, ham=meq, time=time)

Ω = 2 * pi * 100 J13, J23 = 2 * pi * 10, 2 * pi * 10 J14, J24 = 2 * pi * 5, 2 * pi * 5 J12 = 2 * pi * 10 meq = ( + Ω * (I1.z + I2.z) + J12 * J(I1, I2) + J13 * J(I1, I3) + J14 * J(I1, I4) + J23 * J(I2, I3) + J24 * J(I2, I4) ) start = I1.x + I2.x detect = I1.p + I2.p time = np.linspace(0, 5, 2000) fid = mesolve(start=start, detect=detect, ham=meq, time=time)

In [7]:

fid = fid * np.exp(-3 * time)
ft = np.fft.fftshift(np.fft.fft(fid))

fig, ax = plt.subplots(figsize=(7, 3))
ax.set_xlim(1250, 1750)
ax.plot(ft.real)

plt.show()

fid = fid * np.exp(-3 * time) ft = np.fft.fftshift(np.fft.fft(fid)) fig, ax = plt.subplots(figsize=(7, 3)) ax.set_xlim(1250, 1750) ax.plot(ft.real) plt.show()

Magnetic Inequivalence¶

In [10]:

Ω = 2 * pi * 100
J13, J23 = 2 * pi * 10, 2 * pi * 5
J14, J24 = 2 * pi * 5, 2 * pi * 10
J12 = 2 * pi * 10

# continue

Ω = 2 * pi * 100 J13, J23 = 2 * pi * 10, 2 * pi * 5 J14, J24 = 2 * pi * 5, 2 * pi * 10 J12 = 2 * pi * 10 # continue

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