Quadrupole spin precession trajectory

[awein]

I'm trying to simulate the precession trajectory of a quadrupole nuclear spin under an electric field gradient with a zero magnetic field. It is the effect of nuclear quadrupolar coupling. But my simulation turns out that the direction of the nuclear spin hasn't changed at all, and the trajectory is a point on the Bloch sphere.

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In contrast, I am correct in simulating the precession of a nuclear spin under an applied magnetic field (without an electric field gradient).

氮核在磁场进动归一化，无弛豫.jpg (70.57 KiB) Viewed 60227 times

Here is my code：

single_atom.m

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Is there something wrong with my code, or is there something wrong with my understanding?

[kuprov]

The quadrupolar interaction goes into the anisotropic component of the Hamiltonian (Q variable). It was requested from Spinach, but then left unused - only the empty isotropic part H was sent to the evolution function. Note also that at zero field the initial condition would not be Z magnetisation.

I fixed the code and updated the syntax to Spinach 2.8 (much neater) - enclosed.

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[awein]

Thanks! It helps me a lot, but I'm still having some doubts about this result.
Here the nuclear spin is initialized to the Lx state and begins to evolve under the Hamiltonian. In my understanding, shouldn't the starting point be at the coordinate (1,0,0), and the entire trajectory be on the Bloch sphere surface? Why should the result be inside the Bloch sphere?
This question may be related to another problem I'm having. When I simulate the precession trajectory of a nuclear spin in a magnetic field, the entire trajectory is also not on the Bloch sphere surface, as shown below.

single_atom.jpg (52.76 KiB) Viewed 60196 times

[kuprov]

For a quadrupolar interaction, you do not expect the spin to stay on the surface of the Bloch sphere because the dynamics is actually not three-, but eight-dimensional (Sx, Sy, Sz, and five second-rank operators). So you are seeing a three-dimensional projection of eight-dimensional dynamics.

For Zeeman Hamiltonians, spin-1 particles, magnetisation vectors do stay on the Bloch sphere, but for quadrupolar Hamiltonians they do not.