Landau-Zener-Stuckelberg inteferometry

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Leeseok Kim

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Nov 3, 2021, 2:17:51 AM11/3/21
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Hi, I'm new to QuTip! 

I'm trying to simulate Landau-Zener Stcukelberg inteferometry, very similar to what this tutorial notebook has done: https://nbviewer.ipython.org/github/qutip/qutip-notebooks/blob/master/examples/landau-zener-stuckelberg.ipynb

I'm little bit confused of the notebook. So basically in the notebook, they set the value for w and T, and find the propagator U(T, 0). But isn't then U always the same and thus can't get the figure depicted in the bottom of the notebook? I'm confused because the notebook actually fixed the value of w and T, which would make constant values for the time-dependent Hamiltonian term. 

In fact, I ran the notebook and couldn't reproduce the same figure, and verified that actually U is always the same, and therefore I got a monotonic mesh graph. What am I missing here? I'd really appreciate it if someone can clarify this to me! 

Asier Galicia

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Nov 15, 2021, 1:31:50 PM11/15/21
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Hi, thanks for letting us know that this notebook was behaving unexpectedly. It turns out it was a a little bit outdated (last time it was executed was on 2017). I just updated it. You can see the changes here:https://app.reviewnb.com/qutip/qutip-notebooks/pull/135 .

The reason U changes is because of the A and eps changing. However, due to how the hamiltonian was defined and the `rhs_reuse` option being set to `True`, the final propagator was being computed only  for the same eps and A value (which is why you may have seen the final figure completely blue coloured). If `rhs_reuse` is set to `True` then the hamiltonian is compiled just once. Hence, if you want to change A and eps in `propagator`, you need to include it in `args`.

Hope this helps!

Best regards,

Asier Galicia.
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