custom Hamiltonian with a sinusoidal term

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pgarbacz
Posts: 2
Joined: Wed Oct 06, 2021 2:50 pm

custom Hamiltonian with a sinusoidal term

What would be the optimal way of adding a small term to the NMR/EPR Hamiltonian that has the following form:

H_pert = (I+S- - I-S+)*sin((wI - wS)*t)?

I would like to compute the effect of the acting of H_pert for a given time on the initial density matrix of the spin system.
kuprov
Posts: 73
Joined: Mon Mar 29, 2021 4:26 pm

Re: custom Hamiltonian with a sinusoidal term

Use the operator function to get those operators, for example:

LpSm=operator(spin_system,{'L+','L-'},{1,2});

then add them together and multiply by your modulation term. The Hamiltonian would of course be time-dependent; propagating the system under time-dependent Hamiltonians is separate long story.
pgarbacz
Posts: 2
Joined: Wed Oct 06, 2021 2:50 pm

Re: custom Hamiltonian with a sinusoidal term

OK, I added this term to the Hamiltonian. However, I am not sure how to use the time variable in Spinach.
If, as in the attached file, I simply write "t," then the message "t is unrecognized variable" appears.

Should I use the step function in a loop and approximate my modulation by a series of short intervals of fixed modulation amplitude?
The frequency of modulation is quite high, approx. 100 GHz (modulation time 1 s).

The other option would be a transformation to the rotating frame. In this case, I do not need to use time explicitly.
Is there practically any other way to treat this issue in Spinach?
Attachments
H_e.zip
kuprov
Posts: 73
Joined: Mon Mar 29, 2021 4:26 pm

Re: custom Hamiltonian with a sinusoidal term

Yes, there's shaped_pulse_af() function for off-resonance irradiation; it would work in the laboratory frame:

https://spindynamics.org/wiki/index.php ... pulse_af.m

Alternatively, a numerical rotating frame transformation may be performed by calling rotframe():

https://spindynamics.org/wiki/index.php ... Rotframe.m

It looks like you are running DNP simulations. There are plenty of examples of solid and liquid state DNP simulations in the example set. Do you really need the time-domain trajectory, or would the steady state under microwave irradiation be sufficient? The latter is massively easier to compute.