Does it effective for a special spectral density?

[ZhiGuangLu]

I find that there are only three cutting types: hard, exponential, and gaussian. If there is a special spectral density, i.e.,
$$J(\omega)=\frac{\sqrt{\omega-\omega_c}}{\omega}\Theta(\omega-\omega_c),$$
does it still effective?

Thanks!

[piperfw]

Hi @ZhiGuangLu, thanks for the question. What I believe you are describing is a spectral density with a low frequency (IR) cutoff. OQuPy supports arbitrary spectral densities through the oqupy.bath_correlations.CustomSD class which takes, as its first argument, a callable j_function which you could define as

def j_function(w):
	if w <= wc:
		return 0.0
	return np.sqrt(w-wc)/w

You will still need to specify an upper cutoff $\omega_2$, so the overall spectral density is $J(\omega)=\frac{\sqrt{\omega-\omega_c}}{\omega}\Theta(\omega-\omega_c)\Theta(\omega_2-\omega)$
for example (cutoff_type='hard'), but you can potentially set $\omega_2$ to be very large so it has no effect on your results.

That's all in principle. I'm not sure whether in practice such a spectral density will give you useful results, meaning the bath correlation functions decay fast enough to get tractable numerics, but I expect you have motivation for believing such a spectral density should do (it at least has a finite reorganisation energy). I would firstly use the oqupy.helpers.plot_correlations_with_parameters to see if the spectral density works as you expect, before trying full dynamics computations. More on that helper function can be read in the 'Computational parameters tutorial.

[ZhiGuangLu]

Hi @piperfw, thank you very much for your response. I tried the code you provided, and it indeed seems to be effective. However, I may need to compare the numberical results with the analytical ones to ensure its true validity. I will update you on my findings later.

Besides that, while running the program, I noticed that if t_end is relatively large, e.g., omega_c=2 and 20<=t_end<=40, the computation takes a very long time. Therefore, when the system parameters are change, I wanted to use the function oqupy.guess_tempo_parameters to adjust dt. However, since I am using system_chain=oqupy.System(hilbert_space_dimensions=[2]*N), I found that the following function does not seem to work properly:

system = oqupy.System(system_chain, gammas=None, lindblad_operator=None).

This issue arises because I would like to use the function:

guessed_paramsA = oqupy.guess_tempo_parameters(bath=bath1, system=system, start_time=0.0, end_time=t_end, tolerance=0.01).

After checking the source code, I found that in this function, the system variable must be an ndarray, while system_chain does not meet this requirement. Therefore, I would like to ask: how can I correctly use oqupy.System for a dissipative spin chain coupled to baths?

I really appreciate your help!

[piperfw]

Hi @ZhiGuangLu. I can explain further when I'm next at my desk, but to give you a quick fix: run the guess... command without any system argument. It isn't required, and in fact doesn't do anything in most cases (the parameters are guessed using the properties of the bath).

Glad to hear about the spectral density!