Re: How does the grid spacing in kwant.continuum.discretize effect the system?
Dear Christoph, Thank you so much for your reply. I've had a look at the Kwant tutorial about the discretization. However, the response I am seeing isn't consistent with the idea of an energy limit being reached. It appears that as I change the number of lattice points, therefore the grid spacing, the response of the system changes as shown in the attached image. The graphs show the state being evolved in Tkwant with the expectation values of the Pauli spin matrices plotted. For 20, 40 and 120 lattice points the graphs show an expected and similar response. For 60, 70 and 100 the graphs show no evolving of the state or an unphysical response. It appears to be very inconsistent with the grid spacing value. Could there be another cause of this result, for example how the system is built rather than a continuum limit? Thank you for any more help with this. Best wishes, Isobel ________________________________ From: Christoph Groth Sent: Thursday, March 16, 2023 15:05 To: Clarke, Isobel Cc: kwant-discuss@python.org Subject: Re: [Kwant] How does the grid spacing in kwant.continuum.discretize effect the system? Hi Isobel, As you decrease the discretization grid spacing you should approach the continuum limit. For example, the band structure should become more and more accurate also for larger momenta. Did you check the Kwant tutorial on the discretizer? In particular the example comparing a=1.0 and a=0.25: https://kwant-project.org/doc/1/tutorial/discretize#limitations-of-discretiz... Tkwant should not really matter here. I suggest that you first check whether your discretization behaves as it should without even using tkwant, for example by looking at the band structure. Cheers Christoph
Clarke, Isobel wrote:
I've had a look at the Kwant tutorial about the discretization. However, the response I am seeing isn't consistent with the idea of an energy limit being reached.
Sorry, I have no more specific idea about what the problem could be in your case. When seeing such inconsistent behavior within a sequence of discretizations, I would try to verify the consistency of that sequence in simpler circumstances. For example, one could verify that the bandstructure evolves as expected as one changes the discretization length. A second possible check would be to do some time-independent transport computation. If you find an inconsistency already with these simpler checks, it will be easier to understand. If you do not, you have narrowed down the problem already.
participants (2)
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Christoph Groth
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Clarke, Isobel