conservation_law and particle_hole in finite systems

I am trying to simulate a finite size rectangular 2d electron gas inside a josephson junction. There is one rectangular scattering region on each end that is coupled to a different superconductor, while the middle rectangular scattering region is just a part of the semiconductor 2DEG. I am only simulating the 2DEG and not the superconductors, but there is still spin-orbit coupling and hole interactions. I was told that the "conservation_law" and "particle_hole” parameters are not needed for systems such as this one that do not have infinite length regions, but I don't understand why. Could somebody please help me understand this?

Dear Konner, When one considers infinite lead with symmetries (e.g. particle hole), there is an amiguity in the definition of the scattering states because e.g. the linear combination particle + hole is a valid definition. Conservation laws is a way to define what you need. See the tutorial section of kwant or the corresponding section in our review: https://arxiv.org/abs/2407.16257 If you only consider the normal section of the Hamiltonian you indeed don't need this feature. Best, Xavier ________________________________ De : Konner Feldman <blackknight@feldmanfamily.net> Envoyé : lundi 28 octobre 2024 01:44:52 À : kwant-discuss@python.org Objet : [Kwant] conservation_law and particle_hole in finite systems I am trying to simulate a finite size rectangular 2d electron gas inside a josephson junction. There is one rectangular scattering region on each end that is coupled to a different superconductor, while the middle rectangular scattering region is just a part of the semiconductor 2DEG. I am only simulating the 2DEG and not the superconductors, but there is still spin-orbit coupling and hole interactions. I was told that the "conservation_law" and "particle_hole” parameters are not needed for systems such as this one that do not have infinite length regions, but I don't understand why. Could somebody please help me understand this?
participants (2)
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Konner Feldman
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WAINTAL Xavier