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Abstract: Grid-based discretizations of the time dependent Schr\-odinger equationcoupled to an external magnetic field are converted to manifest gauge invariantdiscretizations. This is done using generalizations of ideas used in classicallattice gauge theory, and the process defined is applicable to a large class ofdiscretized differential operators. In particular, popular discretizations suchas pseudospectral discretizations using the fast Fourier transform can betransformed to gauge invariant schemes. Also generic gauge invariant versionsof generic time integration methods are considered, enabling completely gaugeinvariant calculations of the time dependent Schr\-odinger equation. Numericalexamples illuminating the differences between a gauge invariant discretizationand conventional discretization procedures are also presented.



Author: Tore Gunnar Halvorsen, Simen Kvaal

Source: https://arxiv.org/



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