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- W4387635679 abstract "The widespread Wigner formulation of quantum mechanics is obtained with the help of the Weyl transform of the density matrix and the corresponding von Neumann equation formulated in terms of scalar potentials only. To obtain a gauge-invariant Wigner theory in an electromagnetic field, one can apply a Weyl-Stratonovich transform to remove the vector potential from the evolution equation of the Wigner function. This corresponds to a variable transform replacing the canonical momentum with the kinetic momentum, which, being a physical quantity, is gauge-invariant. The obtained multidimensional equation is, however, numerically very challenging. In this work, we apply simplifying assumptions for linear electromagnetic fields and the evolution of an electron in a plane (two-dimensional transport), which reduces the complexity and enables to gain first experience with a gauge-invariant Wigner equation. In the latter, the Liouville operator interplays with a term containing high-order mixed derivatives on position and momentum, which replaces the Wigner potential of the electrostatic Wigner theory. We present an equation analysis and show that a finite difference approach to the high-order derivatives allows for reformulation into a Fredholm integral equation. The resolvent expansion of the latter contains consecutive integrals, which is favorable for Monte Carlo solution approaches. To that end, we present two stochastic (Monte Carlo) algorithms that evaluate averages of generic physical quantities or directly the Wigner function. The algorithms give rise to a quantum particle model, which interprets quantum transport in heuristic terms." @default.
- W4387635679 created "2023-10-14" @default.
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- W4387635679 date "2023-10-12" @default.
- W4387635679 modified "2023-10-15" @default.
- W4387635679 title "Wigner transport in linear electromagnetic fields" @default.
- W4387635679 doi "https://doi.org/10.48550/arxiv.2310.08376" @default.
- W4387635679 hasPublicationYear "2023" @default.
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