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Semiclassics of the quantum current in very strong magnetic fields. (English) Zbl 1013.81059

Summary: We prove a formula for the current in an electron gas in a semiclassical limit corresponding to strong, constant, magnetic fields. Little regularity is assumed for the scalar potential \(V\). In particular, the result can be applied to the mean field from magnetic Thomas-Fermi theory \(V_{\text{MTF}}\). The proof is based on an estimate on the density of states in the second Landau band.

MSC:

81V45 Atomic physics
81V70 Many-body theory; quantum Hall effect
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References:

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