On the absence of stationary currents

Abstract

We review proofs of a theorem of Bloch on the absence of macroscopic stationary currents in quantum systems. The standard proof shows that the current in 1D vanishes in the large volume limit under rather general conditions. In higher dimension, the total current across a cross-section does not need to vanish in gapless systems but it does vanish in gapped systems. We focus on the latter claim and give a self-contained proof motivated by a recently introduced index for many-body charge transport in quantum lattice systems having a conserved $U(1)$-charge.

arXiv commentWritten for QMATH14 Proceedings; To appear in Rev. Math. Phys

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Cited by in corpus (3)

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• Persistent current-carrying state of charge quasuparticles in $np$-ribbon featuring single Dirac cone