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arXiv · 1507.06114

Peierls substitution and magnetic pseudo-differential calculus

Horia D. Cornean·Viorel Iftimie·Radu Purice
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Abstract

We revisit the celebrated Peierls-Onsager substitution employing the magnetic pseudo-differential calculus for weak magnetic fields with no spatial decay conditions, when the non-magnetic symbols have a certain spatial periodicity. We show in great generality that the symbol of the magnetic band Hamiltonian admits a convergent expansion. Moreover, if the non-magnetic band Hamiltonian admits a localized composite Wannier basis, we show that the magnetic band Hamiltonian is unitarily equivalent to a Hofstadter-like magnetic matrix. In addition, if the magnetic field perturbation is slowly variable, then the spectrum of this matrix is close to the spectrum of a Weyl quantized, minimally coupled symbol.

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Horia D. Cornean, Viorel Iftimie, Radu Purice. 2015-07-22. Peierls substitution and magnetic pseudo-differential calculus. https://arxiv.org/abs/1507.06114

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