Rapid calculation of static magnetic field perturbation generated by magnetized objects in arbitrary orientations

Author(s):  
Seok‐Jin Yeo ◽  
So‐Hee Lee ◽  
Seung‐Kyun Lee

2019 ◽  
Vol 31 (03) ◽  
pp. 1950008
Author(s):  
Horia D. Cornean ◽  
Viorel Iftimie ◽  
Radu Purice

We revisit the celebrated Peierls–Onsager substitution for weak magnetic fields with no spatial decay conditions. We assume that the non-magnetic [Formula: see text]-periodic Hamiltonian has an isolated spectral band whose Riesz projection has a range which admits a basis generated by [Formula: see text] exponentially localized composite Wannier functions. Then we show that the effective magnetic band Hamiltonian is unitarily equivalent to a Hofstadter-like magnetic matrix living in [Formula: see text]. In addition, if the magnetic field perturbation is slowly variable in space, then the perturbed spectral island is close (in the Hausdorff distance) to the spectrum of a Weyl quantized minimally coupled symbol. This symbol only depends on [Formula: see text] and is [Formula: see text]-periodic; if [Formula: see text], the symbol equals the Bloch eigenvalue itself. In particular, this rigorously formulates a result from 1951 by J. M. Luttinger.







2011 ◽  
Vol 44 (1) ◽  
pp. 1-7 ◽  
Author(s):  
Yanhua Sun ◽  
Yihua Kang ◽  
Chen Qiu




2008 ◽  
Vol 48 (12) ◽  
pp. 122001 ◽  
Author(s):  
M.E. Fenstermacher ◽  
T.E. Evans ◽  
T.H. Osborne ◽  
M.J. Schaffer ◽  
J.S. deGrassie ◽  
...  




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