Second order semiclassics with self generated magnetic fields
László Erdös
Fournais, Søren
Solovej, Jan P
We consider the semiclassical asymptotics of the sum of negative eigenvalues of the three-dimensional Pauli operator with an external potential and a self-generated magnetic field B. We also add the field energy β ∫ B 2 and we minimize over all magnetic fields. The parameter β effectively determines the strength of the field. We consider the weak field regime with βh 2 ≥ const > 0, where h is the semiclassical parameter. For smooth potentials we prove that the semiclassical asymptotics of the total energy is given by the non-magnetic Weyl term to leading order with an error bound that is smaller by a factor h 1+e{open}, i. e. the subleading term vanishes. However for potentials with a Coulomb singularity, the subleading term does not vanish due to the non-semiclassical effect of the singularity. Combined with a multiscale technique, this refined estimate is used in the companion paper (Erdo{double acute}s et al. in Scott correction for large molecules with a self-generated magnetic field, Preprint, 2011) to prove the second order Scott correction to the ground state energy of large atoms and molecules.
Birkhäuser
2012
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http://purl.org/coar/resource_type/c_6501
https://research-explorer.app.ist.ac.at/record/2772
Erdös L, Fournais S, Solovej J. Second order semiclassics with self generated magnetic fields. <i>Annales Henri Poincare</i>. 2012;13(4):671-730. doi:<a href="https://doi.org/10.1007/s00023-011-0150-z">10.1007/s00023-011-0150-z</a>
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00023-011-0150-z
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