{"month":"05","day":"01","publisher":"Birkhäuser","volume":13,"year":"2012","type":"journal_article","date_published":"2012-05-01T00:00:00Z","date_created":"2018-12-11T11:59:31Z","publication_status":"published","extern":1,"title":"Second order semiclassics with self generated magnetic fields","status":"public","intvolume":"        13","citation":{"short":"L. Erdös, S. Fournais, J. Solovej, Annales Henri Poincare 13 (2012) 671–730.","ama":"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>","ista":"Erdös L, Fournais S, Solovej J. 2012. Second order semiclassics with self generated magnetic fields. Annales Henri Poincare. 13(4), 671–730.","ieee":"L. Erdös, S. Fournais, and J. Solovej, “Second order semiclassics with self generated magnetic fields,” <i>Annales Henri Poincare</i>, vol. 13, no. 4. Birkhäuser, pp. 671–730, 2012.","apa":"Erdös, L., Fournais, S., &#38; Solovej, J. (2012). Second order semiclassics with self generated magnetic fields. <i>Annales Henri Poincare</i>. Birkhäuser. <a href=\"https://doi.org/10.1007/s00023-011-0150-z\">https://doi.org/10.1007/s00023-011-0150-z</a>","mla":"Erdös, László, et al. “Second Order Semiclassics with Self Generated Magnetic Fields.” <i>Annales Henri Poincare</i>, vol. 13, no. 4, Birkhäuser, 2012, pp. 671–730, doi:<a href=\"https://doi.org/10.1007/s00023-011-0150-z\">10.1007/s00023-011-0150-z</a>.","chicago":"Erdös, László, Søren Fournais, and Jan Solovej. “Second Order Semiclassics with Self Generated Magnetic Fields.” <i>Annales Henri Poincare</i>. Birkhäuser, 2012. <a href=\"https://doi.org/10.1007/s00023-011-0150-z\">https://doi.org/10.1007/s00023-011-0150-z</a>."},"publist_id":"4118","author":[{"last_name":"Erdös","full_name":"László Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László"},{"first_name":"Søren","full_name":"Fournais, Søren","last_name":"Fournais"},{"first_name":"Jan","last_name":"Solovej","full_name":"Solovej, Jan P"}],"doi":"10.1007/s00023-011-0150-z","issue":"4","page":"671 - 730","date_updated":"2021-01-12T06:59:36Z","quality_controlled":0,"publication":"Annales Henri Poincare","_id":"2772","abstract":[{"lang":"eng","text":"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 &gt; 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."}]}