{"page":"2093 - 2113","status":"public","author":[{"last_name":"Erdös","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","full_name":"Erdös, László"},{"last_name":"Fournais","full_name":"Fournais, Søren","first_name":"Søren"},{"full_name":"Solovej, Jan","first_name":"Jan","last_name":"Solovej"}],"language":[{"iso":"eng"}],"date_created":"2018-12-11T11:59:07Z","year":"2013","abstract":[{"text":"We consider non-interacting particles subject to a fixed external potential V and a self-generated magnetic field B. The total energy includes the field energy β∫B2 and we minimize over all particle states and magnetic fields. In the case of spin-1/2 particles this minimization leads to the coupled Maxwell-Pauli system. The parameter β tunes the coupling strength between the field and the particles and it effectively determines the strength of the field. We investigate the stability and the semiclassical asymptotics, h→0, of the total ground state energy E(β,h,V). The relevant parameter measuring the field strength in the semiclassical limit is κ=βh. We are not able to give the exact leading order semiclassical asymptotics uniformly in κ or even for fixed κ. We do however give upper and lower bounds on E with almost matching dependence on κ. In the simultaneous limit h→0 and κ→∞ we show that the standard non-magnetic Weyl asymptotics holds. The same result also holds for the spinless case, i.e. where the Pauli operator is replaced by the Schrödinger operator.","lang":"eng"}],"doi":"10.4171/JEMS/416","intvolume":"        15","date_published":"2013-10-16T00:00:00Z","quality_controlled":"1","title":"Stability and semiclassics in self-generated fields","volume":15,"external_id":{"arxiv":["1105.0506"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Erdös, László, et al. “Stability and Semiclassics in Self-Generated Fields.” <i>Journal of the European Mathematical Society</i>, vol. 15, no. 6, European Mathematical Society, 2013, pp. 2093–113, doi:<a href=\"https://doi.org/10.4171/JEMS/416\">10.4171/JEMS/416</a>.","ama":"Erdös L, Fournais S, Solovej J. Stability and semiclassics in self-generated fields. <i>Journal of the European Mathematical Society</i>. 2013;15(6):2093-2113. doi:<a href=\"https://doi.org/10.4171/JEMS/416\">10.4171/JEMS/416</a>","ieee":"L. Erdös, S. Fournais, and J. Solovej, “Stability and semiclassics in self-generated fields,” <i>Journal of the European Mathematical Society</i>, vol. 15, no. 6. European Mathematical Society, pp. 2093–2113, 2013.","apa":"Erdös, L., Fournais, S., &#38; Solovej, J. (2013). Stability and semiclassics in self-generated fields. <i>Journal of the European Mathematical Society</i>. European Mathematical Society. <a href=\"https://doi.org/10.4171/JEMS/416\">https://doi.org/10.4171/JEMS/416</a>","short":"L. Erdös, S. Fournais, J. Solovej, Journal of the European Mathematical Society 15 (2013) 2093–2113.","ista":"Erdös L, Fournais S, Solovej J. 2013. Stability and semiclassics in self-generated fields. Journal of the European Mathematical Society. 15(6), 2093–2113.","chicago":"Erdös, László, Søren Fournais, and Jan Solovej. “Stability and Semiclassics in Self-Generated Fields.” <i>Journal of the European Mathematical Society</i>. European Mathematical Society, 2013. <a href=\"https://doi.org/10.4171/JEMS/416\">https://doi.org/10.4171/JEMS/416</a>."},"oa":1,"publisher":"European Mathematical Society","department":[{"_id":"LaEr"}],"publication":"Journal of the European Mathematical Society","publication_status":"published","publist_id":"4198","month":"10","day":"16","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1105.0506"}],"oa_version":"Preprint","type":"journal_article","_id":"2698","issue":"6","date_updated":"2021-01-12T06:59:07Z"}