[{"type":"journal_article","issue":"6","abstract":[{"lang":"eng"}],"intvolume":" 15","status":"public","_id":"2698","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint","dc":{"identifier":["https://research-explorer.ista.ac.at/record/2698"],"type":["info:eu-repo/semantics/article","doc-type:article","text","http://purl.org/coar/resource_type/c_6501"],"description":["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."],"creator":["Erdös, László","Fournais, Søren","Solovej, Jan"],"source":["Erdös L, Fournais S, Solovej J. Stability and semiclassics in self-generated fields. Journal of the European Mathematical Society. 2013;15(6):2093-2113. doi:10.4171/JEMS/416"],"rights":["info:eu-repo/semantics/openAccess"],"title":["Stability and semiclassics in self-generated fields"],"publisher":["European Mathematical Society"],"relation":["info:eu-repo/semantics/altIdentifier/doi/10.4171/JEMS/416","info:eu-repo/semantics/altIdentifier/arxiv/1105.0506"],"date":["2013"],"language":["eng"]},"uri_base":"https://research-explorer.ista.ac.at","day":"16","page":"2093 - 2113","citation":{"chicago":"Erdös, László, Søren Fournais, and Jan Solovej. “Stability and Semiclassics in Self-Generated Fields.” Journal of the European Mathematical Society. European Mathematical Society, 2013. https://doi.org/10.4171/JEMS/416.","mla":"Erdös, László, et al. “Stability and Semiclassics in Self-Generated Fields.” Journal of the European Mathematical Society, vol. 15, no. 6, European Mathematical Society, 2013, pp. 2093–113, doi:10.4171/JEMS/416.","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.","apa":"Erdös, L., Fournais, S., & Solovej, J. (2013). Stability and semiclassics in self-generated fields. Journal of the European Mathematical Society. European Mathematical Society. https://doi.org/10.4171/JEMS/416","ieee":"L. Erdös, S. Fournais, and J. Solovej, “Stability and semiclassics in self-generated fields,” Journal of the European Mathematical Society, vol. 15, no. 6. European Mathematical Society, pp. 2093–2113, 2013."},"publication":"Journal of the European Mathematical Society","date_published":"2013-10-16T00:00:00Z","creator":{"login":"dernst","id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},"publist_id":"4198","department":[{"_id":"LaEr","tree":[{"_id":"ResearchGroups"},{"_id":"IST"}]}],"publication_status":"published","volume":15,"date_updated":"2021-01-12T06:59:07Z","dini_type":"doc-type:article","date_created":"2018-12-11T11:59:07Z","author":[{"last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Fournais","first_name":"Søren"},{"last_name":"Solovej","first_name":"Jan"}],"month":"10","quality_controlled":"1","oa":1,"external_id":{"arxiv":[]},"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1105.0506"}],"language":[{}]}]