{"abstract":[{"lang":"eng","text":"Diamagnetism of the magnetic Schrödinger operator and paramagnetism of the Pauli operator are rigorously proven for nonhomogeneous magnetic fields in the large field, in the large temperature and in the semiclassical asymptotic regimes. New counterexamples are presented which show that neither dia-nor paramagnetism is true in a robust sense (without asymptotics). In particular, we demonstrate that the recent diamagnetic comparison result by Loss and Thaller [M. Loss and B. Thaller, Commun. Math. Phys. (submitted)] is essentially the best one can hope for."}],"issue":"3","date_published":"1997-03-01T00:00:00Z","publication_status":"published","extern":"1","date_updated":"2022-08-22T09:48:50Z","article_processing_charge":"No","month":"03","day":"01","type":"journal_article","status":"public","title":"Dia- and paramagnetism for nonhomogeneous magnetic fields","quality_controlled":"1","scopus_import":"1","publisher":"American Institute of Physics","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","date_created":"2018-12-11T11:59:17Z","oa_version":"None","language":[{"iso":"eng"}],"_id":"2727","citation":{"short":"L. Erdös, Journal of Mathematical Physics 38 (1997) 1289–1317.","ama":"Erdös L. Dia- and paramagnetism for nonhomogeneous magnetic fields. <i>Journal of Mathematical Physics</i>. 1997;38(3):1289-1317. doi:<a href=\"https://doi.org/10.1063/1.531909\">10.1063/1.531909</a>","chicago":"Erdös, László. “Dia- and Paramagnetism for Nonhomogeneous Magnetic Fields.” <i>Journal of Mathematical Physics</i>. American Institute of Physics, 1997. <a href=\"https://doi.org/10.1063/1.531909\">https://doi.org/10.1063/1.531909</a>.","ista":"Erdös L. 1997. Dia- and paramagnetism for nonhomogeneous magnetic fields. Journal of Mathematical Physics. 38(3), 1289–1317.","apa":"Erdös, L. (1997). Dia- and paramagnetism for nonhomogeneous magnetic fields. <i>Journal of Mathematical Physics</i>. American Institute of Physics. <a href=\"https://doi.org/10.1063/1.531909\">https://doi.org/10.1063/1.531909</a>","ieee":"L. Erdös, “Dia- and paramagnetism for nonhomogeneous magnetic fields,” <i>Journal of Mathematical Physics</i>, vol. 38, no. 3. American Institute of Physics, pp. 1289–1317, 1997.","mla":"Erdös, László. “Dia- and Paramagnetism for Nonhomogeneous Magnetic Fields.” <i>Journal of Mathematical Physics</i>, vol. 38, no. 3, American Institute of Physics, 1997, pp. 1289–317, doi:<a href=\"https://doi.org/10.1063/1.531909\">10.1063/1.531909</a>."},"article_type":"original","publication_identifier":{"issn":["0022-2488"]},"doi":"10.1063/1.531909","page":"1289 - 1317","author":[{"last_name":"Erdös","first_name":"László","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"}],"publication":"Journal of Mathematical Physics","acknowledgement":"This work was started in the stimulating environment and with the financial support of the PCMI Summer School on Probability Theory ~IAS Princeton, 1996!. The author also expresses his gratitude to M. Loss and B. Thaller for explaining their paper to him.","year":"1997","publist_id":"4165","volume":38,"intvolume":"        38"}