{"abstract":[{"lang":"eng","text":"We study the generalizations of the well-known Lieb-Thirring inequality for the magnetic Schrödinger operator with nonconstant magnetic field. Our main result is the naturally expected magnetic Lieb-Thirring estimate on the moments of the negative eigenvalues for a certain class of magnetic fields (including even some unbounded ones). We develop a localization technique in path space of the stochastic Feynman-Kac representation of the heat kernel which effectively estimates the oscillatory effect due to the magnetic phase factor."}],"publication":"Communications in Mathematical Physics","publication_status":"published","doi":"10.1007/BF02099152","author":[{"orcid":"0000-0001-5366-9603","first_name":"László","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös"}],"_id":"2724","publication_identifier":{"issn":["0010-3616"]},"type":"journal_article","extern":"1","volume":170,"date_updated":"2022-06-28T09:19:36Z","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","page":"629 - 668","status":"public","date_created":"2018-12-11T11:59:16Z","month":"06","citation":{"apa":"Erdös, L. (1995). Magnetic Lieb-Thirring inequalities. <i>Communications in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/BF02099152\">https://doi.org/10.1007/BF02099152</a>","ista":"Erdös L. 1995. Magnetic Lieb-Thirring inequalities. Communications in Mathematical Physics. 170(3), 629–668.","chicago":"Erdös, László. “Magnetic Lieb-Thirring Inequalities.” <i>Communications in Mathematical Physics</i>. Springer, 1995. <a href=\"https://doi.org/10.1007/BF02099152\">https://doi.org/10.1007/BF02099152</a>.","ieee":"L. Erdös, “Magnetic Lieb-Thirring inequalities,” <i>Communications in Mathematical Physics</i>, vol. 170, no. 3. Springer, pp. 629–668, 1995.","short":"L. Erdös, Communications in Mathematical Physics 170 (1995) 629–668.","mla":"Erdös, László. “Magnetic Lieb-Thirring Inequalities.” <i>Communications in Mathematical Physics</i>, vol. 170, no. 3, Springer, 1995, pp. 629–68, doi:<a href=\"https://doi.org/10.1007/BF02099152\">10.1007/BF02099152</a>.","ama":"Erdös L. Magnetic Lieb-Thirring inequalities. <i>Communications in Mathematical Physics</i>. 1995;170(3):629-668. doi:<a href=\"https://doi.org/10.1007/BF02099152\">10.1007/BF02099152</a>"},"article_processing_charge":"No","oa_version":"None","issue":"3","title":"Magnetic Lieb-Thirring inequalities","quality_controlled":"1","main_file_link":[{"url":"https://link.springer.com/article/10.1007/BF02099152"}],"language":[{"iso":"eng"}],"intvolume":"       170","publist_id":"4168","date_published":"1995-06-01T00:00:00Z","day":"01","year":"1995","publisher":"Springer","article_type":"original"}