[{"abstract":[{"lang":"eng","text":"For given positive integers a, b, q we investigate the density of solutions (x, y) ∈ Z2 to congruences ax + by2 ≡ 0 mod q."}],"acknowledgement":"EP/E053262/1\tEngineering and Physical Sciences Research Council","publisher":"Adam Mickiewicz University Press","quality_controlled":0,"intvolume":" 47","month":"12","year":"2012","publication_status":"published","publication":"Functiones et Approximatio, Commentarii Mathematici","day":"20","page":"267 - 286","date_created":"2018-12-11T11:45:22Z","issue":"2","doi":"10.7169/facm/2012.47.2.9","volume":47,"date_published":"2012-12-20T00:00:00Z","_id":"238","type":"journal_article","status":"public","date_updated":"2021-01-12T06:57:08Z","citation":{"ista":"Baier S, Browning TD. 2012. Inhomogeneous quadratic congruences. Functiones et Approximatio, Commentarii Mathematici. 47(2), 267–286.","chicago":"Baier, Stephan, and Timothy D Browning. “Inhomogeneous Quadratic Congruences.” Functiones et Approximatio, Commentarii Mathematici. Adam Mickiewicz University Press, 2012. https://doi.org/10.7169/facm/2012.47.2.9.","ama":"Baier S, Browning TD. Inhomogeneous quadratic congruences. Functiones et Approximatio, Commentarii Mathematici. 2012;47(2):267-286. doi:10.7169/facm/2012.47.2.9","apa":"Baier, S., & Browning, T. D. (2012). Inhomogeneous quadratic congruences. Functiones et Approximatio, Commentarii Mathematici. Adam Mickiewicz University Press. https://doi.org/10.7169/facm/2012.47.2.9","ieee":"S. Baier and T. D. Browning, “Inhomogeneous quadratic congruences,” Functiones et Approximatio, Commentarii Mathematici, vol. 47, no. 2. Adam Mickiewicz University Press, pp. 267–286, 2012.","short":"S. Baier, T.D. Browning, Functiones et Approximatio, Commentarii Mathematici 47 (2012) 267–286.","mla":"Baier, Stephan, and Timothy D. Browning. “Inhomogeneous Quadratic Congruences.” Functiones et Approximatio, Commentarii Mathematici, vol. 47, no. 2, Adam Mickiewicz University Press, 2012, pp. 267–86, doi:10.7169/facm/2012.47.2.9."},"extern":1,"author":[{"first_name":"Stephan","last_name":"Baier","full_name":"Baier, Stephan"},{"last_name":"Browning","full_name":"Timothy Browning","orcid":"0000-0002-8314-0177","first_name":"Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87"}],"publist_id":"7666","title":"Inhomogeneous quadratic congruences"},{"page":"55 - 92","date_created":"2018-12-11T11:57:26Z","date_published":"2012-01-01T00:00:00Z","doi":"10.1007/978-3-642-29511-9_2","volume":2051,"year":"2012","publication_status":"published","publication":"Quantum Many Body Systems","day":"01","quality_controlled":0,"alternative_title":["Lecture Notes in Mathematics"],"publisher":"Springer","intvolume":" 2051","month":"01","abstract":[{"lang":"eng","text":"Bose–Einstein condensation (BEC) in cold atomic gases was first achieved experimentally in 1995 [1, 6]. After initial failed attempts with spin-polarized atomic hydrogen, the first successful demonstrations of this phenomenon used gases of rubidium and sodium atoms, respectively. Since then there has been a surge of activity in this field, with ingenious experiments putting forth more and more astonishing results about the behavior of matter at very cold temperatures.\n"}],"publist_id":"4526","author":[{"first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","orcid":"0000-0002-6781-0521","full_name":"Robert Seiringer"}],"editor":[{"first_name":"Vincent","full_name":"Rivasseau, Vincent","last_name":"Rivasseau"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","orcid":"0000-0002-6781-0521","full_name":"Robert Seiringer","last_name":"Seiringer"},{"last_name":"Solovej","full_name":"Solovej, Jan P","first_name":"Jan"},{"full_name":"Spencer, Thomas","last_name":"Spencer","first_name":"Thomas"}],"title":"Cold quantum gases and bose einstein condensation","citation":{"ama":"Seiringer R. Cold quantum gases and bose einstein condensation. In: Rivasseau V, Seiringer R, Solovej J, Spencer T, eds. Quantum Many Body Systems. Vol 2051. Springer; 2012:55-92. doi:10.1007/978-3-642-29511-9_2","apa":"Seiringer, R. (2012). Cold quantum gases and bose einstein condensation. In V. Rivasseau, R. Seiringer, J. Solovej, & T. Spencer (Eds.), Quantum Many Body Systems (Vol. 2051, pp. 55–92). Springer. https://doi.org/10.1007/978-3-642-29511-9_2","short":"R. Seiringer, in:, V. Rivasseau, R. Seiringer, J. Solovej, T. Spencer (Eds.), Quantum Many Body Systems, Springer, 2012, pp. 55–92.","ieee":"R. Seiringer, “Cold quantum gases and bose einstein condensation,” in Quantum Many Body Systems, vol. 2051, V. Rivasseau, R. Seiringer, J. Solovej, and T. Spencer, Eds. Springer, 2012, pp. 55–92.","mla":"Seiringer, Robert. “Cold Quantum Gases and Bose Einstein Condensation.” Quantum Many Body Systems, edited by Vincent Rivasseau et al., vol. 2051, Springer, 2012, pp. 55–92, doi:10.1007/978-3-642-29511-9_2.","ista":"Seiringer R. 2012.Cold quantum gases and bose einstein condensation. In: Quantum Many Body Systems. Lecture Notes in Mathematics, vol. 2051, 55–92.","chicago":"Seiringer, Robert. “Cold Quantum Gases and Bose Einstein Condensation.” In Quantum Many Body Systems, edited by Vincent Rivasseau, Robert Seiringer, Jan Solovej, and Thomas Spencer, 2051:55–92. Springer, 2012. https://doi.org/10.1007/978-3-642-29511-9_2."},"date_updated":"2021-01-12T06:57:14Z","extern":1,"type":"book_chapter","status":"public","_id":"2399"},{"month":"01","intvolume":" 53","publisher":"American Institute of Physics","quality_controlled":0,"abstract":[{"text":"We study the BCS gap equation for a Fermi gas with unequal population of spin-up and spin-down states. For cosh (δ μ/T) ≤ 2, with T the temperature and δμ the chemical potential difference, the question of existence of non-trivial solutions can be reduced to spectral properties of a linear operator, similar to the unpolarized case studied previously in [Frank, R. L., Hainzl, C., Naboko, S., and Seiringer, R., J., Geom. Anal.17, 559-567 (2007)10.1007/BF02937429; Hainzl, C., Hamza, E., Seiringer, R., and Solovej, J. P., Commun., Math. Phys.281, 349-367 (2008)10.1007/s00220-008-0489-2; and Hainzl, C. and Seiringer, R., Phys. Rev. B77, 184517-110 435 (2008)]10.1103/PhysRevB.77.184517. For cosh (δ μ/T) > 2 the phase diagram is more complicated, however. We derive upper and lower bounds for the critical temperature, and study their behavior in the small coupling limit.","lang":"eng"}],"doi":"10.1063/1.3670747","date_published":"2012-01-01T00:00:00Z","volume":53,"issue":"1","date_created":"2018-12-11T11:57:25Z","day":"01","publication":"Journal of Mathematical Physics","year":"2012","publication_status":"published","status":"public","type":"journal_article","_id":"2394","title":"The gap equation for spin-polarized fermions","publist_id":"4532","author":[{"full_name":"Freiji, Abraham","last_name":"Freiji","first_name":"Abraham"},{"full_name":"Hainzl, Christian","last_name":"Hainzl","first_name":"Christian"},{"first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","orcid":"0000-0002-6781-0521","full_name":"Robert Seiringer"}],"extern":1,"citation":{"mla":"Freiji, Abraham, et al. “The Gap Equation for Spin-Polarized Fermions.” Journal of Mathematical Physics, vol. 53, no. 1, American Institute of Physics, 2012, doi:10.1063/1.3670747.","short":"A. Freiji, C. Hainzl, R. Seiringer, Journal of Mathematical Physics 53 (2012).","ieee":"A. Freiji, C. Hainzl, and R. Seiringer, “The gap equation for spin-polarized fermions,” Journal of Mathematical Physics, vol. 53, no. 1. American Institute of Physics, 2012.","apa":"Freiji, A., Hainzl, C., & Seiringer, R. (2012). The gap equation for spin-polarized fermions. Journal of Mathematical Physics. American Institute of Physics. https://doi.org/10.1063/1.3670747","ama":"Freiji A, Hainzl C, Seiringer R. The gap equation for spin-polarized fermions. Journal of Mathematical Physics. 2012;53(1). doi:10.1063/1.3670747","chicago":"Freiji, Abraham, Christian Hainzl, and Robert Seiringer. “The Gap Equation for Spin-Polarized Fermions.” Journal of Mathematical Physics. American Institute of Physics, 2012. https://doi.org/10.1063/1.3670747.","ista":"Freiji A, Hainzl C, Seiringer R. 2012. The gap equation for spin-polarized fermions. Journal of Mathematical Physics. 53(1)."},"date_updated":"2021-01-12T06:57:13Z"},{"volume":25,"issue":"3","date_published":"2012-01-01T00:00:00Z","doi":"10.1090/S0894-0347-2012-00735-8","date_created":"2018-12-11T11:57:25Z","page":"667 - 713","day":"01","publication":"Journal of the American Mathematical Society","year":"2012","publication_status":"published","month":"01","intvolume":" 25","quality_controlled":0,"publisher":"American Mathematical Society","oa":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1102.4001"}],"abstract":[{"lang":"eng","text":"We give the first rigorous derivation of the celebrated Ginzburg-Landau (GL) theory, starting from the microscopic Bardeen-Cooper-Schrieffer (BCS) model. Close to the critical temperature, GL arises as an effective theory on the macroscopic scale. The relevant scaling limit is semiclassical in nature, and semiclassical analysis, with minimal regularity assumptions, plays an important part in our proof. "}],"title":"Microscopic derivation of Ginzburg-Landau theory","publist_id":"4531","author":[{"full_name":"Frank, Rupert L","last_name":"Frank","first_name":"Rupert"},{"last_name":"Hainzl","full_name":"Hainzl, Christian","first_name":"Christian"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","last_name":"Seiringer","orcid":"0000-0002-6781-0521","full_name":"Robert Seiringer"},{"full_name":"Solovej, Jan P","last_name":"Solovej","first_name":"Jan"}],"extern":1,"date_updated":"2021-01-12T06:57:13Z","citation":{"ama":"Frank R, Hainzl C, Seiringer R, Solovej J. Microscopic derivation of Ginzburg-Landau theory. Journal of the American Mathematical Society. 2012;25(3):667-713. doi:10.1090/S0894-0347-2012-00735-8","apa":"Frank, R., Hainzl, C., Seiringer, R., & Solovej, J. (2012). Microscopic derivation of Ginzburg-Landau theory. Journal of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/S0894-0347-2012-00735-8","ieee":"R. Frank, C. Hainzl, R. Seiringer, and J. Solovej, “Microscopic derivation of Ginzburg-Landau theory,” Journal of the American Mathematical Society, vol. 25, no. 3. American Mathematical Society, pp. 667–713, 2012.","short":"R. Frank, C. Hainzl, R. Seiringer, J. Solovej, Journal of the American Mathematical Society 25 (2012) 667–713.","mla":"Frank, Rupert, et al. “Microscopic Derivation of Ginzburg-Landau Theory.” Journal of the American Mathematical Society, vol. 25, no. 3, American Mathematical Society, 2012, pp. 667–713, doi:10.1090/S0894-0347-2012-00735-8.","ista":"Frank R, Hainzl C, Seiringer R, Solovej J. 2012. Microscopic derivation of Ginzburg-Landau theory. Journal of the American Mathematical Society. 25(3), 667–713.","chicago":"Frank, Rupert, Christian Hainzl, Robert Seiringer, and Jan Solovej. “Microscopic Derivation of Ginzburg-Landau Theory.” Journal of the American Mathematical Society. American Mathematical Society, 2012. https://doi.org/10.1090/S0894-0347-2012-00735-8."},"status":"public","type":"journal_article","_id":"2395"},{"publisher":"Springer","quality_controlled":0,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1111.1683"}],"oa":1,"month":"06","intvolume":" 100","abstract":[{"lang":"eng","text":"A positive temperature analogue of the scattering length of a potential V can be defined via integrating the difference of the heat kernels of -Δ and, with Δ the Laplacian. An upper bound on this quantity is a crucial input in the derivation of a bound on the critical temperature of a dilute Bose gas (Seiringer and Ueltschi in Phys Rev B 80:014502, 2009). In (Seiringer and Ueltschi in Phys Rev B 80:014502, 2009), a bound was given in the case of finite range potentials and sufficiently low temperature. In this paper, we improve the bound and extend it to potentials of infinite range."}],"page":"237 - 243","issue":"3","volume":100,"date_published":"2012-06-01T00:00:00Z","doi":"10.1007/s11005-012-0566-5","date_created":"2018-12-11T11:57:25Z","publication_status":"published","year":"2012","day":"01","publication":"Letters in Mathematical Physics","type":"journal_article","status":"public","_id":"2396","publist_id":"4529","author":[{"full_name":"Landon, Benjamin","last_name":"Landon","first_name":"Benjamin"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","orcid":"0000-0002-6781-0521","full_name":"Robert Seiringer","last_name":"Seiringer"}],"title":"The scattering length at positive temperature","citation":{"chicago":"Landon, Benjamin, and Robert Seiringer. “The Scattering Length at Positive Temperature.” Letters in Mathematical Physics. Springer, 2012. https://doi.org/10.1007/s11005-012-0566-5.","ista":"Landon B, Seiringer R. 2012. The scattering length at positive temperature. Letters in Mathematical Physics. 100(3), 237–243.","mla":"Landon, Benjamin, and Robert Seiringer. “The Scattering Length at Positive Temperature.” Letters in Mathematical Physics, vol. 100, no. 3, Springer, 2012, pp. 237–43, doi:10.1007/s11005-012-0566-5.","ama":"Landon B, Seiringer R. The scattering length at positive temperature. Letters in Mathematical Physics. 2012;100(3):237-243. doi:10.1007/s11005-012-0566-5","apa":"Landon, B., & Seiringer, R. (2012). The scattering length at positive temperature. Letters in Mathematical Physics. Springer. https://doi.org/10.1007/s11005-012-0566-5","short":"B. Landon, R. Seiringer, Letters in Mathematical Physics 100 (2012) 237–243.","ieee":"B. Landon and R. Seiringer, “The scattering length at positive temperature,” Letters in Mathematical Physics, vol. 100, no. 3. Springer, pp. 237–243, 2012."},"date_updated":"2021-01-12T06:57:13Z","extern":1}]