--- _id: '238' 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" author: - first_name: Stephan full_name: Baier, Stephan last_name: Baier - first_name: Timothy D full_name: Timothy Browning id: 35827D50-F248-11E8-B48F-1D18A9856A87 last_name: Browning orcid: 0000-0002-8314-0177 citation: 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 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. 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. ista: Baier S, Browning TD. 2012. Inhomogeneous quadratic congruences. Functiones et Approximatio, Commentarii Mathematici. 47(2), 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. short: S. Baier, T.D. Browning, Functiones et Approximatio, Commentarii Mathematici 47 (2012) 267–286. date_created: 2018-12-11T11:45:22Z date_published: 2012-12-20T00:00:00Z date_updated: 2021-01-12T06:57:08Z day: '20' doi: 10.7169/facm/2012.47.2.9 extern: 1 intvolume: ' 47' issue: '2' month: '12' page: 267 - 286 publication: Functiones et Approximatio, Commentarii Mathematici publication_status: published publisher: Adam Mickiewicz University Press publist_id: '7666' quality_controlled: 0 status: public title: Inhomogeneous quadratic congruences type: journal_article volume: 47 year: '2012' ... --- _id: '2399' 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. alternative_title: - Lecture Notes in Mathematics author: - first_name: Robert full_name: Robert Seiringer id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 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 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. 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. ista: 'Seiringer R. 2012.Cold quantum gases and bose einstein condensation. In: Quantum Many Body Systems. Lecture Notes in Mathematics, vol. 2051, 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. short: R. Seiringer, in:, V. Rivasseau, R. Seiringer, J. Solovej, T. Spencer (Eds.), Quantum Many Body Systems, Springer, 2012, pp. 55–92. date_created: 2018-12-11T11:57:26Z date_published: 2012-01-01T00:00:00Z date_updated: 2021-01-12T06:57:14Z day: '01' doi: 10.1007/978-3-642-29511-9_2 editor: - first_name: Vincent full_name: Rivasseau, Vincent last_name: Rivasseau - first_name: Robert full_name: Robert Seiringer id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 - first_name: Jan full_name: Solovej, Jan P last_name: Solovej - first_name: Thomas full_name: Spencer, Thomas last_name: Spencer extern: 1 intvolume: ' 2051' month: '01' page: 55 - 92 publication: Quantum Many Body Systems publication_status: published publisher: Springer publist_id: '4526' quality_controlled: 0 status: public title: Cold quantum gases and bose einstein condensation type: book_chapter volume: 2051 year: '2012' ... --- _id: '2394' abstract: - lang: eng 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. author: - first_name: Abraham full_name: Freiji, Abraham last_name: Freiji - first_name: Christian full_name: Hainzl, Christian last_name: Hainzl - first_name: Robert full_name: Robert Seiringer id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: 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 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 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. 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. ista: Freiji A, Hainzl C, Seiringer R. 2012. The gap equation for spin-polarized fermions. Journal of Mathematical Physics. 53(1). 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). date_created: 2018-12-11T11:57:25Z date_published: 2012-01-01T00:00:00Z date_updated: 2021-01-12T06:57:13Z day: '01' doi: 10.1063/1.3670747 extern: 1 intvolume: ' 53' issue: '1' month: '01' publication: Journal of Mathematical Physics publication_status: published publisher: American Institute of Physics publist_id: '4532' quality_controlled: 0 status: public title: The gap equation for spin-polarized fermions type: journal_article volume: 53 year: '2012' ... --- _id: '2395' 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. ' author: - first_name: Rupert full_name: Frank, Rupert L last_name: Frank - first_name: Christian full_name: Hainzl, Christian last_name: Hainzl - first_name: Robert full_name: Robert Seiringer id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 - first_name: Jan full_name: Solovej, Jan P last_name: Solovej 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 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. 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. 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. 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. short: R. Frank, C. Hainzl, R. Seiringer, J. Solovej, Journal of the American Mathematical Society 25 (2012) 667–713. date_created: 2018-12-11T11:57:25Z date_published: 2012-01-01T00:00:00Z date_updated: 2021-01-12T06:57:13Z day: '01' doi: 10.1090/S0894-0347-2012-00735-8 extern: 1 intvolume: ' 25' issue: '3' main_file_link: - open_access: '1' url: http://arxiv.org/abs/1102.4001 month: '01' oa: 1 page: 667 - 713 publication: Journal of the American Mathematical Society publication_status: published publisher: American Mathematical Society publist_id: '4531' quality_controlled: 0 status: public title: Microscopic derivation of Ginzburg-Landau theory type: journal_article volume: 25 year: '2012' ... --- _id: '2396' 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. author: - first_name: Benjamin full_name: Landon, Benjamin last_name: Landon - first_name: Robert full_name: Robert Seiringer id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: 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 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. 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. 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. short: B. Landon, R. Seiringer, Letters in Mathematical Physics 100 (2012) 237–243. date_created: 2018-12-11T11:57:25Z date_published: 2012-06-01T00:00:00Z date_updated: 2021-01-12T06:57:13Z day: '01' doi: 10.1007/s11005-012-0566-5 extern: 1 intvolume: ' 100' issue: '3' main_file_link: - open_access: '1' url: http://arxiv.org/abs/1111.1683 month: '06' oa: 1 page: 237 - 243 publication: Letters in Mathematical Physics publication_status: published publisher: Springer publist_id: '4529' quality_controlled: 0 status: public title: The scattering length at positive temperature type: journal_article volume: 100 year: '2012' ... --- _id: '2398' abstract: - lang: eng text: We extend the mathematical theory of quantum hypothesis testing to the general W*-algebraic setting and explore its relation with recent developments in non-equilibrium quantum statistical mechanics. In particular, we relate the large deviation principle for the full counting statistics of entropy flow to quantum hypothesis testing of the arrow of time. author: - first_name: Vojkan full_name: Jakšić, Vojkan last_name: Jakšić - first_name: Yoshiko full_name: Ogata, Yoshiko last_name: Ogata - first_name: Claude full_name: Pillet, Claude A last_name: Pillet - first_name: Robert full_name: Robert Seiringer id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Jakšić V, Ogata Y, Pillet C, Seiringer R. Quantum hypothesis testing and non-equilibrium statistical mechanics. Reviews in Mathematical Physics. 2012;24(6). doi:10.1142/S0129055X12300026 apa: Jakšić, V., Ogata, Y., Pillet, C., & Seiringer, R. (2012). Quantum hypothesis testing and non-equilibrium statistical mechanics. Reviews in Mathematical Physics. World Scientific Publishing. https://doi.org/10.1142/S0129055X12300026 chicago: Jakšić, Vojkan, Yoshiko Ogata, Claude Pillet, and Robert Seiringer. “Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics.” Reviews in Mathematical Physics. World Scientific Publishing, 2012. https://doi.org/10.1142/S0129055X12300026. ieee: V. Jakšić, Y. Ogata, C. Pillet, and R. Seiringer, “Quantum hypothesis testing and non-equilibrium statistical mechanics,” Reviews in Mathematical Physics, vol. 24, no. 6. World Scientific Publishing, 2012. ista: Jakšić V, Ogata Y, Pillet C, Seiringer R. 2012. Quantum hypothesis testing and non-equilibrium statistical mechanics. Reviews in Mathematical Physics. 24(6). mla: Jakšić, Vojkan, et al. “Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics.” Reviews in Mathematical Physics, vol. 24, no. 6, World Scientific Publishing, 2012, doi:10.1142/S0129055X12300026. short: V. Jakšić, Y. Ogata, C. Pillet, R. Seiringer, Reviews in Mathematical Physics 24 (2012). date_created: 2018-12-11T11:57:26Z date_published: 2012-07-01T00:00:00Z date_updated: 2020-07-14T12:45:40Z day: '01' doi: 10.1142/S0129055X12300026 extern: 1 intvolume: ' 24' issue: '6' main_file_link: - open_access: '1' url: http://arxiv.org/abs/1109.3804 month: '07' oa: 1 publication: Reviews in Mathematical Physics publication_status: published publisher: World Scientific Publishing publist_id: '4528' quality_controlled: 0 status: public title: Quantum hypothesis testing and non-equilibrium statistical mechanics type: review volume: 24 year: '2012' ... --- _id: '2397' abstract: - lang: eng text: We consider the low-density limit of a Fermi gas in the BCS approximation. We show that if the interaction potential allows for a two-particle bound state, the system at zero temperature is well approximated by the Gross-Pitaevskii functional, describing a Bose-Einstein condensate of fermion pairs. author: - first_name: Christian full_name: Hainzl, Christian last_name: Hainzl - first_name: Robert full_name: Robert Seiringer id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Hainzl C, Seiringer R. Low density limit of BCS theory and Bose-Einstein condensation of Fermion pairs. Letters in Mathematical Physics. 2012;100(2):119-138. doi:10.1007/s11005-011-0535-4 apa: Hainzl, C., & Seiringer, R. (2012). Low density limit of BCS theory and Bose-Einstein condensation of Fermion pairs. Letters in Mathematical Physics. Springer. https://doi.org/10.1007/s11005-011-0535-4 chicago: Hainzl, Christian, and Robert Seiringer. “Low Density Limit of BCS Theory and Bose-Einstein Condensation of Fermion Pairs.” Letters in Mathematical Physics. Springer, 2012. https://doi.org/10.1007/s11005-011-0535-4. ieee: C. Hainzl and R. Seiringer, “Low density limit of BCS theory and Bose-Einstein condensation of Fermion pairs,” Letters in Mathematical Physics, vol. 100, no. 2. Springer, pp. 119–138, 2012. ista: Hainzl C, Seiringer R. 2012. Low density limit of BCS theory and Bose-Einstein condensation of Fermion pairs. Letters in Mathematical Physics. 100(2), 119–138. mla: Hainzl, Christian, and Robert Seiringer. “Low Density Limit of BCS Theory and Bose-Einstein Condensation of Fermion Pairs.” Letters in Mathematical Physics, vol. 100, no. 2, Springer, 2012, pp. 119–38, doi:10.1007/s11005-011-0535-4. short: C. Hainzl, R. Seiringer, Letters in Mathematical Physics 100 (2012) 119–138. date_created: 2018-12-11T11:57:25Z date_published: 2012-05-01T00:00:00Z date_updated: 2021-01-12T06:57:14Z day: '01' doi: 10.1007/s11005-011-0535-4 extern: 1 intvolume: ' 100' issue: '2' main_file_link: - open_access: '1' url: http://arxiv.org/abs/1105.1100 month: '05' oa: 1 page: 119 - 138 publication: Letters in Mathematical Physics publication_status: published publisher: Springer publist_id: '4530' quality_controlled: 0 status: public title: Low density limit of BCS theory and Bose-Einstein condensation of Fermion pairs type: journal_article volume: 100 year: '2012' ... --- _id: '240' abstract: - lang: eng text: We investigate the frequency of positive squareful numbers x, y, z≤B for which x+y=z and present a conjecture concerning its asymptotic behavior. acknowledgement: "EP/E053262/1\tEngineering and Physical Sciences Research Council" author: - first_name: Timothy D full_name: Timothy Browning id: 35827D50-F248-11E8-B48F-1D18A9856A87 last_name: Browning orcid: 0000-0002-8314-0177 - first_name: K Van full_name: Valckenborgh, K Van last_name: Valckenborgh citation: ama: Browning TD, Valckenborgh KV. Sums of three squareful numbers. Experimental Mathematics. 2012;21(2):204-211. doi:10.1080/10586458.2011.605733 apa: Browning, T. D., & Valckenborgh, K. V. (2012). Sums of three squareful numbers. Experimental Mathematics. Taylor & Francis. https://doi.org/10.1080/10586458.2011.605733 chicago: Browning, Timothy D, and K Van Valckenborgh. “Sums of Three Squareful Numbers.” Experimental Mathematics. Taylor & Francis, 2012. https://doi.org/10.1080/10586458.2011.605733. ieee: T. D. Browning and K. V. Valckenborgh, “Sums of three squareful numbers,” Experimental Mathematics, vol. 21, no. 2. Taylor & Francis, pp. 204–211, 2012. ista: Browning TD, Valckenborgh KV. 2012. Sums of three squareful numbers. Experimental Mathematics. 21(2), 204–211. mla: Browning, Timothy D., and K. Van Valckenborgh. “Sums of Three Squareful Numbers.” Experimental Mathematics, vol. 21, no. 2, Taylor & Francis, 2012, pp. 204–11, doi:10.1080/10586458.2011.605733. short: T.D. Browning, K.V. Valckenborgh, Experimental Mathematics 21 (2012) 204–211. date_created: 2018-12-11T11:45:23Z date_published: 2012-05-23T00:00:00Z date_updated: 2021-01-12T06:57:15Z day: '23' doi: 10.1080/10586458.2011.605733 extern: 1 intvolume: ' 21' issue: '2' month: '05' page: 204 - 211 publication: Experimental Mathematics publication_status: published publisher: Taylor & Francis publist_id: '7664' quality_controlled: 0 status: public title: Sums of three squareful numbers type: journal_article volume: 21 year: '2012' ... --- _id: '2400' abstract: - lang: eng text: If the polaron coupling constant α is large enough, bipolarons or multi-polarons will form. When passing through the critical α c from above, does the radius of the system simply get arbitrarily large or does it reach a maximum and then explode? We prove that it is always the latter. We also prove the analogous statement for the Pekar-Tomasevich (PT) approximation to the energy, in which case there is a solution to the PT equation at α c. Similarly, we show that the same phenomenon occurs for atoms, e. g., helium, at the critical value of the nuclear charge. Our proofs rely only on energy estimates, not on a detailed analysis of the Schrödinger equation, and are very general. They use the fact that the Coulomb repulsion decays like 1/r, while 'uncertainty principle' localization energies decay more rapidly, as 1/r 2. author: - first_name: Rupert full_name: Frank, Rupert L last_name: Frank - first_name: Élliott full_name: Lieb, Élliott H last_name: Lieb - first_name: Robert full_name: Robert Seiringer id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Frank R, Lieb É, Seiringer R. Binding of polarons and atoms at threshold. Communications in Mathematical Physics. 2012;313(2):405-424. doi:10.1007/s00220-012-1436-9 apa: Frank, R., Lieb, É., & Seiringer, R. (2012). Binding of polarons and atoms at threshold. Communications in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-012-1436-9 chicago: Frank, Rupert, Élliott Lieb, and Robert Seiringer. “Binding of Polarons and Atoms at Threshold.” Communications in Mathematical Physics. Springer, 2012. https://doi.org/10.1007/s00220-012-1436-9. ieee: R. Frank, É. Lieb, and R. Seiringer, “Binding of polarons and atoms at threshold,” Communications in Mathematical Physics, vol. 313, no. 2. Springer, pp. 405–424, 2012. ista: Frank R, Lieb É, Seiringer R. 2012. Binding of polarons and atoms at threshold. Communications in Mathematical Physics. 313(2), 405–424. mla: Frank, Rupert, et al. “Binding of Polarons and Atoms at Threshold.” Communications in Mathematical Physics, vol. 313, no. 2, Springer, 2012, pp. 405–24, doi:10.1007/s00220-012-1436-9. short: R. Frank, É. Lieb, R. Seiringer, Communications in Mathematical Physics 313 (2012) 405–424. date_created: 2018-12-11T11:57:27Z date_published: 2012-07-01T00:00:00Z date_updated: 2021-01-12T06:57:15Z day: '01' doi: 10.1007/s00220-012-1436-9 extern: 1 intvolume: ' 313' issue: '2' main_file_link: - open_access: '1' url: http://arxiv.org/abs/1106.0729 month: '07' oa: 1 page: 405 - 424 publication: Communications in Mathematical Physics publication_status: published publisher: Springer publist_id: '4527' quality_controlled: 0 status: public title: Binding of polarons and atoms at threshold type: journal_article volume: 313 year: '2012' ... --- _id: '2403' abstract: - lang: eng text: We study the effects of random scatterers on the ground state of the one-dimensional Lieb-Liniger model of interacting bosons on the unit interval in the Gross-Pitaevskii regime. We prove that Bose-Einstein condensation survives even a strong random potential with a high density of scatterers. The character of the wavefunction of the condensate, however, depends in an essential way on the interplay between randomness and the strength of the two-body interaction. For low density of scatterers and strong interactions the wavefunction extends over the whole interval. A high density of scatterers and weak interactions, on the other hand, lead to localization of the wavefunction in a fragmented subset of the interval. author: - first_name: Robert full_name: Robert Seiringer id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 - first_name: Jakob full_name: Yngvason, Jakob last_name: Yngvason - first_name: Valentin full_name: Zagrebnov, Valentin A last_name: Zagrebnov citation: ama: Seiringer R, Yngvason J, Zagrebnov V. Disordered Bose-Einstein condensates with interaction in one dimension. Journal of Statistical Mechanics Theory and Experiment. 2012;2012(11). doi:10.1088/1742-5468/2012/11/P11007 apa: Seiringer, R., Yngvason, J., & Zagrebnov, V. (2012). Disordered Bose-Einstein condensates with interaction in one dimension. Journal of Statistical Mechanics Theory and Experiment. IOP Publishing Ltd. https://doi.org/10.1088/1742-5468/2012/11/P11007 chicago: Seiringer, Robert, Jakob Yngvason, and Valentin Zagrebnov. “Disordered Bose-Einstein Condensates with Interaction in One Dimension.” Journal of Statistical Mechanics Theory and Experiment. IOP Publishing Ltd., 2012. https://doi.org/10.1088/1742-5468/2012/11/P11007. ieee: R. Seiringer, J. Yngvason, and V. Zagrebnov, “Disordered Bose-Einstein condensates with interaction in one dimension,” Journal of Statistical Mechanics Theory and Experiment, vol. 2012, no. 11. IOP Publishing Ltd., 2012. ista: Seiringer R, Yngvason J, Zagrebnov V. 2012. Disordered Bose-Einstein condensates with interaction in one dimension. Journal of Statistical Mechanics Theory and Experiment. 2012(11). mla: Seiringer, Robert, et al. “Disordered Bose-Einstein Condensates with Interaction in One Dimension.” Journal of Statistical Mechanics Theory and Experiment, vol. 2012, no. 11, IOP Publishing Ltd., 2012, doi:10.1088/1742-5468/2012/11/P11007. short: R. Seiringer, J. Yngvason, V. Zagrebnov, Journal of Statistical Mechanics Theory and Experiment 2012 (2012). date_created: 2018-12-11T11:57:28Z date_published: 2012-11-01T00:00:00Z date_updated: 2021-01-12T06:57:16Z day: '01' doi: 10.1088/1742-5468/2012/11/P11007 extern: 1 intvolume: ' 2012' issue: '11' main_file_link: - open_access: '1' url: http://arxiv.org/abs/1207.7054 month: '11' oa: 1 publication: Journal of Statistical Mechanics Theory and Experiment publication_status: published publisher: IOP Publishing Ltd. publist_id: '4523' quality_controlled: 0 status: public title: Disordered Bose-Einstein condensates with interaction in one dimension type: journal_article volume: 2012 year: '2012' ...