[{"month":"01","extern":1,"_id":"2340","date_updated":"2020-07-14T12:45:39Z","editor":[{"last_name":"Demuth","full_name":"Demuth, Michael","first_name":"Michael"},{"first_name":"Bert","full_name":"Schultze, Bert-Wolfgang","last_name":"Schultze"}],"alternative_title":["Operator Theory: Advances and Applications"],"publist_id":"4586","date_created":"2018-12-11T11:57:05Z","author":[{"orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","first_name":"Robert","full_name":"Robert Seiringer"}],"year":"2001","abstract":[{"text":"\nRecent experimental breakthroughs in the treatment of dilute Bose gases have renewed interest in their quantum mechanical description, respectively in approximations to it. The ground state properties of dilute Bose gases confined in external potentials and interacting via repulsive short range forces are usually described by means of the Gross-Pitaevskii energy functional. In joint work with Elliott H. Lieb and Jakob Yngvason its status as an approximation for the quantum mechanical many-body ground state problem has recently been rigorously clarified. We present a summary of this work, for both the two-and three-dimensional case.\n","lang":"eng"}],"citation":{"mla":"Seiringer, Robert. *Bosons in a Trap: Asymptotic Exactness of the Gross-Pitaevskii Ground State Energy Formula*. Edited by Michael Demuth and Bert Schultze, vol. 126, Birkhäuser, 2001, pp. 307–14, doi:10.1007/978-3-0348-8231-6.","chicago":"Seiringer, Robert. “Bosons in a Trap: Asymptotic Exactness of the Gross-Pitaevskii Ground State Energy Formula.” edited by Michael Demuth and Bert Schultze, 126:307–14. Birkhäuser, 2001. https://doi.org/10.1007/978-3-0348-8231-6.","ieee":"R. Seiringer, “Bosons in a trap: Asymptotic exactness of the Gross-Pitaevskii ground state energy formula,” presented at the PDE: Partial Differential Equations and Spectral Theory, 2001, vol. 126, pp. 307–314.","short":"R. Seiringer, in:, M. Demuth, B. Schultze (Eds.), Birkhäuser, 2001, pp. 307–314.","ama":"Seiringer R. Bosons in a trap: Asymptotic exactness of the Gross-Pitaevskii ground state energy formula. In: Demuth M, Schultze B, eds. Vol 126. Birkhäuser; 2001:307-314. doi:10.1007/978-3-0348-8231-6","ista":"Seiringer R. 2001. Bosons in a trap: Asymptotic exactness of the Gross-Pitaevskii ground state energy formula. PDE: Partial Differential Equations and Spectral Theory, Operator Theory: Advances and Applications, vol. 126. 307–314.","apa":"Seiringer, R. (2001). Bosons in a trap: Asymptotic exactness of the Gross-Pitaevskii ground state energy formula. In M. Demuth & B. Schultze (Eds.) (Vol. 126, pp. 307–314). Presented at the PDE: Partial Differential Equations and Spectral Theory, Birkhäuser. https://doi.org/10.1007/978-3-0348-8231-6"},"main_file_link":[{"url":"http://arxiv.org/abs/math-ph/0010006","open_access":"1"}],"conference":{"name":"PDE: Partial Differential Equations and Spectral Theory"},"page":"307 - 314","quality_controlled":0,"status":"public","oa":1,"publication_status":"published","date_published":"2001-01-01T00:00:00Z","publisher":"Birkhäuser","doi":"10.1007/978-3-0348-8231-6","volume":126,"intvolume":" 126","type":"conference","title":"Bosons in a trap: Asymptotic exactness of the Gross-Pitaevskii ground state energy formula","day":"01"},{"day":"01","title":"Atoms with bosonic "electrons" in strong magnetic fields","intvolume":" 2","type":"journal_article","doi":"10.1007/PL00001032","date_published":"2001-02-01T00:00:00Z","volume":2,"publisher":"Birkhäuser","publication":"Annales Henri Poincare","oa":1,"publication_status":"published","status":"public","citation":{"apa":"Baumgartner, B., & Seiringer, R. (2001). Atoms with bosonic "electrons" in strong magnetic fields. *Annales Henri Poincare*, *2*(1), 41–76. https://doi.org/10.1007/PL00001032","ama":"Baumgartner B, Seiringer R. Atoms with bosonic "electrons" in strong magnetic fields. *Annales Henri Poincare*. 2001;2(1):41-76. doi:10.1007/PL00001032","ista":"Baumgartner B, Seiringer R. 2001. Atoms with bosonic "electrons" in strong magnetic fields. Annales Henri Poincare. 2(1), 41–76.","short":"B. Baumgartner, R. Seiringer, Annales Henri Poincare 2 (2001) 41–76.","ieee":"B. Baumgartner and R. Seiringer, “Atoms with bosonic "electrons" in strong magnetic fields,” *Annales Henri Poincare*, vol. 2, no. 1, pp. 41–76, 2001.","chicago":"Baumgartner, Bernhard, and Robert Seiringer. “Atoms with Bosonic "Electrons" in Strong Magnetic Fields.” *Annales Henri Poincare* 2, no. 1 (2001): 41–76. https://doi.org/10.1007/PL00001032.","mla":"Baumgartner, Bernhard, and Robert Seiringer. “Atoms with Bosonic "Electrons" in Strong Magnetic Fields.” *Annales Henri Poincare*, vol. 2, no. 1, Birkhäuser, 2001, pp. 41–76, doi:10.1007/PL00001032."},"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/math-ph/0007007"}],"quality_controlled":0,"page":"41 - 76","year":"2001","author":[{"last_name":"Baumgartner","full_name":"Baumgartner, Bernhard","first_name":"Bernhard"},{"full_name":"Robert Seiringer","first_name":"Robert","orcid":"0000-0002-6781-0521","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"abstract":[{"lang":"eng","text":"We study the ground state properties of an atom with nuclear charge Z and N bosonic "electrons" in the presence of a homogeneous magnetic field B. We investigate the mean field limit N→∞ with N / Z fixed, and identify three different asymptotic regions, according to B≪Z2,B∼Z2,andB≫Z2 . In Region 1 standard Hartree theory is applicable. Region 3 is described by a one-dimensional functional, which is identical to the so-called Hyper-Strong functional introduced by Lieb, Solovej and Yngvason for atoms with fermionic electrons in the region B≫Z3 ; i.e., for very strong magnetic fields the ground state properties of atoms are independent of statistics. For Region 2 we introduce a general magnetic Hartree functional, which is studied in detail. It is shown that in the special case of an atom it can be restricted to the subspace of zero angular momentum parallel to the magnetic field, which simplifies the theory considerably. The functional reproduces the energy and the one-particle reduced density matrix for the full N-particle ground state to leading order in N, and it implies the description of the other regions as limiting cases."}],"date_created":"2018-12-11T11:57:06Z","publist_id":"4585","_id":"2341","date_updated":"2020-07-14T12:45:39Z","extern":1,"month":"02","issue":"1"},{"publication_status":"published","oa":1,"status":"public","quality_controlled":0,"page":"1943 - 1948","main_file_link":[{"url":"http://arxiv.org/abs/math-ph/0006002","open_access":"1"}],"citation":{"ieee":"R. Seiringer, “On the maximal ionization of atoms in strong magnetic fields,” *Journal of Physics A: Mathematical and General*, vol. 34, no. 9, pp. 1943–1948, 2001.","short":"R. Seiringer, Journal of Physics A: Mathematical and General 34 (2001) 1943–1948.","chicago":"Seiringer, Robert. “On the Maximal Ionization of Atoms in Strong Magnetic Fields.” *Journal of Physics A: Mathematical and General* 34, no. 9 (2001): 1943–48. https://doi.org/10.1088/0305-4470/34/9/311.","mla":"Seiringer, Robert. “On the Maximal Ionization of Atoms in Strong Magnetic Fields.” *Journal of Physics A: Mathematical and General*, vol. 34, no. 9, IOP Publishing Ltd., 2001, pp. 1943–48, doi:10.1088/0305-4470/34/9/311.","apa":"Seiringer, R. (2001). On the maximal ionization of atoms in strong magnetic fields. *Journal of Physics A: Mathematical and General*, *34*(9), 1943–1948. https://doi.org/10.1088/0305-4470/34/9/311","ista":"Seiringer R. 2001. On the maximal ionization of atoms in strong magnetic fields. Journal of Physics A: Mathematical and General. 34(9), 1943–1948.","ama":"Seiringer R. On the maximal ionization of atoms in strong magnetic fields. *Journal of Physics A: Mathematical and General*. 2001;34(9):1943-1948. doi:10.1088/0305-4470/34/9/311"},"day":"09","title":"On the maximal ionization of atoms in strong magnetic fields","publication":"Journal of Physics A: Mathematical and General","intvolume":" 34","type":"journal_article","doi":"10.1088/0305-4470/34/9/311","publisher":"IOP Publishing Ltd.","date_published":"2001-03-09T00:00:00Z","volume":34,"_id":"2345","date_updated":"2020-07-14T12:45:39Z","issue":"9","extern":1,"month":"03","abstract":[{"text":"We give upper bounds for the number of spin-1/2 particles that can be bound to a nucleus of charge Z in the presence of a magnetic field B, including the spin-field coupling. We use Lieb's strategy, which is known to yield Nc < 2Z + 1 for magnetic fields that go to zero at infinity, ignoring the spin-field interaction. For particles with fermionic statistics in a homogeneous magnetic field our upper bound has an additional term of the order of Z × min {(B/Z3)2/5, 1 + | 1n(B/Z3)|2}.","lang":"eng"}],"year":"2001","author":[{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","orcid":"0000-0002-6781-0521","first_name":"Robert","full_name":"Robert Seiringer"}],"date_created":"2018-12-11T11:57:07Z","publist_id":"4580"},{"title":"Bounds on one-dimensional exchange energies with application to lowest Landau band quantum mechanics","day":"01","publication":"Letters in Mathematical Physics","date_published":"2001-02-01T00:00:00Z","volume":55,"publisher":"Springer","doi":"10.1023/A:1010951905548","type":"journal_article","intvolume":" 55","status":"public","oa":1,"publication_status":"published","page":"133 - 142","quality_controlled":0,"citation":{"mla":"Hainzl, Christian, and Robert Seiringer. “Bounds on One-Dimensional Exchange Energies with Application to Lowest Landau Band Quantum Mechanics.” *Letters in Mathematical Physics*, vol. 55, no. 2, Springer, 2001, pp. 133–42, doi:10.1023/A:1010951905548.","chicago":"Hainzl, Christian, and Robert Seiringer. “Bounds on One-Dimensional Exchange Energies with Application to Lowest Landau Band Quantum Mechanics.” *Letters in Mathematical Physics* 55, no. 2 (2001): 133–42. https://doi.org/10.1023/A:1010951905548.","short":"C. Hainzl, R. Seiringer, Letters in Mathematical Physics 55 (2001) 133–142.","ieee":"C. Hainzl and R. Seiringer, “Bounds on one-dimensional exchange energies with application to lowest Landau band quantum mechanics,” *Letters in Mathematical Physics*, vol. 55, no. 2, pp. 133–142, 2001.","ista":"Hainzl C, Seiringer R. 2001. Bounds on one-dimensional exchange energies with application to lowest Landau band quantum mechanics. Letters in Mathematical Physics. 55(2), 133–142.","ama":"Hainzl C, Seiringer R. Bounds on one-dimensional exchange energies with application to lowest Landau band quantum mechanics. *Letters in Mathematical Physics*. 2001;55(2):133-142. doi:10.1023/A:1010951905548","apa":"Hainzl, C., & Seiringer, R. (2001). Bounds on one-dimensional exchange energies with application to lowest Landau band quantum mechanics. *Letters in Mathematical Physics*, *55*(2), 133–142. https://doi.org/10.1023/A:1010951905548"},"main_file_link":[{"url":"http://arxiv.org/abs/cond-mat/0102118","open_access":"1"}],"abstract":[{"text":"By means of a generalization of the Fefferman - de la Llave decomposition we derive a general lower bound on the interaction energy of one-dimensional quantum systems. We apply this result to a specific class of lowest Landau band wave functions.","lang":"eng"}],"year":"2001","author":[{"last_name":"Hainzl","full_name":"Hainzl, Christian","first_name":"Christian"},{"last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","first_name":"Robert","full_name":"Robert Seiringer"}],"publist_id":"4581","date_created":"2018-12-11T11:57:07Z","date_updated":"2020-07-14T12:45:39Z","_id":"2346","issue":"2","month":"02","extern":1},{"issue":"1","extern":1,"month":"11","_id":"2347","date_updated":"2020-07-14T12:45:39Z","date_created":"2018-12-11T11:57:08Z","publist_id":"4579","abstract":[{"text":"We consider the ground state properties of an inhomogeneous two-dimensional Bose gas with a repulsive, short range pair interaction and an external confining potential. In the limit when the particle number N is large but ρ̄a2 is small, where ρ̄ is the average particle density and a the scattering length, the ground state energy and density are rigorously shown to be given to leading order by a Gross-Pitaevskii (GP) energy functional with a coupling constant g ∼ 1/| 1n(ρ̄a2)|. In contrast to the 3D case the coupling constant depends on N through the mean density. The GP energy per particle depends only on Ng. In 2D this parameter is typically so large that the gradient term in the GP energy functional is negligible and the simpler description by a Thomas-Fermi type functional is adequate.","lang":"eng"}],"author":[{"last_name":"Lieb","first_name":"Élliott","full_name":"Lieb, Élliott H"},{"full_name":"Robert Seiringer","first_name":"Robert","orcid":"0000-0002-6781-0521","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Yngvason","first_name":"Jakob","full_name":"Yngvason, Jakob"}],"year":"2001","quality_controlled":0,"page":"17 - 31","citation":{"ama":"Lieb É, Seiringer R, Yngvason J. A rigorous derivation of the Gross-Pitaevskii energy functional for a two-dimensional Bose gas. *Communications in Mathematical Physics*. 2001;224(1):17-31. doi:10.1007/s002200100533","ista":"Lieb É, Seiringer R, Yngvason J. 2001. A rigorous derivation of the Gross-Pitaevskii energy functional for a two-dimensional Bose gas. Communications in Mathematical Physics. 224(1), 17–31.","apa":"Lieb, É., Seiringer, R., & Yngvason, J. (2001). A rigorous derivation of the Gross-Pitaevskii energy functional for a two-dimensional Bose gas. *Communications in Mathematical Physics*, *224*(1), 17–31. https://doi.org/10.1007/s002200100533","mla":"Lieb, Élliott, et al. “A Rigorous Derivation of the Gross-Pitaevskii Energy Functional for a Two-Dimensional Bose Gas.” *Communications in Mathematical Physics*, vol. 224, no. 1, Springer, 2001, pp. 17–31, doi:10.1007/s002200100533.","ieee":"É. Lieb, R. Seiringer, and J. Yngvason, “A rigorous derivation of the Gross-Pitaevskii energy functional for a two-dimensional Bose gas,” *Communications in Mathematical Physics*, vol. 224, no. 1, pp. 17–31, 2001.","short":"É. Lieb, R. Seiringer, J. Yngvason, Communications in Mathematical Physics 224 (2001) 17–31.","chicago":"Lieb, Élliott, Robert Seiringer, and Jakob Yngvason. “A Rigorous Derivation of the Gross-Pitaevskii Energy Functional for a Two-Dimensional Bose Gas.” *Communications in Mathematical Physics* 224, no. 1 (2001): 17–31. https://doi.org/10.1007/s002200100533."},"main_file_link":[{"url":"http://arxiv.org/abs/cond-mat/0005026","open_access":"1"}],"oa":1,"publication_status":"published","status":"public","publication":"Communications in Mathematical Physics","intvolume":" 224","type":"journal_article","publisher":"Springer","doi":"10.1007/s002200100533","date_published":"2001-11-01T00:00:00Z","volume":224,"day":"01","title":"A rigorous derivation of the Gross-Pitaevskii energy functional for a two-dimensional Bose gas"}]