[{"scopus_import":"1","ddc":["510"],"fulldoi":"https://doi.org/10.1007/s00220-014-1923-2","date_updated":"2025-09-29T12:08:54Z","day":"01","page":"333 - 350","type":"journal_article","has_accepted_license":"1","status":"public","file":[{"content_type":"application/pdf","relation":"main_file","file_name":"2014_CommMathPhysics_Giuliani.pdf","creator":"dernst","date_updated":"2022-05-24T08:30:40Z","file_size":334064,"date_created":"2022-05-24T08:30:40Z","access_level":"open_access","file_id":"11409","checksum":"c8423271cd1e1ba9e44c47af75efe7b6","success":1}],"year":"2014","department":[{"_id":"RoSe"}],"publist_id":"5159","arxiv":1,"quality_controlled":"1","acknowledgement":"2014 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes.\r\n\r\nThe research leading to these results has received funding from the European Research\r\nCouncil under the European Union’s Seventh Framework Programme ERC Starting Grant CoMBoS (Grant Agreement No. 239694; A.G. and R.S.), the U.S. National Science Foundation (Grant PHY 0965859; E.H.L.), the Simons Foundation (Grant # 230207; E.H.L) and the NSERC (R.S.). The work is part of a project started in collaboration with Joel Lebowitz, whom we thank for many useful discussions and for his constant encouragement.","article_type":"original","title":"Formation of stripes and slabs near the ferromagnetic transition","_id":"1935","publisher":"Springer","volume":331,"month":"10","date_published":"2014-10-01T00:00:00Z","oa":1,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","isi":1,"language":[{"iso":"eng"}],"citation":{"short":"A. Giuliani, É. Lieb, R. Seiringer, Communications in Mathematical Physics 331 (2014) 333–350.","ama":"Giuliani A, Lieb É, Seiringer R. Formation of stripes and slabs near the ferromagnetic transition. <i>Communications in Mathematical Physics</i>. 2014;331:333-350. doi:<a href=\"https://doi.org/10.1007/s00220-014-1923-2\">10.1007/s00220-014-1923-2</a>","ista":"Giuliani A, Lieb É, Seiringer R. 2014. Formation of stripes and slabs near the ferromagnetic transition. Communications in Mathematical Physics. 331, 333–350.","ieee":"A. Giuliani, É. Lieb, and R. Seiringer, “Formation of stripes and slabs near the ferromagnetic transition,” <i>Communications in Mathematical Physics</i>, vol. 331. Springer, pp. 333–350, 2014.","chicago":"Giuliani, Alessandro, Élliott Lieb, and Robert Seiringer. “Formation of Stripes and Slabs near the Ferromagnetic Transition.” <i>Communications in Mathematical Physics</i>. Springer, 2014. <a href=\"https://doi.org/10.1007/s00220-014-1923-2\">https://doi.org/10.1007/s00220-014-1923-2</a>.","mla":"Giuliani, Alessandro, et al. “Formation of Stripes and Slabs near the Ferromagnetic Transition.” <i>Communications in Mathematical Physics</i>, vol. 331, Springer, 2014, pp. 333–50, doi:<a href=\"https://doi.org/10.1007/s00220-014-1923-2\">10.1007/s00220-014-1923-2</a>.","apa":"Giuliani, A., Lieb, É., &#38; Seiringer, R. (2014). Formation of stripes and slabs near the ferromagnetic transition. <i>Communications in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s00220-014-1923-2\">https://doi.org/10.1007/s00220-014-1923-2</a>"},"intvolume":"       331","publication":"Communications in Mathematical Physics","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"oa_version":"Published Version","date_created":"2018-12-11T11:54:48Z","article_processing_charge":"No","publication_status":"published","doi":"10.1007/s00220-014-1923-2","abstract":[{"lang":"eng","text":"We consider Ising models in d = 2 and d = 3 dimensions with nearest neighbor ferromagnetic and long-range antiferromagnetic interactions, the latter decaying as (distance)-p, p &gt; 2d, at large distances. If the strength J of the ferromagnetic interaction is larger than a critical value J c, then the ground state is homogeneous. It has been conjectured that when J is smaller than but close to J c, the ground state is periodic and striped, with stripes of constant width h = h(J), and h → ∞ as J → Jc -. (In d = 3 stripes mean slabs, not columns.) Here we rigorously prove that, if we normalize the energy in such a way that the energy of the homogeneous state is zero, then the ratio e 0(J)/e S(J) tends to 1 as J → Jc -, with e S(J) being the energy per site of the optimal periodic striped/slabbed state and e 0(J) the actual ground state energy per site of the system. Our proof comes with explicit bounds on the difference e 0(J)-e S(J) at small but positive J c-J, and also shows that in this parameter range the ground state is striped/slabbed in a certain sense: namely, if one looks at a randomly chosen window, of suitable size ℓ (very large compared to the optimal stripe size h(J)), one finds a striped/slabbed state with high probability."}],"author":[{"first_name":"Alessandro","full_name":"Giuliani, Alessandro","last_name":"Giuliani"},{"first_name":"Élliott","full_name":"Lieb, Élliott","last_name":"Lieb"},{"last_name":"Seiringer","first_name":"Robert","full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521"}],"external_id":{"isi":["000339732500011"],"arxiv":["1304.6344"]},"file_date_updated":"2022-05-24T08:30:40Z"},{"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.math/0508206","open_access":"1"}],"article_type":"original","title":"A counterexample to dispersive estimates for Schrödinger operators in higher dimensions","_id":"22076","publisher":"Springer Nature","month":"08","volume":266,"oa":1,"date_published":"2006-08-01T00:00:00Z","OA_place":"repository","das_tickbox":"1","extern":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"publication":"Communications in Mathematical Physics","intvolume":"       266","citation":{"mla":"Goldberg, Michael, and Monica Vişan. “A Counterexample to Dispersive Estimates for Schrödinger Operators in Higher Dimensions.” <i>Communications in Mathematical Physics</i>, vol. 266, Springer Nature, 2006, pp. 211–38, doi:<a href=\"https://doi.org/10.1007/s00220-006-0013-5\">10.1007/s00220-006-0013-5</a>.","apa":"Goldberg, M., &#38; Vişan, M. (2006). A counterexample to dispersive estimates for Schrödinger operators in higher dimensions. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-006-0013-5\">https://doi.org/10.1007/s00220-006-0013-5</a>","ama":"Goldberg M, Vişan M. A counterexample to dispersive estimates for Schrödinger operators in higher dimensions. <i>Communications in Mathematical Physics</i>. 2006;266:211-238. doi:<a href=\"https://doi.org/10.1007/s00220-006-0013-5\">10.1007/s00220-006-0013-5</a>","short":"M. Goldberg, M. Vişan, Communications in Mathematical Physics 266 (2006) 211–238.","ista":"Goldberg M, Vişan M. 2006. A counterexample to dispersive estimates for Schrödinger operators in higher dimensions. Communications in Mathematical Physics. 266, 211–238.","chicago":"Goldberg, Michael, and Monica Vişan. “A Counterexample to Dispersive Estimates for Schrödinger Operators in Higher Dimensions.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2006. <a href=\"https://doi.org/10.1007/s00220-006-0013-5\">https://doi.org/10.1007/s00220-006-0013-5</a>.","ieee":"M. Goldberg and M. Vişan, “A counterexample to dispersive estimates for Schrödinger operators in higher dimensions,” <i>Communications in Mathematical Physics</i>, vol. 266. Springer Nature, pp. 211–238, 2006."},"publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"oa_version":"Preprint","article_processing_charge":"No","date_created":"2026-06-19T08:23:36Z","doi":"10.1007/s00220-006-0013-5","publication_status":"published","external_id":{"arxiv":["math/0508206"]},"abstract":[{"text":"In dimension n > 3 we show the existence of a compactly supported potential in the differentiability class Cα, α < n-3/2, for which the solutions to the linear Schrödinger equation in ℝn, ∂tu = - Δ u + Vu, u(0)=f, fail to satisfy an evolution estimate of the form ||u(t, ̇)||∞ ≤ C |t| -n/2 ||u(0,\\̇)||1̇. This contrasts with known results in dimensions n ≤ 3, where a pointwise decay condition on V is generally sufficient to imply dispersive bounds. The obstructions in our example are generated by an expression with scaling law |t|-n+3/2+α, which becomes dominant in the time interval |t| ≪ 1.","lang":"eng"}],"author":[{"first_name":"Michael","full_name":"Goldberg, Michael","last_name":"Goldberg"},{"last_name":"Visan","first_name":"Monica","full_name":"Visan, Monica","id":"056daca0-b8d1-11f0-964f-f91054abf8ca"}],"scopus_import":"1","day":"01","date_updated":"2026-06-30T11:26:34Z","fulldoi":"https://doi.org/10.1007/s00220-006-0013-5","page":"211-238","type":"journal_article","status":"public","year":"2006","arxiv":1,"quality_controlled":"1","OA_type":"green"},{"page":"347 - 393","issue":"2","type":"journal_article","status":"public","fulldoi":"https://doi.org/10.1007/s00220-003-0993-3","date_updated":"2026-09-30T13:17:48Z","day":"01","OA_type":"green","year":"2004","publist_id":"4569","arxiv":1,"month":"01","volume":244,"date_published":"2004-01-01T00:00:00Z","OA_place":"repository","oa":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/math-ph/0305025"}],"article_type":"original","title":"One-dimensional behavior of dilute, trapped Bose gases","_id":"2356","publisher":"Springer Nature","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"oa_version":"None","doi":"10.1007/s00220-003-0993-3","date_created":"2018-12-11T11:57:11Z","publication_status":"published","article_processing_charge":"No","author":[{"last_name":"Lieb","full_name":"Lieb, Élliott","first_name":"Élliott"},{"orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","full_name":"Seiringer, Robert","last_name":"Seiringer"},{"last_name":"Yngvason","first_name":"Jakob","full_name":"Yngvason, Jakob"}],"abstract":[{"lang":"eng","text":"Recent experimental and theoretical work has shown that there are conditions in which a trapped, low-density Bose gas behaves like the one-dimensional delta-function Bose gas solved years ago by Lieb and Liniger. This is an intrinsically quantum-mechanical phenomenon because it is not necessary to have a trap width that is the size of an atom - as might have been supposed - but it suffices merely to have a trap width such that the energy gap for motion in the transverse direction is large compared to the energy associated with the motion along the trap. Up to now the theoretical arguments have been based on variational - perturbative ideas or numerical investigations. In contrast, this paper gives a rigorous proof of the one-dimensional behavior as far as the ground state energy and particle density are concerned. There are four parameters involved: the particle number, N, transverse and longitudinal dimensions of the trap, r and L, and the scattering length a of the interaction potential. Our main result is that if r/L → 0 and N → ∞ the ground state energy and density can be obtained by minimizing a one-dimensional density functional involving the Lieb-Liniger energy density with coupling constant ∼ a/r 2. This density functional simplifies in various limiting cases and we identify five asymptotic parameter regions altogether. Three of these, corresponding to the weak coupling regime, can also be obtained as limits of a three-dimensional Gross-Pitaevskii theory. We also show that Bose-Einstein condensation in the ground state persists in a part of this regime. In the strong coupling regime the longitudinal motion of the particles is strongly correlated. The Gross-Pitaevskii description is not valid in this regime and new mathematical methods come into play."}],"external_id":{"arxiv":["0305025"]},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","extern":"1","language":[{"iso":"eng"}],"intvolume":"       244","citation":{"ista":"Lieb É, Seiringer R, Yngvason J. 2004. One-dimensional behavior of dilute, trapped Bose gases. Communications in Mathematical Physics. 244(2), 347–393.","ieee":"É. Lieb, R. Seiringer, and J. Yngvason, “One-dimensional behavior of dilute, trapped Bose gases,” <i>Communications in Mathematical Physics</i>, vol. 244, no. 2. Springer Nature, pp. 347–393, 2004.","chicago":"Lieb, Élliott, Robert Seiringer, and Jakob Yngvason. “One-Dimensional Behavior of Dilute, Trapped Bose Gases.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2004. <a href=\"https://doi.org/10.1007/s00220-003-0993-3\">https://doi.org/10.1007/s00220-003-0993-3</a>.","short":"É. Lieb, R. Seiringer, J. Yngvason, Communications in Mathematical Physics 244 (2004) 347–393.","ama":"Lieb É, Seiringer R, Yngvason J. One-dimensional behavior of dilute, trapped Bose gases. <i>Communications in Mathematical Physics</i>. 2004;244(2):347-393. doi:<a href=\"https://doi.org/10.1007/s00220-003-0993-3\">10.1007/s00220-003-0993-3</a>","apa":"Lieb, É., Seiringer, R., &#38; Yngvason, J. (2004). One-dimensional behavior of dilute, trapped Bose gases. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-003-0993-3\">https://doi.org/10.1007/s00220-003-0993-3</a>","mla":"Lieb, Élliott, et al. “One-Dimensional Behavior of Dilute, Trapped Bose Gases.” <i>Communications in Mathematical Physics</i>, vol. 244, no. 2, Springer Nature, 2004, pp. 347–93, doi:<a href=\"https://doi.org/10.1007/s00220-003-0993-3\">10.1007/s00220-003-0993-3</a>."},"publication":"Communications in Mathematical Physics"},{"arxiv":1,"year":"2003","publist_id":"5740","acknowledgement":"We would like to acknowledge the financial support by Prof. P. Major (R ́ enyi Institute, Hungary) from his OTKA grant No. T26176 and of the Miller Institute for Basic Research in Science at UC Berkeley.","OA_type":"green","quality_controlled":"1","fulldoi":"https://doi.org/10.1007/s00220-003-0806-8","date_updated":"2026-05-28T12:12:13Z","day":"01","scopus_import":"1","type":"journal_article","status":"public","page":"275 - 288","citation":{"ama":"Etesi G, Hausel T. On Yang-Mills instantons over multi-centered gravitational instantons. <i>Communications in Mathematical Physics</i>. 2003;235:275-288. doi:<a href=\"https://doi.org/10.1007/s00220-003-0806-8\">10.1007/s00220-003-0806-8</a>","short":"G. Etesi, T. Hausel, Communications in Mathematical Physics 235 (2003) 275–288.","chicago":"Etesi, Gábor, and Tamás Hausel. “On Yang-Mills Instantons over Multi-Centered Gravitational Instantons.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2003. <a href=\"https://doi.org/10.1007/s00220-003-0806-8\">https://doi.org/10.1007/s00220-003-0806-8</a>.","ieee":"G. Etesi and T. Hausel, “On Yang-Mills instantons over multi-centered gravitational instantons,” <i>Communications in Mathematical Physics</i>, vol. 235. Springer Nature, pp. 275–288, 2003.","ista":"Etesi G, Hausel T. 2003. On Yang-Mills instantons over multi-centered gravitational instantons. Communications in Mathematical Physics. 235, 275–288.","mla":"Etesi, Gábor, and Tamás Hausel. “On Yang-Mills Instantons over Multi-Centered Gravitational Instantons.” <i>Communications in Mathematical Physics</i>, vol. 235, Springer Nature, 2003, pp. 275–88, doi:<a href=\"https://doi.org/10.1007/s00220-003-0806-8\">10.1007/s00220-003-0806-8</a>.","apa":"Etesi, G., &#38; Hausel, T. (2003). On Yang-Mills instantons over multi-centered gravitational instantons. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-003-0806-8\">https://doi.org/10.1007/s00220-003-0806-8</a>"},"intvolume":"       235","publication":"Communications in Mathematical Physics","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","extern":"1","language":[{"iso":"eng"}],"author":[{"last_name":"Etesi","full_name":"Etesi, Gábor","first_name":"Gábor"},{"orcid":"0000-0002-9582-2634","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","full_name":"Hausel, Tamas","first_name":"Tamas","last_name":"Hausel"}],"abstract":[{"text":"In this paper we explicitly calculate the analogue of the 't Hooft SU (2) Yang-Mills instantons on Gibbons-Hawking multi-centered gravitational instantons, which come in two parallel families: the multi-Eguchi-Hanson, or Ak ALE gravitational instantons and the multi-Taub-NUT spaces, or Ak ALF gravitational instantons. We calculate their energy and find the reducible ones. Following Kronheimer we also exploit the U(1) invariance of our solutions and study the corresponding explicit singular SU (2) magnetic monopole solutions of the Bogomolny equations on flat ℝ3.","lang":"eng"}],"external_id":{"arxiv":["0207196"]},"publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"oa_version":"Preprint","date_created":"2018-12-11T11:52:09Z","publication_status":"published","article_processing_charge":"No","doi":"10.1007/s00220-003-0806-8","_id":"1459","publisher":"Springer Nature","main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.hep-th/0207196"}],"article_type":"original","title":"On Yang-Mills instantons over multi-centered gravitational instantons","month":"04","volume":235,"OA_place":"repository","date_published":"2003-04-01T00:00:00Z","oa":1}]