The mean-field approximation and the non-linear Schrödinger functional for trapped Bose gases
Lewin, Mathieu; Nam, Phan Thành; Rougerie, Nicolas (2016), The mean-field approximation and the non-linear Schrödinger functional for trapped Bose gases, Transactions of the American Mathematical Society, 368, 9, p. 6131-6157. 10.1090/tran/6537
TypeArticle accepté pour publication ou publié
Journal nameTransactions of the American Mathematical Society
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Abstract (EN)We study the ground state of a trapped Bose gas, starting from the full many-body Schrödinger Hamiltonian, and derive the nonlinear Schrödinger energy functional in the limit of large particle number, when the interaction potential converges slowly to a Dirac delta function. Our method is based on quantitative estimates on the discrepancy between the full many-body energy and its mean-field approximation using Hartree states. These are proved using finite dimensional localization and a quantitative version of the quantum de Finetti theorem. Our approach covers the case of attractive interactions in the regime of stability. In particular, our main new result is a derivation of the 2D attractive nonlinear Schrödinger ground state.
Subjects / KeywordsBose gas; non-linear Schrödinger functional
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