Abstract
We study the norm approximation to the Schrodinger dynamics of N bosons in R-d (d = 1,2) with an interaction potential of the form N(d beta-1)w(N-beta (x - y)). Here we are interested in the focusing case w <= 0. Assuming that there is complete Bose-Einstein condensation in the initial state, we show that in the large N limit, the evolution of the condensate is effectively described by a nonlinear Schrodinger equation and the evolution of the fluctuations around the condensate is governed by a quadratic Hamiltonian, resulting from Bogoliubov approximation. Our result holds true for all beta > 0 when d = 1 and for all 0 < beta < 1 when d = 2. (C) 2019 Elsevier Inc. All rights reserved.
Item Type: | Journal article |
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Faculties: | Mathematics, Computer Science and Statistics > Mathematics |
Subjects: | 500 Science > 510 Mathematics |
ISSN: | 0001-8708 |
Language: | English |
Item ID: | 82374 |
Date Deposited: | 15. Dec 2021, 15:01 |
Last Modified: | 13. Aug 2024, 12:43 |