Norm approximation for many-body quantum dynamics: Focusing case in low dimensions

Nam, Phan Thanh; Napiorkowski, Marcin (2019): Norm approximation for many-body quantum dynamics: Focusing case in low dimensions. In: Advances in Mathematics, Vol. 350: pp. 547-587

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
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0001-8708
• Language: English