科研之友
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摘要
We consider a 2D quantum system of N bosons in a trapping potential |x|(s), interacting via a pair potential of the form N(2 beta-1)w(N(beta)x). We show that for all 0 < beta < (s + 1)/(s + 2), the leading order behavior of ground states of the many-body system is described in the large N limit by the corresponding cubic nonlinear Schr " odinger energy functional. Our result covers the focusing case (w < 0) where even the stability of the many-body system is not obvious. This answers an open question mentioned by X. Chen and J. Holmer for harmonic traps (s = 2). Together with the BBGKY hierarchy approach used by these authors, our result implies the convergence of the many-body quantum dynamics to the focusing NLS equation with harmonic trap for all 0 < beta < 3/4.
- 出版日期2017-6
