Derivation of the Time Dependent Two Dimensional Focusing NLS Equation


Journal Article

© 2018, Springer Science+Business Media, LLC, part of Springer Nature. We present a microscopic derivation of the two-dimensional focusing cubic nonlinear Schrödinger equation starting from an interacting N-particle system of Bosons. The interaction potential we consider is given by Wβ(x) = N-1+2βW(Nβx) for some spherically symmetric and compactly supported potential W∈ L∞(R2, R). The class of initial wave functions is chosen such that the variance in energy is small. Furthermore, we assume that the Hamiltonian HWβ,t=-∑j=1NΔj+∑1≤j 2 , or in trace norm, for more general external potentials. For trapping potentials of the form A(x)=C|x|s,C>0, the condition HWβ,t≥-CN can be fulfilled for a certain class of interactions Wβ, for all 0<β

Full Text

Cited Authors

  • Jeblick, M; Pickl, P

Published Date

  • September 1, 2018

Published In

Volume / Issue

  • 172 / 5

Start / End Page

  • 1398 - 1426

International Standard Serial Number (ISSN)

  • 0022-4715

Digital Object Identifier (DOI)

  • 10.1007/s10955-018-2095-9

Citation Source

  • Scopus