Seminar Analysis and Mathematical Physics: Jinyeop Lee (LMU Munich)

Microscopic derivation of a nonlinear Schrödinger equation with a nonlinear point interaction in 1D

The study of the Schrödinger equation in dimension one with a nonlinear point interaction has been the focus of research over the past few decades. In this seminar, we talk about a work on deriving this partial differential equation as the effective dynamics of N identical bosons in one dimension.
We assume introducing a tiny impurity located at the origin and considering that the interaction between every pair of bosons is mediated by the impurity through a three-body interaction. Moreover, by assuming short-range scaling and choosing an initial fully condensed state, we prove convergence of one-particle density operators in the trace-class topology. This is the first derivation of the so-called nonlinear delta model. This research is a collaborative work with Prof. Riccardo Adami.

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