Derivation of the Time Dependent Two Dimensional Focusing NLS Equation

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 W β ( x ) = N - 1 + 2 β W ( N β x ) for some spherically symmetric and compactly suppo...

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