Quantum resolution of the nonlinear super-Schrodinger equation
V. Caudrelier, E. Ragoucy
TL;DR
This paper introduces a supersymmetric extension of the nonlinear Schrödinger equation incorporating fermions and bosons, revealing super-Yangian symmetry, and provides a quantum solution with a Lax pair formulation.
Contribution
It presents a novel supersymmetric nonlinear Schrödinger equation with super-Yangian symmetry and a quantum solution including a Lax pair formulation.
Findings
The equation exhibits supersymmetry and super-Yangian symmetry.
A super version of the classical Rosales solution is constructed.
A Lax pair formulation for the quantum model is provided.
Abstract
We introduce a Z_2-graded version of the nonlinear Schrodinger equation that includes one fermion and one boson at the same time. This equation is shown to possess a supersymmetry which proves to be itself part of a super-Yangian symmetry based on gl(1|1). The solution exhibits a super version form of the classical Rosales solution. Then, we second quantize these results, and give a Lax pair formulation (based on gl(2|1)) for the model.
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