Approximation Theorems for the Schrödinger Equation and Quantum Vortex Reconnection
Approximation Theorems for the Schrödinger Equation and Quantum Vortex Reconnection
Abstract We prove the existence of smooth solutions to the Gross–Pitaevskii equation on $$\mathbb {R}^3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msup> </mml:math> that feature arbitrarily complex quantum vortex reconnections. We can track the evolution of the vortices during the whole process. This permits to describe the reconnection events …