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On the Gross-Pitaevskii evolution linearized around the degree-one vortex

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arxiv 2503.07345 v2 pith:CN5JZSLD submitted 2025-03-10 math.AP

Jonas Luhrmann , Wilhelm Schlag , Sohrab Shahshahani This is my paper · ORCID
classification math.AP
keywords aroundlinearizedevolutiongross-pitaevskiismallvortexzero-energyanalysis
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abstract

We study the evolution of the Gross-Pitaevskii equation linearized around the Ginzburg-Landau vortex of degree one under equivariant symmetry. Among the main results of this work, we determine the spectrum of the linearized operator, uncover a remarkable $L^2$-norm growth phenomenon related to a zero-energy resonance, and provide a complete construction of the distorted Fourier transform at small energies. The latter hinges upon a meticulous analysis of the behavior of the resolvent in the upper and lower half-planes in a small disk around zero-energy.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Asymptotic stability of the degree-one vortex in the abelian Yang-Mills-Higgs model

    math.AP 2026-08 conditional novelty 8.0 of 10

    Small equivariant perturbations of the degree-one vortex decay with radiation rate, while the internal mode damps like epsilon squared over one plus Gamma epsilon squared t, proving asymptotic stability.

  2. Nondegeneracy and Morse Index of Ginzburg--Landau Vortices

    math.AP 2026-08 conditional novelty 7.0 of 10

    For Ginzburg-Landau vortices of degree 2 and 3, the only bounded zero modes are the three geometric symmetries, and the Morse indices are 2 and 6.

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