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PreprintCC BY 4.0arXiv

The stochastic Ginzburg-Landau equation with harmonic potential in the full subcritical regime

  • Samaël Mackowiak
  • Aurélien Minguella
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Abstract

In this paper, we construct the complex Ginzburg-Landau dynamic associated with the harmonic oscillator, with a random force which is white in time and covers the full subcritical range in space. We are able to renormalise the non-linearity using the same constant as the one used to renormalise the problem associated to the Laplacian. By an extension of the problem to complex times, we are able to prove that the solution of the complex Ginzburg-Landau is equal in law to the solution of the purely dissipative case, i.e. the associated complex Φ4 model, but along a complex axis of time.

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Cite

BibTeXRIS
BibTeX
@misc{mackowiak2026stochastic,
  title = {{The stochastic Ginzburg-Landau equation with harmonic potential in the full subcritical regime}},
  author = {Samaël Mackowiak and Aurélien Minguella},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.08038},
  eprint = {2611.08038},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.08038},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The stochastic Ginzburg-Landau equation with harmonic potential in the full subcritical regime
AU  - Samaël Mackowiak
AU  - Aurélien Minguella
PY  - 2026
DA  - 2026/11/05
PB  - arXiv
DO  - 10.48550/arxiv.2611.08038
UR  - https://arxiv.org/abs/2611.08038
AB  - In this paper, we construct the complex Ginzburg-Landau dynamic associated with the harmonic oscillator, with a random force which is white in time and covers the full subcritical range in space. We are able to renormalise the non-linearity using the same constant as the one used to renormalise the problem associated to the Laplacian. By an extension of the problem to complex times, we are able to prove that the solution of the complex Ginzburg-Landau is equal in law to the solution of the purely dissipative case, i.e. the associated complex Φ^4 model, but along a complex axis of time.
ER  -