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PreprintCC BY 4.0arXiv

An Effective SPDE Model for a Schrödinger Equation with a Fluctuating Magnetic Potential

  • Franco Flandoli
  • Reika Fukuizumi
  • Francesco Grotto
  • Eliseo Luongo
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Abstract

We consider the Schrödinger equation for a charged particle in a randomly fluctuating external magnetic field and establish a singular perturbation limit in which the solution converges to a deterministic Schrödinger equation with Gaussian fluctuations. We propose a stochastic Schrödinger equation incorporating the behavior of both the deterministic average and the fluctuations and show that it has the same limiting behavior as the original model, while providing a simpler way to study the distribution of relevant observables.

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Cite

BibTeXRIS
BibTeX
@misc{flandoli2026effective,
  title = {{An Effective SPDE Model for a Schrödinger Equation with a Fluctuating Magnetic Potential}},
  author = {Franco Flandoli and Reika Fukuizumi and Francesco Grotto and Eliseo Luongo},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.03556},
  eprint = {2609.03556},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.03556},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - An Effective SPDE Model for a Schrödinger Equation with a Fluctuating Magnetic Potential
AU  - Franco Flandoli
AU  - Reika Fukuizumi
AU  - Francesco Grotto
AU  - Eliseo Luongo
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2609.03556
UR  - https://arxiv.org/abs/2609.03556
AB  - We consider the Schrödinger equation for a charged particle in a randomly fluctuating external magnetic field and establish a singular perturbation limit in which the solution converges to a deterministic Schrödinger equation with Gaussian fluctuations. We propose a stochastic Schrödinger equation incorporating the behavior of both the deterministic average and the fluctuations and show that it has the same limiting behavior as the original model, while providing a simpler way to study the distribution of relevant observables.
ER  -