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PreprintCC BY 4.0HAL

Global Energy Solutions for Normalized Linear Stochastic Schrödinger Equations

  • Théo Hérouard
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Abstract

In this paper, we study nonlinear Schrödinger equations arising in the study of Markovian open quantum systems. These equations are derived from the normalization of linear stochastic Schrödinger equations. First, we prove the global well-posedness of the linear equation in the energy space, which is less regular than the usual space for this equation. Then, we show the indistinguishability of solutions to the nonlinear SPDE under a relaxation of the usual monotonicity assumption. Finally, by proving the pathwise uniqueness and normalizing the solutions to the linear equation, we are able to prove the well-posedness of solutions to the required class of nonlinear stochastic equations.

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Cite

BibTeXRIS
BibTeX
@misc{herouard2026global,
  title = {{Global Energy Solutions for Normalized Linear Stochastic Schrödinger Equations}},
  author = {Théo Hérouard},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.39244},
  eprint = {2609.39244},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05769240v1},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Global Energy Solutions for Normalized Linear Stochastic Schrödinger Equations
AU  - Théo Hérouard
PY  - 2026
DA  - 2026/09/29
PB  - HAL
DO  - 10.48550/arxiv.2609.39244
UR  - https://hal.science/hal-05769240v1
AB  - In this paper, we study nonlinear Schrödinger equations arising in the study of Markovian open quantum systems. These equations are derived from the normalization of linear stochastic Schrödinger equations. First, we prove the global well-posedness of the linear equation in the energy space, which is less regular than the usual space for this equation. Then, we show the indistinguishability of solutions to the nonlinear SPDE under a relaxation of the usual monotonicity assumption. Finally, by proving the pathwise uniqueness and normalizing the solutions to the linear equation, we are able to prove the well-posedness of solutions to the required class of nonlinear stochastic equations.
ER  -