arXiv subjects

Théo Hérouard

Publications and source records attributed to Théo Hérouard.

2 recordsLinked to original sources

arXiv2026

Global Energy Solutions for Normalized Linear Stochastic Schr{ö}dinger Equations

In this paper, we study nonlinear Schr{ö}dinger equations arising in the study of Markovian open quantum systems. These equations are derived from the normalization of linear stochastic Schr{ö}dinger 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.

math.AP↗

arXiv2025

Infinite Dimensional Mean-Field Belavkin Equation: Well-posedness and Derivation

We analyze the mean-field limit of a stochastic Schr{ö}dinger equation arising in quantum optimal control and mean-field games, where N interacting particles undergo continuous indirect measurement. For the open quantum system described by Belavkin's filtering equation, we derive a mean-field approximation under minimal assumptions, extending prior results limited to bounded operators and finitedimensional settings. By establishing global well-posedness via fixed-point methods-avoiding measure-change techniques-we obtain higher regularity solutions. Furthermore, we prove rigorous convergence to the mean-field limit in an infinitedimensional framework. Our work provides the first derivation of such limits for wave functions in $L^2 (R^d)$, with implications for simulating and controlling large quantum systems.

math.AP↗