An Effective SPDE Model for a Schrödinger Equation with a Fluctuating Magnetic Potential
Franco Flandoli, Reika Fukuizumi, Francesco Grotto, Eliseo Luongo
Source 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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