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A stochastic controlled Schr¨odinger equation: convergence and robust stability for numerical solutions

Cutberto Romero-Meléndez, David Castillo-Fernández
In this paper we study the stochastic stability of numerical solutions of a stochastic controlled Schr¨odinger equation. We investigate the boundedness in second moment, the convergence and the stability of the zero solution for this equation, using two new definitions of
almost sure exponential robust stability and asymptotic stability, for the Euler-Maruyama numerical scheme. Considering that the diffusion term is controlled, by using the method of Lyapunov functions and the corresponding diffusion operator associated, we apply techniques of X. Mao and A. Tsoi for achieve our task. Finally,
we illustrate this method with a problem in Nuclear Magnetic Resonance (NMR).
CYBERNETICS AND PHYSICS 2021, Vol. 10, Is.3, 178-184 https://doi.org/10.35470/2226-4116-2021-10-3-178-184
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