doi: 10.17706/ijapm.2021.11.1.1-8
Numerical Exponential Stability of a Time-Dependent Stochastic Schrödinger Equation
- 1 Department of Basic Sciences, Autonomous Metropolitan University, Mexico
- 2 Engineering Department, La Salle University, México.
Abstract
In this work, we will define two new types of exponential asymptotic stability for the Euler-Maruyama numerical scheme in the stochastic controlled Schrödinger equation dependent on time, corresponding to a stochastic quantum two-level system, namely, almost sure exponential robust stability and asymptotic stability. These types of stability are variants of Mao and Mora definitions for the stability of numerical schemes, in the control case. Through the techniques used by Tsoi, we demonstrate the almost sure exponential robust stability and the asymptotic stability of the Euler-Maruyama numerical scheme for the stochastic controlled Schrödinger equation.
Keywords
- Asymptotic stability
- Euler-Maruyama numerical scheme
- exponential robust stability
- time-dependent stochastic controlled Schrödinger equation
How to Cite
Cutberto Romero-Meléndez and David Castillo-Fernández, "Numerical Exponential Stability of a Time-Dependent Stochastic Schrödinger Equation," International Journal of Applied Physics and Mathematics, vol. 11, no. 1, pp. 1-8, 2021. https://doi.org/ 10.17706/ijapm.2021.11.1.1-8
Copyright & License
Copyright © 2021 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).