# Decay of the stochastic linear Schr\"odinger equation in \$d \geq 3\$ with small multiplicative noise

```@article{Fan2018DecayOT,
title={Decay of the stochastic linear Schr\"odinger equation in \\$d \geq 3\\$ with small multiplicative noise},
author={C. Fan and W. Xu},
journal={arXiv: Analysis of PDEs},
year={2018}
}```
• Published 2018
• Mathematics
• arXiv: Analysis of PDEs
• We give decay estimates of the solution to the linear Schr\"odinger equation in dimension \$d \geq 3\$ with a small noise which is white in time and colored in space. As a consequence, we also obtain certain asymptotic behaviour of the solution. The proof relies on the bootstrapping argument used by Journ\'e-Soffer-Sogge for decay of deterministic Schr\"odinger operators.
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