For the 1D Schrödinger equation with a mollified spacetime white noise, we show that the average wave function converges to the Schrödinger equation with an effective potential after an appropriate renormalization.
Accepté le :
DOI : 10.1051/ps/2019010
Keywords: Random Schrödinger equation, renormalization, path integral
Gu, Yu 1
@article{PS_2019__23__338_0,
author = {Gu, Yu},
title = {The {1D} {Schr\"odinger} equation with a spacetime white noise: the average wave function},
journal = {ESAIM: Probability and Statistics},
pages = {338--349},
year = {2019},
publisher = {EDP Sciences},
volume = {23},
doi = {10.1051/ps/2019010},
zbl = {1418.35392},
mrnumber = {3963531},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ps/2019010/}
}
TY - JOUR AU - Gu, Yu TI - The 1D Schrödinger equation with a spacetime white noise: the average wave function JO - ESAIM: Probability and Statistics PY - 2019 SP - 338 EP - 349 VL - 23 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/ps/2019010/ DO - 10.1051/ps/2019010 LA - en ID - PS_2019__23__338_0 ER -
Gu, Yu. The 1D Schrödinger equation with a spacetime white noise: the average wave function. ESAIM: Probability and Statistics, Tome 23 (2019), pp. 338-349. doi: 10.1051/ps/2019010
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