PreprintCC0arXiv
Quantitative observability of the Schrödinger equation in the torus from open sets
Abstract
We study the observability of the Schrödinger equation on the d-dimensional torus Td=Rd/(2πZ)d, d ≥ 1, from an open subset ω⊂ Td. Our main result establishes a quantitative observability estimate for the free Schrödinger equation in the regime of small times T and small observation sets of the form ω= ∏j=1d(aj,bj). A central ingredient in the proof is a cluster decomposition method combined with an induction scheme introduced by Bourgain and further developed by Burq and Zhu.
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BibTeX
@misc{balch2026quantitative,
title = {{Quantitative observability of the Schrödinger equation in the torus from open sets}},
author = {Kévin Le Balc'h and Jiaqi Yu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.02480},
eprint = {2605.02480},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.02480},
note = {CC0},
}
RIS
TY - UNPB
TI - Quantitative observability of the Schrödinger equation in the torus from open sets
AU - Kévin Le Balc'h
AU - Jiaqi Yu
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2605.02480
UR - https://arxiv.org/abs/2605.02480
AB - We study the observability of the Schrödinger equation on the d-dimensional torus T^d=R^d/(2πZ)^d, d ≥ 1, from an open subset ω⊂ T^d. Our main result establishes a quantitative observability estimate for the free Schrödinger equation in the regime of small times T and small observation sets of the form ω= ∏_j=1^d(a_j,b_j). A central ingredient in the proof is a cluster decomposition method combined with an induction scheme introduced by Bourgain and further developed by Burq and Zhu.
ER -