PreprintCC0arXiv
Optimal relaxation for Witten Lindbladians
Abstract
We prove optimal trace-norm relaxation for the one-dimensional Lindbladian associated with the Witten differential a=h∂x+V' which annihilates the classical Gibbs density: if λ1(h) is the first positive eigenvalue of H=a*a, then the relaxation rate is γh=λ1(h)/(2h). It applies to initial operators whose Schwartz kernels, after a Gibbs conjugation, satisfy $ L^2 $ estimates for the restriction to the diagonal and for the normal derivative. An appendix by Chat GPT 6 presents a stronger result specialised to positive initial data.
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BibTeX
@misc{becker2026optimal,
title = {{Optimal relaxation for Witten Lindbladians}},
author = {Simon Becker and Maciej Zworski},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.13121},
eprint = {2609.13121},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13121},
note = {CC0},
}
RIS
TY - UNPB
TI - Optimal relaxation for Witten Lindbladians
AU - Simon Becker
AU - Maciej Zworski
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.13121
UR - https://arxiv.org/abs/2609.13121
AB - We prove optimal trace-norm relaxation for the one-dimensional Lindbladian associated with the Witten differential a=h∂_x+V' which annihilates the classical Gibbs density: if λ_1(h) is the first positive eigenvalue of H=a^*a, then the relaxation rate is γ_h=λ_1(h)/(2h). It applies to initial operators whose Schwartz kernels, after a Gibbs conjugation, satisfy $ L^2 $ estimates for the restriction to the diagonal and for the normal derivative. An appendix by Chat GPT 6 presents a stronger result specialised to positive initial data.
ER -