Optimal relaxation for Witten Lindbladians

Abstract:We prove optimal trace-norm relaxation for the one-dimensional Lindbladian associated with the Witten differential $a=h\partial_x+V'$ which annihilates the classical Gibbs density: if $\lambda_1(h)$ is the first positive eigenvalue of $H=a^*a$, then the relaxation rate is $\gamma_h=\lambda_1(h)/(2h)$. 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.

Mathematical Physics (math-ph); Spectral Theory (math.SP); Quantum Physics (quant-ph)

arXiv:2609.13121 [math-ph]

(or arXiv:2609.13121v1 [math-ph] for this version)

https://doi.org/10.48550/arXiv.2609.13121 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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