Long-Time Quantum–Classical Correspondence for Open Systems in Trace Norm
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23_2025_Article_1613.pdf
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Author(s)
Li, Zhenhao
Date Issued
August 21, 2025
Journal
Annales Henri Poincaré
Publisher
Springer International Publishing
Citation
Li, Z. Long-Time Quantum–Classical Correspondence for Open Systems in Trace Norm. Ann. Henri Poincaré (2025).
Version
Final published version
Abstract
We consider a frictionless system coupled to an external Markovian environment. The quantum and classical evolution of such systems are described by the Lindblad and the Fokker–Planck equation, respectively. We show that when such a system is given by an at most quadratically growing Hamiltonian and at most linearly growing real jump functions, the quantum and classical evolutions remain close on time scales much longer than Ehrenfest time. In particular, we show that the evolution of a density matrix by the Lindblad equation is close in trace norm to the quantization of the corresponding evolution by the Fokker–Planck equation. Such agreement improves upon recent results (Galokowski and Zworski in Classical quantum correspondence in Lindblad evolution, 2024. arXiv:2403.09345 ; Hernández et al. in Decoherence ensures classicality beyond the Ehrenfest time as ħ → 0 , 2023. arXiv:2306.13717 , Hernández et al. in The limit of open quantum systems with general Lindbladians: vanishing noise ensures classicality beyond the ehrenfest time, 2023. arXiv:2307.05326 ), which proved long-time agreement in weaker norms.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1007/s00023-025-01613-8
