Finite-Memory Extension of Tegmark's Decoherence Bound in Biological Media
Abstract
Tegmark's decoherence bound is derived under the assumption of a strictly memoryless environment. We show that this result corresponds to the singular limit of a finite-memory theory. For exponentially correlated environments decoherence is generically quadratic at short times and the decoherence time scales as the square root of the bath correlation time. For the Ornstein-Uhlenbeck bath we derive the exact non-Markovian coherence equation and verify the predicted scaling using an exact pseudomode mapping. Tegmark's bound is recovered only in the vanishing-memory limit.
Keywords
Cite
@article{arxiv.2601.07689,
title = {Finite-Memory Extension of Tegmark's Decoherence Bound in Biological Media},
author = {Ramandeep Dewan},
journal= {arXiv preprint arXiv:2601.07689},
year = {2026}
}
Comments
This version incorporates substantial revisions: - Added references and clarification of the universal short-time quadratic decoherence regime. - Added full derivation of the Ornstein-Uhlenbeck NMQSD closure in Appendix E. - Strengthened biological interpretation and removed overclaims. - Improved numerical verification section