Non Markovian Corrections to Tegmark's Decoherence Bound in Biological Media

TL;DR

Tegmark's decoherence bound for biological systems relies on a memoryless, delta-correlated environment, an idealization not representative of real media. The paper derives a universal short-time non-Markovian decoherence law, showing $C(t)=C(0)(1-\Gamma t^2)+O(t^3)$ with $\Gamma=\frac{a^2}{\hbar^2}\int_0^{\infty} d\omega\, J(\omega) \coth\left(\frac{\beta\omega}{2}\right)$, and treats an Ornstein–Uhlenbeck bath to obtain $\tau_{\mathrm{dec}}=\sqrt{\frac{\hbar^2 \tau_c}{a^2 D}}$ that recovers $\tau_{\mathrm{T}}=\frac{\hbar^2}{a^2 D}$ as $\tau_c\to 0$. Exact non-Markovian simulations using pseudomodes verify the $\sqrt{\tau_c}$ scaling, supporting the view that Tegmark's bound is a singular Markovian limit and does not rule out mesoscopic coherence in structured biological media. These results motivate refined bath models for neuronal and microtubular environments and clarify the conditions under which quantum effects could persist in biology.

Abstract

Tegmark's widely cited bound on decoherence times in biological systems is derived under the assumption of a delta correlated, memoryless environment. In this work we show that any finite environmental memory universally induces quadratic short time decoherence, in validating the exponential decay law at early times. For an Ornstein Uhlenbeck environment we derive a closed non markovian expression for the coherence dynamics and obtain a de-coherence time that scales as the square root of the bath correlation time. In the singular limit of vanishing bath memory our result reduces exactly to Tegmark's bound. Numerical simulations based on an exact pseudomode mapping confirm the predicted scaling. These findings demonstrate that Tegmark's result applies only in the Markovian limit and does not rule out mesoscopic quantum coherence in structured biological media.

Figures (2)

• Figure 1: Decoherence time $\tau_{\mathrm{dec}}$ extracted from pseudomode simulations as a function of bath correlation time $\tau_c$. The dashed line indicates the $\sqrt{\tau_c}$ scaling predicted analytically.
• Figure 2: Representative coherence decay curves $C(t)$ obtained from the pseudomode simulation for different bath correlation times $\tau_c$. The short-time behaviour is quadratic for all finite $\tau_c$.