Transient and universal regimes in quantum reaction-transport kinetics

• URL: http://arxiv.org/abs/2609.09305v1
• Date: Tue, 08 Sep 2026 18:01:11 GMT
• Title: Transient and universal regimes in quantum reaction-transport kinetics
• Abstract summary: We study the quantum binary annihilation, $A+A to emptyset$, where reaction processes acquire singular fluctuation corrections below the upper critical dimension $D_c=2$.<n>In one dimension, they render mean-field relaxation transient and drive the system toward a transport-limited regime with $nsim t-1/2$, governed by a quantum-Zeno scale even for arbitrarily weak loss.<n>We also show that the same fluctuations generate effective elastic collisions despite the absence of microscopic coherent interactions.
• Score: 0.0036884721748026168
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum reaction-transport systems consist of coherently propagating particles that irreversibly react upon encounter. Their relaxation is commonly classified as reaction-limited or transport-limited, depending on the relative timescales of reaction and particle transport. We show that this expectation fails in low dimensions by studying the quantum binary annihilation, $A+A \to \emptyset$, where reaction processes acquire singular fluctuation corrections below the upper critical dimension $D_c=2$. Consequently, fluctuations dominate the asymptotic kinetics for $D<2$. In one dimension, they render mean-field relaxation transient and drive the system toward a transport-limited regime with $n\sim t^{-1/2}$, governed by a quantum-Zeno scale even for arbitrarily weak loss. At $D=2$, the kinetics acquires logarithmic corrections, whereas above two dimensions mean-field scaling is asymptotically restored. At and below the upper critical dimension, mean-field behavior can nevertheless persist over parametrically long crossover times before the asymptotic fluctuation-dominated regime emerges. We also show that the same fluctuations generate effective elastic collisions despite the absence of microscopic coherent interactions. In $D>1$, these collisions redistribute momentum populations and are parametrically faster than losses in the transport-limited regime, allowing the system to approach a quasi-stationary thermal state.

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