Transient and universal regimes in quantum reaction-transport kinetics

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.

Statistical Mechanics (cond-mat.stat-mech); Quantum Physics (quant-ph)

arXiv:2609.09305 [cond-mat.stat-mech]

(or arXiv:2609.09305v1 [cond-mat.stat-mech] for this version)

https://doi.org/10.48550/arXiv.2609.09305 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.