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 → ∅, where reaction processes acquire singular fluctuation corrections below the upper critical dimension Dc=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∼ 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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BibTeX
@misc{hosseinabadi2026transient,
title = {{Transient and universal regimes in quantum reaction-transport kinetics}},
author = {Hossein Hosseinabadi and Roderich Moessner},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09305},
eprint = {2609.09305},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09305},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Transient and universal regimes in quantum reaction-transport kinetics
AU - Hossein Hosseinabadi
AU - Roderich Moessner
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.09305
UR - https://arxiv.org/abs/2609.09305
AB - 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 → ∅, 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∼ 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.
ER -