量子反应-输运动力学中的瞬态与普适区间
Transient and universal regimes in quantum reaction-transport kinetics
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中文总结 AI 辅助
研究量子二元湮灭反应-输运系统，发现低维下涨落主导渐近动力学，一维中驱动至输运受限区间并受量子芝诺尺度支配，且涨落产生有效弹性碰撞使系统趋近准稳态热态。
中文摘要 AI 辅助
量子反应-输运系统由相干传播的粒子组成，这些粒子在相遇时发生不可逆反应。它们的弛豫通常根据反应和粒子输运的相对时间尺度被分类为反应受限或输运受限。我们通过研究量子二元湮灭过程 $A+A \to \emptyset$ 表明，在低维情况下这一预期失效，因为在低于上临界维度 $D_c=2$ 时，反应过程会获得奇异的涨落修正。因此，对于 $D<2$，涨落主导渐近动力学。在一维中，涨落使平均场弛豫变为瞬态，并将系统驱动至输运受限区间，其行为为 $n\sim t^{-1/2}$，即使对于任意弱的损耗也受量子芝诺尺度支配。在 $D=2$ 时，动力学获得对数修正，而在二维以上，平均场标度渐近恢复。在上临界维度及以下，平均场行为在渐近涨落主导区间出现之前，仍可在参数上较长的交叉时间内持续存在。我们还表明，尽管缺乏微观相干相互作用，相同的涨落会产生有效的弹性碰撞。在 $D>1$ 时，这些碰撞重新分配动量布居，并且在输运受限区间内参数上比损耗更快，从而使系统能够接近准稳态热态。
英文摘要
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.
发表机构
- Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）
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