发表机构
Universidade Federal de Goiás; Universidade de São Paulo（戈亚斯联邦大学; 圣保罗大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明在Dicke阶梯的集体阻尼两能级系统中，初始更远离稳态的态可在弛豫中超越较近态，与超辐射发射共存，且交叉源于集体辐射动力学。
AI 中文摘要
Mpemba效应发生在初始距离稳态更远的态在弛豫过程中超越距离更近的态时。我们证明这种反常排序可以与集体阻尼的两能级系统系综中的超辐射发射共存。在对称Dicke流形中，零温衰变是一个速率Γn(N-n+1)的粒子数级联。我们构造稀疏族ρ_A=|⌈2N/3⌉⟩⟨⌈2N/3⌉|和ρ_B=(|0⟩⟨0|+|N⟩⟨N|)/2。尽管A初始能量更高且距离稳态基态更远，但它在能量和迹距离上都超越B，因为它起始于Dicke阶梯中辐射更强的区域。两个态都产生大于其独立发射体参考值的发射峰。对于从N=6到60的所有检验尺寸，交叉持续存在，而峰强度显示出接近N^2的有效标度。在独立衰变下，同一对态没有交叉，这确定了集体辐射动力学是该效应的起源。
英文摘要
The Mpemba effect occurs when a state initially farther from stationarity overtakes a closer one during relaxation. We show that this anomalous ordering can coexist with superradiant emission in a collectively damped ensemble of two-level systems. In the symmetric Dicke manifold, zero-temperature decay is a population cascade with rates $Γn(N-n+1)$. We construct the sparse family $ρ_A=|\lceil2N/3\rceil\rangle\langle\lceil2N/3\rceil|$ and $ρ_B=(|0\rangle\langle0|+|N\rangle\langle N|)/2$. Although $A$ is initially more energetic and more distant from the stationary ground state, it crosses $B$ in both energy and trace distance because it starts in a more radiative region of the Dicke ladder. Both states develop emission peaks larger than their independent-emitter references. The crossing persists for all examined sizes from $N=6$ to $60$, while the peak intensities show an effective scaling close to $N^2$. The same pair has no crossing under independent decay, identifying collective radiative kinetics as the origin of the effect.
Comments3 figs, 5 pages
