发表机构
Hanyang University; Seoul National University（汉阳大学; 首尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究缓变相互作用链的共振统计等，推导共振统计量，构建福克空间图，确定长程阈值，明确其非局域化相变属性。
AI 中文摘要
在具有随机幂律密度相互作用 $V_{ij}/|i-j|^\alpha$ 的缓变非周期势 $h_i=h\cos(2\pi\beta i^n+\phi)$ 中，当 Hartree 碎裂作用生效时，共振对象系综在 $\alpha=2n$ 处发生变化：从孤立的两能级键转变为有限密度下仍存在的碎裂多位点团簇与孤立翼键的混合体，而对共振标度 $x_{\rm pair}^{4-2n-\alpha}\ln x_{\rm pair}\propto h^2/(Vt_0)$ 保持不变[文献]。本文发展了支撑这些结果的微观共振理论及其有效域，推导了精确的相平均共振统计量——供应率 $N_0\propto L^{2-n}/h$、关联同相梳以及闭式 Hartree 方差，证明相互作用未改变主导供应律。对 $L\le18$ 时的共振福克空间图的精确构建表明，一阶前分支标度 $h_{\rm FB}\propto L^{2-n}$ 不含巨分量：一步分支与连通性不等价。本文区分了固定对匹配律与键系综的壳平均 $q\ln(1/q)$ 律，将梳发展为介观壳理论，绘制了碎裂域及其支撑阈值 $V_*(\alpha)$ 与边界修复递推关系，并处理了 $\alpha=2$ 的边缘情况，此时壳与匹配边缘性复合为双重对数。出现了三个具有不同含义的长程阈值：$\alpha=1/2$（随机福克空间能量的精确方差阈值与主导 LIOM 修饰估计的平方可和边界）、$\alpha=2n$（局部共振对象的变化）、$\alpha=2$（长程壳和的边缘性），三者本身均非局域化相变。
英文摘要
In a slowly varying aperiodic potential $h_i=h\cos(2πβi^n+ϕ)$ with random power-law density interactions $V_{ij}/|i-j|^α$, the resonant-object ensemble changes across $α=2n$, wherever Hartree fragmentation is operative, from isolated two-level bonds to a mixture of fragmented multi-site clusters and isolated wing bonds that survive at finite density, while the pair-resonance scaling $x_{\rm pair}^{4-2n-α}\ln x_{\rm pair}\propto h^2/(Vt_0)$ is unchanged~\cite{letter}. Here we develop the microscopic resonance theory underlying these results, together with its domain of validity. We derive the exact phase-averaged resonance statistics --- the supply $N_0\propto L^{2-n}/h$, the correlated common-phase comb, and the closed-form Hartree variance --- proving that the interaction leaves the leading supply law unchanged. Exact construction of the resonant Fock-space graph at $L\le18$ shows that the order-one forward-branching scale $h_{\rm FB}\propto L^{2-n}$ carries no giant component: one-step branching and connectivity are inequivalent. We separate the fixed-pair matching law from the shell-averaged $q\ln(1/q)$ law of the bond ensemble and develop the comb into a mesoscopic shell theory; we map the fragmentation domain, with its support threshold $V_*(α)$ and the boundary-healing recursion; and we treat the marginal case $α=2$, where shell and matching marginalities compound into a double logarithm. Three long-range thresholds emerge with distinct meanings --- $α=1/2$ (the exact variance threshold of the random Fock-space energy and the square-summability boundary of the leading LIOM-dressing estimate), $α=2n$ (change of the local resonant objects), and $α=2$ (marginality of the long-range shell sum) --- none of which is, by itself, a localization transition.
Comments34 Pages, 10 Figs
