发表机构
Kyoto University; Tokyo University of Agriculture and Technology（京都大学; 东京农工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究连续一维对称双阱势中的量子隧穿姆潘巴效应，用有效哈密顿量的非厄米谱分解刻画开放系统弛豫动力学，证明谱系数非单调行为是量子统计力学的普遍拓扑性质。
AI 中文摘要
在具有边界（\(x = \pm L\)）外部环境汇的连续一维对称双阱势中研究量子隧穿姆潘巴效应。使用有效哈密顿量的非厄米谱分解，我们表征开放系统弛豫动力学，而不依赖于抽象的状态空间猝灭。我们数学证明了第一个非平凡偶宇称谱系数\(a_{2}(T_{i})\)相对于初始制备温度\(T_{i}\)的非单调行为是量子统计力学产生的普遍拓扑性质。至关重要的是，我们证明这个中间热峰由斯特姆 - 刘维尔振荡定理支配，并且相对于全局系统大小\(L\)完全不变，这与边界驱动的经典姆潘巴效应形成鲜明对比。这个普遍峰源于高度局域化的未受扰动状态与扩展的非厄米衰减通道之间的几何和节点对齐。此外，我们阐明虽然这种机制是稳健的，但在总生存概率迹\(S(t,T_{i})\)和迹距离\(\mathcal{D}(t,T_i)\)中实际观察到异常交叉需要严格的时间尺度分离，要求越过势垒的逃逸率大大超过深阱隧穿双峰的衰减率（\(\Gamma_{2}\gg \Gamma_{0}\)且\(\Gamma_2\gg \Gamma_1\)）。我们的连续公式成功地将实空间经典边界驱动的耗散与开放量子动力学联系起来，为通过定制边界损耗工程非平衡态提供了新的见解。
英文摘要
We investigate a quantum tunneling Mpemba effect for a particle in a continuous one-dimensional symmetric double-well potential subject to irreversible boundary loss. The dissipation is described by a complex absorbing potential (CAP) and the corresponding conditional no-jump evolution. Using a biorthogonal spectral representation, we derive the exact non-Hermitian decomposition of the subnormalized density matrix and analyze the corresponding relaxation dynamics. We show that the off-diagonal coefficients exhibit a parity selection rule, leaving same-parity interference terms in general. To isolate the interplay between thermal spectral preparation and mode-dependent decay rates, we introduce a diagonal spectral relaxation measure $S(t,T_i)$. For a quartic double well, numerical calculations reveal finite-time crossings of $S(t,T_i)$ prepared at different initial temperatures, as well as a non-monotonic temperature dependence of selected diagonal spectral weights. These features are explained by the enhanced thermal population of spatially extended, rapidly leaking excited states. In contrast, the trace distance of the normalized conditional state to the asymptotic quasi-stationary state exhibits no crossing, demonstrating that the anomalous ordering is specifically a spectral Mpemba effect rather than a universal acceleration of the complete conditional state. Our continuous-space formulation provides a real-space perspective on anomalous quantum relaxation without invoking universal nodal or topological theorems.
Comments30 pages, 7 figures
