发表机构
University of Science and Technology of China; Max Planck Institute for the Physics of Complex Systems; Wilczek Quantum Center, Shanghai Institute for Advanced Studies; CAS Key Laboratory of Microscale Magnetic Resonance（中国科学技术大学; 马克斯·普朗克复杂系统物理研究所; 复旦张肇韦量子中心，上海高等研究院; 中国科学院微观磁学共振重点实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过半经典分析揭示单粒子混沌系统中本征态热化的标度行为，提出动能相关修正因子，并在广义Sinai台球中验证，为理解量子混沌与热化提供新视角。
AI 中文摘要
我们研究了时间反演不变的单粒子混沌系统中实空间算符的非对角矩阵元。通过分析基于Berry猜想的非对角方差半经典表达式，我们展示了可观测矩阵的带状结构自然涌现。对于局域算符，我们确定了一个特征带宽，其对应的晚期时间尺度与粒子速度成反比。我们进一步表明，对于具有陡壁约束的系统，预测的幅度遵循本征态热化假说（ETH）的熵标度，并乘以一个额外的动能相关因子，该因子独立于空间维度，且不被传统多体ETH所捕捉。我们通过量子台球案例研究说明了这些结果，并在广义四分之一Sinai台球中数值验证了半经典标度。我们的结果阐明了Berry猜想的动力学意义，并提供了单粒子本征态热化与多体ETH之间的比较。
英文摘要
We study the off-diagonal matrix elements of real-space observables in time-reversal-invariant single-particle chaotic systems. By analyzing the semiclassical expression for the off-diagonal variance derived from Berry's conjecture, we show that the banded structure of the observable matrix emerges naturally. For local observables, we identify a characteristic bandwidth associated with a late-time timescale inversely proportional to the particle velocity. We further show that, for systems with steep-wall confinement, the predicted magnitude follows the entropy scaling of the eigenstate thermalization hypothesis (ETH), multiplied by an additional kinetic-energy-dependent factor that is independent of spatial dimension and is not captured by conventional many-body ETH. We illustrate these results through a case study of quantum billiards and verify the semiclassical scaling numerically in a generalized quarter-Sinai billiard. Our results elucidate the dynamical implications of Berry's conjecture and provide a comparison between single-particle eigenstate thermalization and many-body ETH.
Comments6 pages, 3 figures; Supplemental Material: 3 pages, 1 figure
