大-$q$ SYK模型中非平衡格林函数的解析解
Analytical solutions to the non-equilibrium Green's functions in large-$q$ SYK models
- Gesellschaft für wissenschaftliche Datenverarbeitung mbH Göttingen (GWDG)（哥廷根科学数据有限公司）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文针对非对易$q/2$体SYK哈密顿量间的淬火，给出了所有时间块非平衡格林函数的闭式解析解，并推导出能量比例关系与精确温度更新规则，通过柯西-施瓦茨不等式证明封闭系统必然加热，从而几何地涌现热力学第二定律。
AI中文摘要：
已知Sachdev-Ye-Kitaev (SYK)模型在$1/q$的首阶下是精确可解的；具体而言，淬火后的瞬时热时间块以闭式形式已知。迄今为止，其余（本质上非平衡的）时间块仅能通过数值方法获取。在此，我们提供了非对易的$q/2$体SYK哈密顿量之间淬火的这些时间块的解析解。我们以闭式形式获得了每个时间块的格林函数。我们提取了淬火前后能量之间的简单关系$\epsilon_1 \propto \epsilon_0$，从而得到精确的温度更新规则。通过柯西-施瓦茨不等式，我们证明封闭系统的加热是不可避免的；因此，热力学第二定律以几何方式涌现。该解在配套论文中用于探讨有限$q$下“瞬时热化”的含义。
英文摘要：
It is known that the Sachdev-Ye-Kitaev (SYK) model is exactly solvable at leading order in $1/q$; specifically, the instantaneously thermal time block after the quench is known in closed form. Thus far the remaining (inherently out of equilibrium) blocks have only been numerically accessible. Here we provide their analytical solutions for a quench between non-commuting $q/2$-body SYK Hamiltonians. We obtain the Green's functions in closed form for every time block. We extract a simple relation between the pre- and post-quench energies $ε_1 \propto ε_0$ leading to an exact temperature update rule. Via a Cauchy-Schwarz inequality, we show that heating is inevitable for the closed system; hence, the second law emerges geometrically. The solution is used in a companion paper to address what ``instantaneous thermalization'' means at finite $q$.
