Lindbladian SYK 中的算符动力学：Krylov 复杂度视角
Operator dynamics in Lindbladian SYK: a Krylov complexity perspective
AI总结：
本文通过 Krylov 复杂度研究耗散 SYK 模型中算符增长，解析并数值验证了大 q 极限下系数的线性增长，发现复杂度随耗散强度反比饱和、耗散时间尺度对数增长，并揭示耗散量子混沌系统中算符增长的一般原理。
AI中文摘要：
我们利用 Krylov 复杂度研究 $q$-体耗散 SYK 模型中的算符增长，其中耗散由线性与随机 $p$-体 Lindblad 算符建模。在大 $q$ 极限下，我们解析地建立了任意通用跳跃算符的两组系数的线性增长。我们通过实现双 Lanczos 算法对此进行了数值验证，该算法将 Lindbladian 变换为纯三对角形式。我们发现 Krylov 复杂度随耗散强度呈反比饱和，而耗散时间尺度呈对数增长。这类似于其他 $\mathfrak{q}$-复杂度度量的行为，即我们同样展示的 out-of-time-order correlator（OTOC）和算符尺寸。我们将这些观察与连续量子测量过程联系起来。我们进一步研究了通用自关联的极点结构以及存在耗散时谱函数的高频行为，从而揭示了耗散量子混沌系统中算符增长的一般原理。
英文摘要：
We use Krylov complexity to study operator growth in the $q$-body dissipative SYK model, where the dissipation is modeled by linear and random $p$-body Lindblad operators. In the large $q$ limit, we analytically establish the linear growth of two sets of coefficients for any generic jump operators. We numerically verify this by implementing the bi-Lanczos algorithm, which transforms the Lindbladian into a pure tridiagonal form. We find that the Krylov complexity saturates inversely with the dissipation strength, while the dissipative timescale grows logarithmically. This is akin to the behavior of other $\mathfrak{q}$-complexity measures, namely out-of-time-order correlator (OTOC) and operator size, which we also demonstrate. We connect these observations to continuous quantum measurement processes. We further investigate the pole structure of a generic auto-correlation and the high-frequency behavior of the spectral function in the presence of dissipation, thereby revealing a general principle for operator growth in dissipative quantum chaotic systems.
