Lindbladian SYK 模型中的算符尺寸增长
Operator size growth in Lindbladian SYK
AI总结：
本研究针对含q体相互作用与线性跃迁项的Lindbladian SYK模型，通过数值与解析方法探究算符尺寸增长规律，揭示了不同耗散条件下的演化特征、分布特性及大q极限下的经典动力学行为。
AI中文摘要：
我们研究了具有q体相互作用项和线性跃迁项、处于有限耗散强度下的Lindbladian Sachdev-Ye-Kitaev（SYK）模型中的算符尺寸增长。我们通过数值计算了有限q下的算符尺寸及其分布，并通过解析方法推导了大q极限下的结果。当存在耗散型（产生型）跃迁项时，算符尺寸会收敛到一个小于（大于）Majorana费米子总数一半的值。在弱耗散条件下，算符尺寸的演化呈现出“二次增长-指数增长-平台期”的行为特征；在大q极限下，平台值由相互作用耦合与线性跃迁项耦合的比值决定。即使在晚期时刻，算符尺寸分布仍局域在有限尺寸区域，这与幺正情形形成对比。此外，我们还推导了用于算符展开的与时间无关的正交基，该基展现出有限耗散下的算符尺寸集中效应。最后，我们观察到算符尺寸增长的不确定关系在大q下达到饱和，从而导致含耗散的算符尺寸增长呈现经典动力学行为。
英文摘要：
We investigate the growth of operator size in the Lindbladian Sachdev-Ye-Kitaev model with $q$-body interaction terms and linear jump terms at finite dissipation strength. We compute the operator size as well as its distribution numerically at finite $q$ and analytically at large $q$. With dissipative (productive) jump terms, the size converges to a value smaller (larger) than half the number of Majorana fermions. At weak dissipation, the evolution of operator size displays a quadratic-exponential-plateau behavior. The plateau value is determined by the ratios between the coupling of the interaction and the linear jump term in the large $q$ limit. The operator size distribution remains localized in the finite size region even at late times, contrasting with the unitary case. Moreover, we also derived the time-independent orthogonal basis for operator expansion which exhibits the operator size concentration at finite dissipation. Finally, we observe that the uncertainty relation for operator size growth is saturated at large $q$, leading to classical dynamics of the operator size growth with dissipation.
