AI 中文总结
在大质量间隙的BMN矩阵模型中，用Krylov复杂度诊断量子多体动力学，计算相关物理量，提出矩的表达式，讨论正交多项式，计算谱函数等，分析红外发散，发现集体模式特性，计算Krylov方差和熵，证实量子混沌起始。
AI 中文摘要
我们在大质量间隙的BMN矩阵模型背景下，将Krylov复杂度用作量子多体动力学的典型诊断工具。计算了诸如大质量变形时的矩和返回振幅等物理量，包括态的扩展复杂度和矩阵模型中算符的Krylov增长情况。提出了任意给定阶数\(n\)的矩的一般表达式，还讨论了扩展以及算符Krylov复杂度的正交多项式。在Krylov算符增长的背景下进一步计算了谱函数和态密度。对共振附近谱函数的仔细分析揭示了除物理集体模式外的各种红外发散。由于大质量间隙，这些集体模式似乎异常稳定，而理论的紫外部分因较高散射率而极度衰减。我们仔细诊断了共振附近的这些红外发散，发现这些集体模式实际上是非传播的，应被视为具有无限弛豫时间的扩散模式或弛豫模式。还计算了矩阵模型特别是早期的Krylov方差和Krylov熵。Krylov熵在早期的线性增长证实了大质量间隙下矩阵模型中量子混沌的开始。
英文摘要
We use Krylov complexity as a typical diagnostic of quantum many body dynamics in the context of BMN matrix model at large mass gap. We calculate several physical entities, for example, the moments and return amplitudes at large mass deformation. We calculate them for both spread complexity of states as well as Krylov growth of operators in the matrix model. We propose a general expression for the moments at any given order $n$. We also discuss orthogonal polynomials for spread as well as operator Krylov complexity. In the context of the Krylov operator growth we further compute the spectral function and the density of states. A careful analysis of the spectral function near the resonance reveals various IR divergences in addition to the physical collective modes. These collective modes appear to be exceptionally stable due to large mass gap. On the other hand, the UV of the theory appears to be extremely damped due to higher scattering rates. We carefully diagnose these IR divergences near resonance which reveals that these collective modes are in fact non-propagating and should be thought of as diffusion modes or relaxation modes with infinite relaxation time. We also calculate the Krylov variance and Krylov entropy for the matrix model and in particular at early time. The linear early time growth of the Krylov entropy confirms the onset of quantum chaos in the matrix model at large mass gap.
CommentsLatex, 32 pages plus refs
