论文标题
杆子远离最大混乱
Pole skipping away from maximal chaos
论文作者
论文摘要
杆跳过是最近发现的热能密度的微妙效果,在复合$(ω,p)$平面的特殊点上延迟了两个点功能。我们提出跳过的跳过取决于压力张量对多体混乱的贡献,而特殊点为$(ω,p)_ \ text {张量对Lyapunov指数和蝴蝶速度的贡献。尽管该提案与对最大混乱理论进行的先前研究一致,而应力张量主导了混乱,但它阐明了一个人不能使用杆跳过来提取理论的lyapunov指数,从而遵守$λ\leqλ^{(t)} $。另一方面,在一大批强烈但非最大的混乱理论中,$ u_b^{(t)} $是真正的蝴蝶速度,我们认为$ u_b \ u_b \ leq u_b^{(t)} $是一个通用的绑定。虽然在一般框架中解释杆跳过仍然是一个挑战,但我们在Syk链的巨大Q $限制中对提案进行了严格的测试,在这里,我们确定$λ,\,u_b,$和能量密度的两个点在封闭形式中以封闭形式为耦合,插入的所有值,在自由和最大的chaotical Chaotical intoction intoplotic中。由于热相关器的这种显式表达是一种,因此我们借此机会分析了其许多特性:扩散常数的耦合依赖性,极点的分散关系以及所有顺序流体动力学的收敛性。
Pole skipping is a recently discovered subtle effect in the thermal energy density retarded two point function at a special point in the complex $(ω,p)$ planes. We propose that pole skipping is determined by the stress tensor contribution to many-body chaos, and the special point is at $(ω,p)_\text{p.s.}= i λ^{(T)}(1,1/u_B^{(T)})$, where $λ^{(T)}=2π/β$ and $u_B^{(T)}$ are the stress tensor contributions to the Lyapunov exponent and the butterfly velocity respectively. While this proposal is consistent with previous studies conducted for maximally chaotic theories, where the stress tensor dominates chaos, it clarifies that one cannot use pole skipping to extract the Lyapunov exponent of a theory, which obeys $λ\leq λ^{(T)}$. On the other hand, in a large class of strongly coupled but non-maximally chaotic theories $u_B^{(T)}$ is the true butterfly velocity and we conjecture that $u_B\leq u_B^{(T)}$ is a universal bound. While it remains a challenge to explain pole skipping in a general framework, we provide a stringent test of our proposal in the large-$q$ limit of the SYK chain, where we determine $λ,\, u_B,$ and the energy density two point function in closed form for all values of the coupling, interpolating between the free and maximally chaotic limits. Since such an explicit expression for a thermal correlator is one of a kind, we take the opportunity to analyze many of its properties: the coupling dependence of the diffusion constant, the dispersion relations of poles, and the convergence properties of all order hydrodynamics.