论文标题
多体无序系统中的新兴偏光元和Wigner-dyson分布：使用隐藏变量的多变量PDE和集合主导的重量分布的基于隐藏变量的优化算法的数值证据
Emerging polaron and Wigner-Dyson distribution in many-body disordered system: Numerical evidence using a hidden variable based optimization algorithm for the multi-variable PDE and ensemble-dominated weight distribution
论文作者
论文摘要
我们提出了一个可模拟的隐藏变量和步长的算法基础，该算法是受启发式统计物理学和复制方法的启发，以研究相互关联的效果以及在多体系统中的新出现的Wigner-Dyson分布的效果，这是渐进的高度统计制度。我们认为北极子系统可以限制在动量或位置空间中IR/UV截止的效果。偏极是一种长寿命的准粒子，可以在不可症状的状态下发现，在费米液相中具有缓慢的动量和电流松弛。我们揭示了polaronic动量$λ_{q} $的UV临界值与其SYK行为之间的关系。北极子系统的SYK行为以及散射动量与相关统计行为之间的关系很少进行。我们发现，反向动量截止$λ_{q}^{ - 1} $，它扮演着基本的自由度（DOF）的作用，而不是费米子（DOF），与偏光式耦合项的分布和统计差异有关。通过投影到2D方格晶格，我们在位置空间中考虑了这个问题，在该位置空间中，北极星散射动量的DOF被另一种味道取代（表示为$η_δ$，其风味数量为$ o（m）$），这是由$ o（m）$的订单确定的，而该站点的潜在潜力$δ$以及我们还以搜索自我目的的方式来搜索更多的途径，以搜索更多的途径。
We propose an algorithm base on the modulable hidden variables and step length, which is inspired by the heuristic statistical physics and replica method, to study the effect of mutual correlations and the emergent Wigner-Dyson distribution in a many-body system which is of the asymptotic high-dimensional statistics regime. We consider the polaron system to illustate the effect of IR/UV cutoff in the momentum or position space. The polaron as a long-lived quasiparticle which can be found in the imcompressible state has slow momenta and current relaxation in Fermi liquid phase. We reveal the relation between UV cutoff of polaronic momentum $Λ_{q}$ and its SYK behavior. The SYK behavior of a polaron system, as well as the relation between scattering momentum and the related statistical behaviors has rarely been investigated before. We found that the inversed momentum cutoff $Λ_{q}^{-1}$, which plays the role of an essential degree-of-freedom (DOF) other than the fermions, relates to the distribution and statistical variance of polaronic coupling term. By projecting to a 2d square lattice, we consider this problem in position space where the DOF of polaron scattering momenta is replaced by another flavor (denoted as $η_Δ$ with flavor number of order of $O(M)$) which is determined by the site potential differece $Δ$ as well as the site index, and we also applying the self-attention method to searching for the more efficient route to exploiting the many-body behaviors.
