标题： Calogero-Sutherland模型中的动态关联 显示英文标题

标题： Dynamic correlations in Calogero-Sutherland model

摘要： 卡洛杰罗-萨瑟兰模型代表了一个可积量子系统的典范例子，其应用范围从冷原子到随机矩阵理论。 结合求和规则与蒙特卡罗技术，我们引入了一种随机方法，使得能够计算动态结构因子，并获得对常规林德勒液体区域之外激发态的精确描述。 我们研究了广泛的相互作用区域，包括弱相互作用，在这种情况下出现类似于玻利乌博夫的谱，汤克斯-吉拉尔多区域，其中激发态类似于理想费米气体的激发态，以及强相互作用，在这种情况下，散射导致布里渊区结构，这是晶体的典型特征。 此外，我们讨论了一维量子气体、液体和固体的流体动力学描述与卡洛杰罗-萨瑟兰波函数之间的联系。 该模型的普适性不仅限于波导中的原子，还对无序系统和随机矩阵理论有影响。 显示英文摘要

摘要： The Calogero-Sutherland model represents a paradigmatic example of an integrable quantum system with applications ranging from cold atoms to random matrix theory. Combining sum rules with the Monte Carlo technique, we introduce a stochastic method that allows one to compute the dynamic structure factor and obtain an exact description of excitations beyond the conventional Luttinger liquid regime. We explore a broad range of interaction regimes, including weak interactions, where a Bogoliubov-type spectrum emerges, the Tonks-Girardeau regime, where excitations resemble those of an ideal Fermi gas, and strong interactions, where umklapp scattering leads to a Brillouin zone structure, typical of a crystal. Additionally, we discuss the connection between the hydrodynamic description of one-dimensional quantum gases, liquids, and solids with the Calogero-Sutherland wave function. The model's universality extends beyond atoms in waveguides, with implications for disordered systems and random matrix theory.