O. Gamayun

M. Panfil

A canonical quantum fluid model is solved exactly, revealing universal correlation patterns governed by Gaussian random-matrix ensembles.

An exact analytic expression is obtained for the dynamical structure factor of a one-dimensional quantum gas of hard rods. The finite size of the particles induces strong many-body correlations in the system. Remarkably, in the static limit, the dynamical structure factor at zero temperature can be expressed in terms of the universal level-spacing distributions of the eigenvalues of random Gaussian unitary matrices. 

We obtain an exact analytic expression for the dynamical structure factor of one-dimensional quantum gas of hard rods. Our result is valid for arbitrary many-body state of the system, with finite temperature states and the ground state being important special cases that we analyse in detail. We demonstrate that the expression obeys fundamental relations such like the f-sum rule and the detailed balance. We also reveal the hidden fermionic structure behind the correlator. In the static limit we show that it can be written in terms of universal functions which, at zero temperature, coincide with the level spacing distribution function of the Gaussian Unitary Ensemble. Our work provides a full and exact characterisation of a dynamic correlation function in a strongly correlated interacting quantum many-body system.

The exact dynamical structure factor of one-dimensional hard rods and its universal random matrix behavior