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Exact Dynamical Structure Factor of One-Dimensional Hard Rods and Its Universal Random Matrix Behavior
Oleksandr Gamayun1, Miłosz Panfil2
1London Institute for Mathematical Sciences, Royal Institution, 21 Albemarle Street, London W1S 4BS, United Kingdom.
Abstract:
We obtain an exact analytic expression for the dynamical structure factor of one-dimensional quantum gas of hard rods. Our result is valid for an arbitrary many-body state of the system, with finite temperature states and the ground state being important special cases that we analyze 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 Letter provides a full and exact characterization of a dynamic correlation function in a strongly correlated interacting quantum many-body system.
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