Emptiness Formation in Polytropic Quantum Liquids

TL;DR

This paper analyzes the probability of finding empty regions in polytropic quantum liquids by solving hydrodynamic equations, providing new analytic solutions for various polytropic indexes and expanding understanding of quantum liquid behavior.

Contribution

It introduces analytic solutions for emptiness formation probability in polytropic quantum liquids across a range of indexes, extending previous results.

Findings

Analytic solutions for rational polytropic indexes

Agreement with previous analytical and numerical results

Discussion of universal spacetime features of instanton solutions

Abstract

We study large deviations in interacting quantum liquids with the polytropic equation of state $P(\rho)\sim \rho^\gamma$, where $\rho$ is density and $P$ is pressure. By solving hydrodynamic equations in imaginary time we evaluate the instanton action and calculate the emptiness formation probability (EFP), the probability that no particle resides in a macroscopic interval of a given size. Analytic solutions are found for a certain infinite sequence of rational polytropic indexes $\gamma$ and the result can be analytically continued to any value of $\gamma\ge 1$. Our findings agree with (and significantly expand on) previously known analytical and numerical results for EFP in quantum liquids. We also discuss interesting universal spacetime features of the instanton solution.