We study large deviations in interacting quantum liquids with the polytropic equation of state P(ρ) ∼ ρ γ , where ρ 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 γ and the result can be analytically continued to any value of γ 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.
|Original language||English (US)|
|Journal||Journal of Physics A: Mathematical and Theoretical|
|State||Published - Feb 11 2022|
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- emptiness formation probability
- integrable system
- quantum liquids