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.
|Number of pages||22|
|Journal||Journal of Physics A: Mathematical and Theoretical|
|Early online date||21 Jan 2022|
|Publication status||Published - 11 Feb 2022|
Bibliographical notePublisher Copyright:
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- emptiness formation probability
- integrable system
- quantum liquids
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Modelling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)