## Abstract

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) |
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Article number | 064002 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 55 |

Issue number | 6 |

DOIs | |

State | Published - Feb 11 2022 |

### Bibliographical note

Publisher Copyright:© 2022 IOP Publishing Ltd.

## Keywords

- emptiness formation probability
- hydrodynamics
- instanton
- integrable system
- quantum liquids