Emptiness formation in polytropic quantum liquids

Hsiu Chung Yeh*, Dimitri M. Gangardt, Alex Kamenev

*Corresponding author for this work

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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 languageEnglish
Article number064002
Number of pages22
JournalJournal of Physics A: Mathematical and Theoretical
Issue number6
Early online date21 Jan 2022
Publication statusPublished - 11 Feb 2022

Bibliographical note

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© 2022 IOP Publishing Ltd.


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

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)


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