Emptiness formation in polytropic quantum liquids

Hsiu Chung Yeh; Dimitri M. Gangardt; Alex Kamenev

doi:10.1088/1751-8121/ac47b1

Emptiness formation in polytropic quantum liquids

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

^*Corresponding author for this work

Physics and Astronomy

Research output: Contribution to journal › Article › peer-review

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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
Article number	064002
Number of pages	22
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	55
Issue number	6
Early online date	21 Jan 2022
DOIs	https://doi.org/10.1088/1751-8121/ac47b1
Publication status	Published - 11 Feb 2022

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Publisher Copyright:
© 2022 IOP Publishing Ltd.

Keywords

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
General Physics and Astronomy

Access to Document

10.1088/1751-8121/ac47b1

YehH2022Emptiness
This is an author-created, un-copyedited version of an article accepted for publication/published in Journal of Physics A: Mathematical and Theoretical. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at: https://doi.org/10.1088/1751-8121/ac47b1
Accepted author manuscript, 1.24 MBLicence: None: All rights reserved

Cite this

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title = "Emptiness formation in polytropic quantum liquids",

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.",

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AU - Gangardt, Dimitri M.

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N2 - 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.

AB - 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.

KW - emptiness formation probability

KW - hydrodynamics

KW - instanton

KW - integrable system

KW - quantum liquids

UR - https://www.scopus.com/pages/publications/85124392836

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JO - Journal of Physics A: Mathematical and Theoretical

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Emptiness formation in polytropic quantum liquids

Abstract

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Keywords

ASJC Scopus subject areas

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