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Nonlinear Luttinger liquid: Exact result for the Green function in terms of the fourth Painlevé transcendent

Abstract:

We show that exact time dependent single particle Green function in the Imambekov–Glazman theory of nonlinear Luttinger liquids can be written, for any value of the Luttinger parameter, in terms of a particular solution of the Painlevé IV equation. Our expression for the Green function has a form analogous to the celebrated Tracy–Widom result connecting the Airy kernel with Painlevé II. The asymptotic power law of the exact solution as a function of a single scaling variable x/√t agrees with ...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Publisher's version

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Publisher copy:
10.21468/SciPostPhys.2.1.005

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Physics; Atomic & Laser Physics
Lamacraft, A More by this author
Publisher:
SciPost Foundation Publisher's website
Journal:
SciPost Physics Journal website
Volume:
2
Issue:
1
Pages:
005
Publication date:
2017-02-21
Acceptance date:
2017-02-13
DOI:
ISSN:
2542-4653
Pubs id:
pubs:843694
URN:
uri:adb6f362-44ab-4550-aad0-45ed048db540
UUID:
uuid:adb6f362-44ab-4550-aad0-45ed048db540
Local pid:
pubs:843694

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