Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Bulletin of the American Physical Society

Nonlinear Luttinger Liquid: Exact solution for the Green function from the fourth Painleve transcendent

Tom Price, Dmitry L. Kovrizhin, Austen Lamacraft

Published Mar 16, 2017• 0 citations
OpenAlex

Related papers

One-Dimensional Luttinger Liquid of Particles for a Class of Infinitely Repulsive Interactions: Exact Solution

G. Gómez-Santos

NATO ASI series. Series B : Physics•Jan 1, 1995•0 citations

Luttinger Liquids coupled to Quantum Impurities; Exact Solutions via Bethe Ansatz

Colin Rylands, Natan Andrei

Bulletin of the American Physical Society•Mar 14, 2017•0 citations

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

Tom Price, Dmitry L. Kovrizhin, Austen Lamacraft

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/\sqrt{t} x / t agrees with the mobile impurity results. The full shape of the Green function in the thermodynamic limit is recovered with arbitrary precision via a simple numerical integration of a nonlinear ODE.

arXiv:1606.08702•SciPost Physics•Feb 20, 2017•5 citations

Theory of Nonlinear Luttinger Liquids

L. I. Glazman

Bulletin of the American Physical Society•Mar 16, 2010•0 citations

Nonlinear Luttinger liquid: exact result for the Green function in terms of the fourth Painleve transcendent

Tom Price, Dmitry L. Kovrizhin, Austen Lamacraft

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/pt agrees with the mobile impurity results. The full shape of the Green function in the thermodynamic limit is recovered with arbitrary precision via a simple numerical integration of a nonlinear ODE.

•Jan 1, 2017•6 citations

Nonlinear Luttinger Liquid from Painlev\'e IV

Tom Price, Dmitry L. Kovrizhin, Austen Lamacraft

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 Painleve IV equation. Our expression for the Green function has a form analogous to the celebrated Tracy-Widom result connecting the Airy kernel with Painleve II. The asymptotic power law of the exact solution as a function of a single scaling variable $x/\sqrt{t}$ agrees with the mobile impurity results. The full shape of the Green function in the thermodynamic limit is recovered with arbitrary precision via a simple numerical integration of a nonlinear ODE.

•Jun 28, 2016•0 citations
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/\sqrt{t} x / t agrees with the mobile impurity results. The full shape of the Green function in the thermodynamic limit is recovered with arbitrary precision via a simple numerical integration of a nonlinear ODE.
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/pt agrees with the mobile impurity results. The full shape of the Green function in the thermodynamic limit is recovered with arbitrary precision via a simple numerical integration of a nonlinear ODE.
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 Painleve IV equation. Our expression for the Green function has a form analogous to the celebrated Tracy-Widom result connecting the Airy kernel with Painleve II. The asymptotic power law of the exact solution as a function of a single scaling variable x/tx/\sqrt{t}x/t​ agrees with the mobile impurity results. The full shape of the Green function in the thermodynamic limit is recovered with arbitrary precision via a simple numerical integration of a nonlinear ODE.