Fredholm determinants and the mKdV/Sinh-Gordon hierarchies

DOI10.1007/BF02103713zbMath0858.35114arXivsolv-int/9506006WikidataQ56950697 ScholiaQ56950697MaRDI QIDQ1924081

Harold Widom, Craig A. Tracy

Publication date: 23 March 1997

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/solv-int/9506006

zbMATH Keywords

correlation functionsFredholm determinantsmKdV hierarchyconjecture of ZamolodchikovSinh-Gordon hierarchy

Mathematics Subject Classification ID

Model quantum field theories (81T10) KdV equations (Korteweg-de Vries equations) (35Q53) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items

On generating functions in the AKNS hierarchy, Seiberg-Witten theory as a Fermi gas, Glass-like transition described by toppling of stability hierarchy*, Partial differential systems with non-local nonlinearities: generation and solutions, Proofs of two conjectures related to the thermodynamic Bethe Ansatz, ABJM matrix model and 2D Toda lattice hierarchy, 40 bilinear relations of \(q\)-Painlevé VI from \(\mathcal{N} = 4\) super Chern-Simons theory, Semiclassical approach to form factors in the sinh-Gordon model, Soliton versus the gas: Fredholm determinants, analysis, and the rapid oscillations behind the kinetic equation, The algebraic structure of the non-commutative nonlinear Schrödinger and modified Korteweg-de Vries hierarchy, On linear systems and \(\tau\) functions associated with Lamé's equation and Painlevé's equation VI, Linear systems, Hankel products and the sinh-Gordon equation, Fredholm determinants and pole-free solutions to the noncommutative Painlevé II equation, ABJM theory as a Fermi gas, M-theoretic matrix models, Solvable statistical models on a random lattice, On the numerical evaluation of Fredholm determinants, Finite temperature correlations in the one-dimensional quantum Ising model, An integral operator solution to the matrix Toda equations

Cites Work

• Unnamed Item
• Unnamed Item
• Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent
• Bäcklund transformations and singular integral equations
• Linear integral equations and nonlinear difference-difference equations
• Linear integral transformations and hierarchies of integrable nonlinear evolution equations
• On a class of polynomials connected with the Korteweg-de Vries equation
• Holonomic quantum fields. I
• Fredholm determinants, differential equations and matrix models
• Differential equations for sine-Gordon correlation functions at the free fermion point
• Painlevé III and \(2\)D polymers
• On some linear integral equations generating solutions of nonlinear partial differential equations
• Painlevé functions of the third kind
• DIFFERENTIAL EQUATIONS FOR QUANTUM CORRELATION FUNCTIONS