Asymptotic analysis of dynamical correlation functions of the Lieb-Liniger model / Mikhail Minin. Wuppertal, October 2025
Inhalt
- 1 Introduction
- 1.1 The Lieb–Liniger model
- 1.2 Fredholm determinant representation
- 1.3 Long-time and large-distance asymptotics
- 1.4 Problem statement
- 2 Riemann–Hilbert analysis
- 2.1 Properties of integrable integral operators
- 2.2 First transformation of the matrix Riemann–Hilbert problem
- 2.3 Scalar Riemann–Hilbert problem
- 2.4 Factorization of the jump matrix
- 2.5 Jump matrix close to identity
- 2.6 Parametrix: local solution in the vicinity of the saddle point
- 2.7 Global solution
- 2.8 Solution of singular integral equation
- 2.9 Pole contributions: solution of the linear system
- 3 Asymptotic analysis: no poles on the real axis
- 3.1 Preparation for the asymptotic analysis: deformation of the contour
- 3.2 Parametrix
- 3.3 Solution of the singular integral equation
- 3.4 Integral over gamma0
- 3.5 Fredholm determinant asymptotics: no poles on the real axis
- 3.6 Integration constant
- 4 Asymptotic analysis: two poles on the real axis
- 5 Application to the impenetrable Bose gas
- 5.1 Specification of functions
- 5.2 Pole structure and contribution
- 5.3 Contribution of the solution of the scalar Riemann–Hilbert problem
- 5.4 Fredholm determinant asymptotics
- 5.5 Asymptotics of the field–field correlation function
- 5.6 Impenetrable Bose gas in thermal equilibrium: cross-checks
- 6 Summary and outlook
- A Logarithmic derivative of the Fredholm determinant
- B Construction of the parametrix
- C Pole contribution: the solution of a linear system
- D Functional identities
- Bibliography
- Acknowledgments