A study of correlation functions for the delta-function Bose gas
type: Item
instance of: scholarly article
title: A study of correlation functions for the delta-function Bose gas
zbMATH Open document ID: 0603.58052
DOI: 10.1016/0167-2789(86)90029-1
author: Dennis B. Creamer
author: Harry B. Thacker
author: David Wilkinson
published in: Physica D
publication date: 1986-01-01T00:00:00Z
review text: The Gel'fand-Levitan equation for the quantum nonlinear Schrödinger field theory is used to investigate the correlation functions of the delta-function Bose gas. Operator expressions are derived for the field and for nonlocal products of fields in terms of the quantized reflection operators which create and annihilate eigenstates of the Hamiltonian. For the two-point function, an explicit series expression is obtained in which the nth term is determined by well-defined n-body combinatorics in an infinite volume. The inductive properties of this series are discussed and used to express the temperature and chemical potential dependence of the correlation functions entirely in terms of previously known thermodynamic functions. The zero separation limit of the series for the two-point function reproduces the thermodynamics derived by Yang and Yang, while the infinite coupling limit gives the Fredholm determinant result of Schultz and Lenard. The latter is related to the Painlevé V equation by the monodromy arguments of Jimbo, Miwa, Mori, and Sato. The \({\mathcal O}(1/c)\) correction to the large coupling limit is calculated from the Gel'fand-Levitan series and expressed in terms of solutions to Painlevé V. The asymptotic behavior of the relevant Painlevé function is discussed and related to the long range behavior of the correlation function.
Mathematics Subject Classification ID: 58J90
Mathematics Subject Classification ID: 81T99
Mathematics Subject Classification ID: 82B40
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 3973923
zbMATH Keywords: Gel'fand-Levitan equation
zbMATH Keywords: quantum nonlinear Schrödinger field theory
zbMATH Keywords: Bose gas
zbMATH Keywords: nonlocal products of fields
zbMATH Keywords: quantized reflection operators
zbMATH Keywords: zero separation limit
zbMATH Keywords: two-point function
MaRDI profile type: Publication
full work available at URL: 0167-2789(86)90029-1
OpenAlex ID: W1979897438
cites work: Q3361250
cites work: Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent
cites work: Correlation functions of the one-dimensional Bose gas in the repulsive case.
cites work: Inverse scattering transform as an operator method in quantum field theory
cites work: Painlevé functions of the third kind
description: scientific article; zbMATH DE number 3973923