Temperature correlators of the impenetrable Bose gas as an integrable system
type: Item
instance of: scholarly article
title: Temperature correlators of the impenetrable Bose gas as an integrable system
zbMATH Open document ID: 0698.60094
DOI: 10.1007/BF02096786
published in: Communications in Mathematical Physics
publication date: 1990-01-01T00:00:00Z
review text: The temperature equal-time correlators of impenetrable bosons in one space dimension are considered. First, the two-point field correlator and the generating functional for correlators of densities are expressed in terms of the Fredholm determinant of some integral operator. The kernel of this operator is constructed from the Fermi weight describing the thermal equilibrium distribution of particles. Then by considering the corresponding integral equation as a Gelfand- Levitan-Marchenko-type equation the classical integrable dynamical system is constructed. The solution to the equation of motion of the latter is simply related to the Fredholm determinant mentioned above. The multi- point correlators are treated in a similar way. The small-distance behaviour of two-point correlators are analyzed and a low density expansion is derived.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 82B10
Mathematics Subject Classification ID: 58Z05
zbMATH DE Number: 4145103
zbMATH Keywords: one-dimensional Bose gas
zbMATH Keywords: generating functional for correlators of densities
zbMATH Keywords: thermal equilibrium distribution of particles
zbMATH Keywords: Gelfand- Levitan-Marchenko-type equation
zbMATH Keywords: multi-point correlators
zbMATH Keywords: low density expansion
author: A. R. Its
author: A. G. Izergin
author: Vladimir E. Korepin
reviewed by: Paweł Maślanka
MaRDI profile type: Publication
cites work: Thermodynamics of a One-Dimensional System of Bosons with Repulsive Delta-Function Interaction
cites work: Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent
cites work: Q5485625
cites work: Dual field formulation of quantum integrable models
cites work: The direct linearization of a class of nonlinear evolution equations
description: scientific article; zbMATH DE number 4145103