Abstract
It is shown that the temperature equal-time correlators of impenetrable bosons in one space dimension are described by a classical integrable system. Partial differential equations for two-point as well as for multipoint correlators are obtained. The short-distance and low-density expansions are constructed.
Similar content being viewed by others
References
Mathematical physics in one dimension. Lieb, E.H., Mattis, D.S. (eds.). New York: Academic Press 1966
Yang, C.N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. J. Math. Phys.10, 1115–1122 (1969)
Lenard, A.: One-dimensional impenetrable bosons in thermal equilibrium. J. Math. Phys.7, 1268–1272 (1965)
Jimbo, A., Miwa, T., Mori, Y., Sato, M.: Density matrix of an impenetrable Bose gas and the fifth Painleve transcendent. Physica1 D, 80–158 (1980)
McCoy, B.M., Wu, T.T.: The two-dimensional Ising model. Cambridge, MA: Harvard University Press 1973
Korepin, V.E.: Dual field formulation of quantum integrable models. Commun. Math. Phys.113, 177–190 (1987)
Korepin, V.E.: Generating functional of correlation functions in completely integrable models. Funk Analiz i Ego Prilozh.23, 15–23 (1989)
Burtsev, S.P., Zacharov, V.E., Mikhailov, A.V.: Inverse scattering method with variable spectral parameter. Teor. Mat. Fiz.70, 323–342 (1987)
Krein, M.G.: On integral equations generating differential equations of the second order. Dokl. AN SSSR97, 21–24 (1954)
Krein, M.G.: On definition of potential of a particle in terms of itsS function. Dokl. AN SSSR105, 433–436 (1955)
Fokas, A.S., Ablowitz, M.J.: Linearization of the Korteweg-de Vries and Painleve II equations. Phys. Rev. Lett.47, 1096–1100 (1981)
Santini, P.M., Ablowitz, M.J., Fokas, A.S.: The direct linearization of a class of non-linear evolution equations. J. Math. Phys.25, 2614–2619 (1984)
Its, A.R., Izergin, A.G., Korepin, V.E.: Correlation radius for one-dimensional impenetrable bosons. ICTP, preprint IC/89/107
Author information
Authors and Affiliations
Additional information
Communicated by A. Jaffe
Rights and permissions
About this article
Cite this article
Its, A.R., Izergin, A.G. & Korepin, V.E. Temperature correlators of the impenetrable Bose gas as an integrable system. Commun.Math. Phys. 129, 205–222 (1990). https://doi.org/10.1007/BF02096786
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02096786