Abstract:
Painlevé analysis of correlation functions of the impenetrable Bose gas by M. Jimbo, T. Miwa, Y. Mori and M. Sato [1] was based on the determinant representation of these correlation functions obtained by A. Lenard [2]. The impenetrable Bose gas is the free fermionic case of the quantum nonlinear Schrödinger equation. In this paper we generalize the Lenard determinant representation for \(\langle \psi (0,0)\psi^{\dagger}(x,t)\rangle\) to the non-free fermionic case. We also include time and temeprature dependence. In forthcoming publications we shall perform the JMMS analysis of this correlationl function. This will give us a completely integrable equation and asymptotic for the quantum correlation function of interacting fermions.
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Received: 11 January 1997 / Accepted: 21 February 1997
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Kojima, T., Korepin, V. & Slavnov, N. Determinant Representation for Dynamical Correlation Functions of the Quantum Nonlinear Schrödinger Equation . Comm Math Phys 188, 657–689 (1997). https://doi.org/10.1007/s002200050182
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DOI: https://doi.org/10.1007/s002200050182