Temperature correlators of the impenetrable Bose gas as an integrable system
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.
generating functional for correlators of densities
thermal equilibrium distribution of particles
Gelfand- Levitan-Marchenko-type equation
scientific article; zbMATH DE number 4145103