Universal correlations of one-dimensional interacting electrons
at low density
Frank Göhmann
Abstract:
I report on a recent calculation of the asymptotics of dynamical
correlation functions of the impenetrable electron gas at finite
temperature. The calculation is based on a determinant representation
of the correlation functions. The determinant representation enables
the derivation of a nonlinear differential equation that drives the
correlations and of a corresponding Riemann-Hilbert problem. The
differential equation and the Riemann-Hilbert problem are used to
calculate the large-time, long-distance asymptotics of the correlation
functions. These asymptotics are universal for a large class of
interesting one-dimensional models of interacting electrons in their
low density phase, which has been called the gas phase.
(In collaboration with A.R. Its and V.E. Korepin.)