TIME AND TEMPERATURE-DEPENDENT CORRELATION-FUNCTIONS OF THE ONE-DIMENSIONAL IMPENETRABLE ELECTRON-GAS

We consider the one-dimensional delta-interacting electron gas in the case of infinite repulsion. We use determinant representations to stud y the long time, large distance asymptotics of correlation functions o f local fields in the gas phase. We derive differential equations whic h drive the correlation functions. Using a related Riemann-Hilbert pro blem we obtain formulae for the asymptotics of the correlation functio ns, which are valid at all finite temperatures. At low temperatures th ese formulae lead to explicit asymptotic expressions for the correlati on functions, which describe power law behavior and exponential decay as functions of temperature, magnetic field and chemical potential.