Long-time and large-distance asymptotic behavior of the current–current correlators in thenon-linear Schrödinger model

Abstract

We present a new method allowing one to derive the long-time and large-distanceasymptotic behavior of the correlation functions of quantum integrable modelsfrom their exact representations. Starting from the form factor expansion of thecorrelation functions in finite volume, we explain how to reduce the complexity of thecomputation in the so-called interacting integrable models to the one appearing infree fermion equivalent models. We apply our method to the time-dependentzero-temperature current–current correlation function in the non-linear Schrödinger modeland compute the first few terms in its asymptotic expansion. Our result goes beyond theconformal field theory based predictions: in the time-dependent case, excitationsother than the ones on the Fermi surface contribute to the leading orders of theasymptotics.