Nonequilibrium steady states on 1-d lattice systems and Goldstone theorem

摘要

On one-dimensional two-way infinite lattice system, a property of stationary(space-) translationally invariant states with nonvanishing currentexpectations are investigated. We consider GNS representation with respect tosuch a state, on which we have a group of space-time translation unitaryoperators. We show, by applying Goldstone-theorem-like argument,that spectrumof the unitary operators, energy-momentum spectrum with respect to the state,has a singularity at the origin.