Plasmon Modes and Correlation Functions in Quantum Wires and Hall Bars
  We present microscopic derivations of the one-dimensional low-energy boson effective Hamiltonians of quantum wire and quantum Hall bar systems. The quantum Hall system is distinguished by its spatial separation of oppositely directed electrons. We discuss qualitative differences in the plasmon collective mode dispersions and the ground state correlation functions of the two systems which are consequences of this difference. The slowly-decaying quasi-solid correlations expected in a quantum wire are strongly suppressed in quantum Hall bar systems. 
U. Zuelicke, A. H. MacDonald