Collective Excitations in Realistic Quantum Wires
  We have used the Hartree-Fock Random Phase Approximation (HF-RPA) to study the interacting electron gas in a quantum wire. The spectra of intersubband spin-flip excitations reveal a considerable red shift with respect to single-particle HF energies. That signals on appearance of collective intersubband spind-density excitations due to the exchange interaction. The long wavelength dispersions of the intrasubband collective spin-density excitations are linear, but the sound velocities are renormalised due to the exchange interaction and screening. The in-phase intrasubband charge-density excitation has the long wavelength form $q[-\ln(q)]^{1/2}$. We found good qualitative agreement of our results with experimental observations. 
Arne Brataas, A. G. Mal'shukov, Vidar Gudmundsson and K. A. Chao