The density of states of one-dimensional disordered electron systems with long range Coulomb interaction is studied in the weak pinning limit. The density of states is found to follow a power law with an exponent determined by localization length, and this power law behavior is consistent with the existing numerical results.Comment: RevTeX4 file, 5 pages, no figures To appear in Physical Reviews

The optical conductivities of two one-dimensional narrow-gap semiconductors, anticrossing quantum Hall edge states and carbon nanotubes, are studied using bosonization method. A lowest order renormalization group analysis indicates that the bare band gap can be treated perturbatively at high frequency/temperature. At very low energy scale the optical conductivity is dominated by the excitonic contribution, while at temperature higher than a crossover temperature the excitonic features are eliminated by thermal fluctuations. In case of carbon nanotubes the crossover temperature scale is estimated to be 300 K.

We study a model of the quantum critical point of cuprates associated with the "circulating current" order parameter proposed by Varma. An effective action of the order parameter in the quantum disordered phase is derived using functional integral method, and the physical properties of the normal state are studied based on the action. The results derived within the ladder approximation indicate that the system is like Fermi liquid near the quantum critical point and in disordered regime up to minor corrections. This implies that the suggested marginal Fermi liquid behavior induced by the circulating current fluctuations will come in from beyond the ladder diagrams.

Resonant Raman scattering of degenerate interacting two-channel quantum wire is studied. All collective excitations of two-channel quantum wire are shown to give rise to peaks in the polarized Raman spectra near resonance. If there exist certain symmetries among interactions, a resonant peak can also appear in the depolarized Raman spectra, in constrast to the single-channel case studied by Sassetti and Kramer. We also calculate the explicit form of the scattering cross-section away from the peaks. The above features may be experimentally verified in armchair carbon nanotube systems.