OPTICAL-PROPERTIES OF QUANTUM WIRES - FERMI-EDGE SINGULARITY EXPONENTS AND THE LOW-DENSITY LIMIT

A simple many-body treatment of the Fermi-edge singularities in absorp tion and photoemission in quasi one-dimensional quantum wires is prese nted. The problem of calculating the transition probabilities is reduc ed to numerically evaluating a sufficient number of determinants descr ibing the overlap of the appropriate many-body wave functions. It is f ound that the edge singularity exponents can be determined from the si ze dependence of these determinants. The well-known connection between these exponents and the phase shifts at the Fermi surface are explici tly checked for one-dimensional quantum wires. The singular edge behav ior is interpreted in terms of Friedel's replacement transitions and i s found to be due to a replacement transition to the bound state, a re sult confirmed by considering the evolution of the spectra in the low- density limit.