TEMPERATURE DEPENDENCE OF INFRARED DIVERGENCE IN DEGENERATE FERMI GAS

A sudden change in a short-range single-particle potential excites an infinite number of low-energy particlehole pairs in a degenerate Fermion gas. Although each order of perturbation theory diverges, the perturbation series can be summed formally. The sum agrees in the limit of zero temperature with a result due to Nozières and De Dominicis. At finite temperature, it confirms a conjecture of Anderson's. The excitation spectrum at energies that are small compared to the temperature can be interpreted in terms of a relaxation frequency, which is proportional to the temperature times the square of the phase shift. © 1969 The American Physical Society.