Dynamical properties of a two-dimensional electron gas in a magnetic fieldwithin the composite fermion model

We investigate the response of a two-dimensional electron gas, in the fract ional quantum Hall regime, to the sudden appearance of a localized charged probe: using the Chern-Simons theory of composite fermions. The dynamic str ucture factor of the electron gas is found to have a major influence on the spectral function of the probe. In particular, there is an orthogonality c atastrophe when the filling factor is an even-denominator filling fraction due to the compressibility of the slate, but there is no catastrophe at odd -denominator filling factors because these states have a gap to excitations . The catastrophe is found to be more severe for composite fermions in zero effective magnetic field than it is for electrons in zero real magnetic fi eld. Oscillations in the spectral function, arising when the composite ferm ions are at integer filling, have a period equal to the composite fermion c yclotron energy. We propose a tunneling experiment which directly measures the spectral function from which one could determine the composite fermion effective mass. [S0163-1829(98)04947-9].