Partition noise and statistics in the fractional quantum Hall effect

A microscopic theory of current partition in fractional quantum Hall liquids, described by chiral Luttinger liquids, is developed to compute the noise correlations, using the Keldysh technique. In this Hanbury-Brown and Twiss experiment, at fractional filling factors, the real time noise correlator exhibits oscillations which persist over larger time scales than that of an uncorrelated Hall fluid. For $\nu<1/2$, quasi-particle transfer process in the direction opposite to the bias contribute, suggesting that quasi-particles can overlap. Accordingly, the zero frequency noise correlations decrease (with decreasing filling factors) from their $\nu=1$ value and become positive for $\nu=1/3$. These positive correlations are interpreted in terms of the composite bosons obtained by flux tube attachment.