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 geometry, at Laughlin filling factors $\nu =1\mathrm{}/3$, the real time noise correlator exhibits oscillations which persist over larger time scales than that of an uncorrelated Hall fluid. The zero frequency noise correlations are negative at filling factor $1/3$ as for bare electrons (antibunching), but are strongly reduced in amplitude. These correlations become positive (bunching) for $\nu \le 1/5$, suggesting a tendency towards bosonic behavior.