Momentum distribution function of a narrow Hall bar in the FQHE regime

The momentum distribution function (n(k)) of a narrow Hall bar in the fractional quantum Hall effect regime is investigated using Luttinger liquid and microscopic many-particle wavefunction approaches. For wide Hall bars with filling factor nu = 1/M, where M is an odd integer, n(k) has singularities at +/- Mk(F). We find that for narrow Hall bars additional singularities occur at smaller odd integral multiples of k(F): n(k) similar to A(p) \k +/- pk(F)\(2 Delta p-1) near k = +/- pk(F), where p is an odd integer M, M - 2, M - 4,...,1. If inter-edge interactions can be neglected, the exponent 2 Delta(p) = (1/nu + p(2) nu)/2 is independent of the width (w) of the Hall bar but the amplitude of the singularity A(p) vanishes exponentially with w for p not equal M.