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We study a quantum point contact in the fractional quantum Hall regime atLandau level filling factors 1/3 and 5/2. By using exact diagonalizations inthe cylinder geometry we identify the edge modes in the presence of a parabolicconfining potential. By changing the sign of the potential we can access boththe tunneling through the bulk of the fluid and the tunneling between spatiallyseparated droplets. This geometry is realized in the quantum point contactgeometry for two-dimensional electron gases. In the case of the modelMoore-Read Pfaffian state at filling factor 5/2 we identify the conformaltowers of many-body eigenstates including the non-Abelian sector. By aMonte-Carlo technique we compute the various scaling exponents thatcharacterize the edge modes. In the case of hard-core interactions whose groundstates are exact model wavefunction we find equality of neutral and chargedvelocities for the Pfaffian state both bosonic and fermionic.

Many-body study of a quantum point contact in the fractional quantum Hall regime at v=5/2