Theory of the Fractional Quantum Hall Effect

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9615005 Jain The present grant is to support the extension of earlier work by the PI on composite fermion description of the fractional quantum Hall effect. More specifically, the PI has devised a formalism to calculate the wave functions of the ground as well as the excited states for large systems using Monte Carlo techniques. The possibility of calculations in thermodynamic limit promises a quantitative understanding of various outstanding experimental issues. In particular the grant plans to calculate the energy gaps and collective mode dispersions at general fractions, degree of polarization including the Zeeman energy, transitions between the fractional quantum Hall states and a Wigner crystal and finally the response of a mesoscopic quantum dot to applied high magnetic fields. %%% The subject of fractional quantum Hall effect has been an active area in recent years, in significant part due to this PI's discovery of the composite fermion description. A serious limitation so far has been that the theoretical calculations are limited to system of smaller sizes, as opposed to the experiments which are generally for larger sizes. A significant development recently by the PI suggests possible removal of this limitation. This grant is to support calculations of various experimental observable in the large system limit. ***