Low Dimensional Electrons

Motivated by recent work on nano tubes indicating one dimensional quantum effects and studies of two dimensional electron gas, we consider a recent model of Fermions as Kerr-Newman type black holes with quantum mechanical effects. Such an anyonic fractionally charged quasi-electron picture is deduced and identified with quarks. Very recently experiments with nano tubes reveal one dimensional Quantum behaviour[1, 2]. On the other hand the study of the fractional quantum Hall effect leads to the study of a two dimensional electron gas, which can be realised for example in GaAs−AlxGa1−xAs semiconductor heterojunctions([3, 4] and references therein). In these low dimensions, we have to consider anyonic statistics with interesting applications[5]. In this note, we consider this problem from a different viewpoint viz., the recent description of electrons as Kerr-Newman type Black Holes in a Quantum Mechanical context[6, 7]. This will be shown to lead to the conclusion that at small length scales applicable in the cases mentioned above, electrons show precisely such an anyonic behaviour with the ”one third” effect built in. The corroboration from the Laughlin[8] analysis will be seen and implications in hadronic physics will emerge. In the Kerr-Newman approach referred to, it was seen that outside the Compton wavelength, the potential is given by ee r = A0 ≈ 2ch̄( mc h̄ ) ∫ η Tıj r dx (1) E-mail:[email protected]