arXiv subjects
Publications and source records attributed to F. Ghaboussi.
We discuss the relation between the Quantum Hall behaviour of charged carriers and their chaotic motion in phase space. It is shown that the quantum Hall diagram is comparable with the stepped diagram in phase space of a chaotic motion.
The physical content of Chern-Simons-action is discussed and it is shown that this action is proportional to the usual charged matter interaction term in electrodynamics.
It is shown that an observed length in the potential drops across IQHE samples is a universal length for a given magnetic field strength which has the magnitude equal to the reciprocal magnitude of magnetic length and which results from the quantum mechanical uncertainty relation in presence of magnetic field. The analytic solution of Ohm's equation for the potential in Corbino sample in IQHE is also given.
We discuss a model of both classical and integer quantum Hall-effect which is based on a semi-classical Schroedinger-Chern-Simons-action, where the Ohm-equations result as equations of motion. The quantization of the classical Chern-Simons-part of action under typical quantum Hall conditions results in the quantized Hall conductivity. We show further that the classical Hall-effect is described by a theory which arises as the classical limit of a theory of quantum Hall-effect. The model explains also the preference and the domain of the edge currents on the boundary of samples.
We discuss a model for the integer quantum Hall effect which is based on a Schroedinger-Chern-Simons-action functional for a non-interacting system of electrons in an electromagnetic field on a mutiply connected manifold. In this model the integer values of the Hall conductivity arises in view of the quantization of the Chern-Simons-action functional for electromagnetic potential.
We introduce a model of superconductivity and discuss its relation to the quantum Hall-effect. This kind of relation is supported by the well known SQUID results. The concept of pure gauge potential as it is involved in various theoretical models concerning solid state effects in magnetic fields is also discussed.