Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2001-05-03
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
submitted to Physical Review B
Scientific paper
We propose a model of an approximatively two--dimensional electron gas in a uniform electric and magnetic field and interacting with a positive background through the Fr\"ohlich Hamiltonian. We consider the stochastic limit of this model and we find the quantum Langevin equation and the generator of the master equation. This allows us to calculate the explicit form of the conductivity and the resistivity tensors and to deduce a {\it fine tuning condition} (FTC) between the electric and the magnetic fields. This condition shows that the $x$--component of the current is zero unless a certain quotient, involving the physical parameters, takes values in a finite set of physically meaningful rational numbers. We argue that this behaviour is quite similar to that observed in the quantum Hall effect. We also show that, under some conditions on the form factors entering in the definition of the model, also the plateaux and the "almost" linear behaviour of the Hall resistivity can be recovered. Our FTC does not distinguish between fractional and integer values.
Accardi Luigi
Bagarello Fabio
No associations
LandOfFree
The stochastic limit of the Fröhlich Hamiltonian: relations with the quantum Hall effect does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The stochastic limit of the Fröhlich Hamiltonian: relations with the quantum Hall effect, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The stochastic limit of the Fröhlich Hamiltonian: relations with the quantum Hall effect will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-477657