Quantum transport in disordered systems under magnetic fields: a study based on operator algebras (Q2854209)

The author, in the framework of \(C^*\)-algebras and noncommutative calculi, develops a canonical finite-volume approximation to the exact noncommutative Kubo formula with dissipation which is suitable for computer simulations. A rigorous error bound for this approximate formula is established. Moreover, he proves that such an error vanishes in the thermodynamic limit.NEWLINENEWLINEA numerical algorithm for the computation of the conductivity tensor in disordered systems under a magnetic field is devised and applications to the integer quantum Hall effect are presented. For a lattice model of a disordered two-dimensional electron gas, subject to a perpendicular magnetic field, the author computes the resistivity tensor in correspondence of several Fermi energies while holding the magnetic field constant. Also, simulations with varying magnetic fluxes, holding the electron density fixed, are performed. The typical Hall plateau is obtained in a sharp and well quantized form.