Sensitivity to lattice structure in the mesoscopic-loop models of planar systems. (English) Zbl 1142.81384

From the summary: As demonstrated in my recent article [the author, J. Geom. Phys. 55, No. 1, 1–18 (2005; Zbl 1078.81520)] mesoscopic feedback’, a certain extension of the Schrödinger equation – namely, an extension via the so-called mesoscopic loop – leads to a PDE model of systems operating in the quantum Hall regime. In the present article, we construct lattice-type solutions of the mesoscopic loop model with periodic potential. The method of construction is geometric, and leads to continuous strong solutions. At the same time, the result brings to light a constraint that the quantum Hall phenomenology imposes on the parameters of the model. This suggests that the model has the capacity to transcribe material-specific information inherent in the spatially distributed Hall conductance data outside the FQHE regime.


81V70 Many-body theory; quantum Hall effect
82D99 Applications of statistical mechanics to specific types of physical systems


Zbl 1078.81520