We propose a relation between the η invariant on a manifold with boundary, the η invariants
of edge states, and the η invariant in an infinite volume limit. With the example of planar …

Abstract The Integer Quantum Hall Effect transverse conductivity is derived assuming the
electrons form a lattice described by the doubly periodic states of Rodrigues and Doria …

The η invariant plays an important role in Quantum Field Theory. It describes the parity
anomaly [1–3] which leads to a Chern–Simons term in the effective action for gauge fields …

We study admissible boundary conditions for a charged quantum particle in a two-
dimensional region subjected to an external magnetic field, ie a quantum magnetic billiard …

Abstract The Integer Quantum Hall Effect transverse conductivityis retrieved in the framework
of doubly periodic states, obtained in Ref.~\cite {rodrigues21}, where electrons form a lattice …

A lattice of free electrons drifts perpendicularly to applied orthogonal magnetic field and
electric fields. We show that this electronic lattice state provides a straightforward description …