Johannes Kellendonk
Gap labelling and the pressure on the boundary
(283K, pdf-file)
ABSTRACT. In quantum systems described by families of $1$-particle
Schr\"odinger operators on half-spaces the pressure on the boundary
per unit energy is topologically quantised if
the Fermi energy lies in a gap of the bulk spectrum.
Its relation with the integrated density of states can be expressed in
an integrated version of Streda's formula.
This leads also to a gap labelling
theorem for systems with constant magnetic field.
The proof uses non-commutative topology.