Abstract

There is a huge literature on Schrodinger or Pauli operators with fixed exterior magnetic fields. If however the magnetic field is not given a-priori but is the field generated by the charged particles themselves we get the coupled Shrodinger-Maxwell or Pauli-Maxwell systems. I will discuss the spectral theory and what is known, but in particular what is not known for these systems. It is known that there is stability of matter for both the Schrodinger and Pauli systems. It is however an open problem if there is existence of the thermodynamic limit. Depending on the coupling strength to the magnetic field it is also known that the semiclassical Weyl law sometimes holds and sometimes does not. A semiclassical eigenvalue estimate that holds generally in all regimes is not known.

The work on stablity of matter is joint work with Lieb and Loss from 1995. The work on semiclassics is more recent work with Erdos and Fournais.