Semiclassical asymptotics for exchange energy
Semiclassics of the quantum current in very strong magnetic fields
We prove a formula for the current in an electron gas in a semiclassical limit corresponding to strong, constant, magnetic fields. Little regularity is assumed for the scalar potential . In particular, the result can be applied to the mean field from magnetic Thomas-Fermi theory . The proof is based on an estimate on the density of states in the second Landau band.
Solitons and Gibbs Measures for Nonlinear Schrödinger Equations
We review some recent results concerning Gibbs measures for nonlinear Schrödinger equations (NLS), with implications for the theory of the NLS, including stability and typicality of solitary wave structures. In particular, we discuss the Gibbs measures of the discrete NLS in three dimensions, where there is a striking phase transition to soliton-like behavior.
Stability of matter in classical and quantized fields.
Stark resonances for random potentials of Anderson type
SUSY quantum Hall effect on non-anti-commutative geometry.
Système à corps dans un champ magnétique