Orateur
Bernard Helffer
(U. Nantes, France)
Description
Consider a two-dimensional domain shaped like a wire, not
necessarily of uniform cross section. Let $V$ denote an electric
potential driven by a voltage drop between the conducting surfaces
of the wire. We consider the operator $A_h=-h^2\Delta+iV$ in the
semi-classical limit $h\to0$. We obtain both the asymptotic behaviour
of the left margin of the spectrum, as well as resolvent estimates
on the left side of this margin. We extend here previous results
obtained for potentials for which the set where the current (or $\nabla
V$) is normal to the boundary is discrete, in contrast with the
present case where $V$ is constant along the conducting surfaces.
Auteur principal
Bernard Helffer
(U. Nantes, France)
Co-auteur
Yaniv Almog
(Lousiana State U., États-Unis)
