Appears in collection : Mathematical aspects of physics with non-self-adjoint operators / Les aspects mathématiques de la physique avec les opérateurs non-auto-adjoints
We consider the operator $\mathcal{A}_h = -h^2 \Delta + iV$ in the semi-classical limit $h \to 0$, where $V$ is a smooth real potential with no critical points. We obtain both 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 the Dirichlet realization of $\mathcal{A}_h$ by removing significant limitations that were formerly imposed on $V$. In addition, we apply our techniques to the more general Robin boundary condition and to a transmission problem which is of significant interest in physical applications.
By Alexandru Ionescu
By Scott Armstrong
