Non-accretive Schr\"odinger operators and exponential decay of their   eigenfunctions
  We consider non-self-adjoint electromagnetic Schr\"odinger operators on arbitrary open sets with complex scalar potentials whose real part is not necessarily bounded from below. Under a suitable sufficient condition on the electromagnetic potential, we introduce a Dirichlet realisation as a closed densely defined operator with non-empty resolvent set and show that the eigenfunctions corresponding to discrete eigenvalues satisfy an Agmon-type exponential decay. 
David Krejcirik, Nicolas Raymond (IRMAR), Julien Royer (IMT), Petr   Siegl (IMSV)
math.SP math-ph math.AP math.MP