Properties of Stark Resonant States in Exactly Solvable Systems

Figure 1

An example contour in the complex plane that serves as a “complexified” spatial axis in a model of an open quantum system in which a non-Hermitian Hamiltonian (1) acts in the space of functions defined along the contour. Both smooth and piecewise linear contours are admissible for our purposes. In this example, the domain of the Hamiltonian would be specified by requiring that and that an analogue of Cauchy-Riemann condition, , is satisfied for derivatives along the contour for all . We also assume that the potential has a compact support with a “radius” smaller than , so that nonanalytic potentials can be considered.