Efficient discretization of the continuum through complex contour deformation

Instances of discrete states coupled to continua are physically ubiquitous. Numerical simulations of such systems often rely on a discrete representation of the continuum by a large but finite set of discrete levels, or "pseudostates." In this paper, we develop a method based on the prior work of Kazansky to derive an efficient discrete representation of an arbitrary continuum. For several test cases, our method allows the simulation of non-Markovian decay dynamics with a far smaller set of pseudostates than previously required. We also discuss how this approach can be viewed as a "complex scaling" of the band energy coordinate.