Tracing the parameter dependence of quantum resonances with numerical continuation
Wim Vanroose, J. Broeckhove, Przemysław Kłosiewicz · Journal of Physics B Atomic Molecular and Optical Physics · 2009
In molecular reactions at the microscopic level the appearance of resonances has an important influence on the reactivity. To study when a bound state transitions into a resonance and how these transitions depend on various system parameters such as internuclear distances, one needs to look at the poles of the S-matrix. Using numerical continuation methods and bifurcation theory, we develop efficient and robust methods to trace the parameter dependence of the poles of the S-matrix. Using pseudo-arclength continuation, we can minimize the numerical complexity of our algorithm. As a proof-of-concept we have applied our methods on a number of model problems.