Recent developments of emulators for quantum continuum states

Quantum continuum states are numerically expensive to compute for systems with more than two particles. Repeating these calculations many times with different theory inputs is even more daunting. However, the outputs of those calculations are needed to explore the theory’s parameter space, for example, in the context of Bayesian model calibrations. To overcome these challenges, nuclear theorists are actively developing continuum-state emulators, which enable fast and accurate interpolations and extrapolations of theoretical calculations in their parameter spaces.

In this talk, I will use nuclear systems as examples to discuss a type of emulator based on the so-called reduced basis method (also known as eigenvector continuation in nuclear theory). I will illustrate how to apply this emulation to extrapolate continuum-state calculations at complex energies, where the calculations can be realized using bound-state methods, to the real energies and the region of the energy’s complex plane where resonances can be identified. In the latter region, traditional bound-state methods are not applicable. I will also show the emulator’s interpolation in the Hamiltonian’s parameter space. The connection between this emulator and the existing continuum calculation methods, including complex scaling and Berggren basis, will be discussed as well.