Identify more effective integration contours for scattering calculations in dimensions greater than one

Develop integration contours that enable accurate and efficient Monte Carlo evaluation of scattering calculations in more than one spatial dimension using the analytic continuation framework and holomorphic gradient flow, overcoming the limitations observed with the contours constructed in this paper.

Background

Using the proposed multi-sheet contour deformation framework and a regulated holomorphic gradient flow, the authors successfully compute real-time scattering in one dimension with a Yukawa-like potential. However, they observe that the constructed contours are insufficient for extending these calculations to higher dimensions, indicating the need for improved contour design.

This open problem asks for the identification or construction of more effective contours suitable for multidimensional scattering problems where non-holomorphic actions arise, ensuring manageable average phase and practical Monte Carlo performance.