Speaker
Description
Path integrals in real time are plagued by violently oscillatory phases, and Lefschetz thimble methods offer one of the cleanest ways to make sense of them — but only if the intersection numbers between thimbles and the original integration contour can be computed reliably. In practice, existing approaches have been limited to just one or two variables, leaving genuinely multivariable problems out of reach. I will present a stable numerical scheme that pushes this frontier dramatically. By recasting the upward flow from saddle points to the original cycle as a multiple shooting problem, the method delivers both the magnitudes and the signs of the intersection numbers, and remains well-behaved up to at least 20 variables — with quadruple precision extending its reach even further. I will apply the method to several complex saddles in a discretized real-time path integral, where it reveals new structural features of the thimble decomposition. The approach should be useful well beyond this setting, anywhere oscillatory integrals appear.