Applications of the Short-Time Approximation: The Unitary Fermi Gas and Neutrino-Nucleus Scattering*

With current and planned neutrino oscillation experiments, it has become increasingly important to develop an accurate theoretical understanding of neutrino-nucleus scattering and exclusive nuclear responses to weak probes. While there are accurate many-body methods to compute quasi-elastic responses to weak probes, they are computationally intensive and limited to the study of the inclusive responses. Recently, the short-time approximation (STA) was developed for the study of nuclear response functions and has been used to compute electromagnetic responses in $Ale 4$ nuclei. This approach, involving a factorization of the response into a two-nucleon component and a spectator system, consistently retains important two-body physics and quantum interference effects while also making possible the study of exclusive response functions. In this talk, I will discuss the theory underpinning the STA and extensions of this work to calculations of the density response in the unitary Fermi gas and the quasi-elastic neutral current response functions in $^2$H with the variational Monte Carlo method.