How machine learning conquers the unitary limit

Abstract

Machine learning has become a premier tool in physics and other fields of science. It has been shown that the quantum mechanical scattering problem cannot only be solved with such techniques, but it was argued that the underlying neural network develops the Born series for shallow potentials. However, classical machine learning algorithms fail in the unitary limit of an infinite scattering length. The unitary limit plays an important role in our understanding of bound strongly interacting fermionic systems and can be realized in cold atom experiments. Here, we develop a formalism that explains the unitary limit in terms of what we define as unitary limit surfaces. This not only allows to investigate the unitary limit geometrically in potential space, but also provides a numerically simple approach towards unnaturally large scattering lengths with standard multilayer perceptrons. Its scope is therefore not limited to applications in nuclear and atomic physics, but includes all systems that exhibit an unnaturally large scale.