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 can not 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 and vanishing effective range parameters. 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.

arXiv comment4+4 pages, 5+4 figures

References in corpus (19)

• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Universality in Few-body Systems with Large Scattering Length
• Evidence for Efimov quantum states in an ultracold gas of cesium atoms
• Jet Substructure at the Large Hadron Collider: A Review of Recent Advances in Theory and Machine Learning
• On Machine-Learned Classification of Variable Stars with Sparse and Noisy Time-Series Data
• Fermi systems with long scattering lengths
• Spin 1/2 Fermions in the Unitary Regime: A Superfluid of a New Type
• Deep learning and the Schrödinger equation
• Constraining Effective Field Theories with Machine Learning
• Machine Learning of Explicit Order Parameters: From the Ising Model to SU(2) Lattice Gauge Theory
• Predictions of nuclear $\beta$-decay half-lives with machine learning and their impacts on $r$ process
• SKYNET: an efficient and robust neural network training tool for machine learning in astronomy
• Nuclear Physics Around the Unitarity Limit
• Methodology study of machine learning for the neutron star equation of state
• Ground state energy of spin-1/2 fermions in the unitary limit
• Lattice Monte Carlo calculations for unitary fermions in a finite box
• A machine learning study to identify spinodal clumping in high energy nuclear collisions
• Fast supersymmetry phenomenology at the Large Hadron Collider using machine learning techniques
• Visualizing Neural Network Developing Perturbation Theory

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