Related papers: Solving two and three-body systems with deep neura…
We use machine learning techniques to solve the nuclear two-body bound state problem, the deuteron. We use a minimal one-layer, feed-forward neural network to represent the deuteron S- and D-state wavefunction in momentum space, and solve…
We propose an enhanced machine learning method to calculate the ground state of two-body systems. By extending the original method [Naito, Naito, and Hashimoto, Phys. Rev. Research 5, 033189 (2023)], the present method enables consideration…
The three body problem is a special case of the n body problem where one takes the initial positions and velocities of three point masses and attempts to predict their motion over time according to Newtonian laws of motion and universal…
We study the possible existence of nonstrange dibaryons and tribaryons by solving the bound-state problem of the two- and three-body systems composed of nucleons and deltas. The two-body systems are $NN$, $N\Delta$, and $\Delta\Delta$,…
We study the three-body systems $DNN$ and $D^{*}NN$ within a hadronic molecular framework by combining a realistic nucleon-nucleon interaction with a $D^{(*)}N$ potential constrained by heavy-quark symmetry. The three-body Schr\"odinger…
This article presents an approach to the two-dimensional Schr\"odinger equation based on automatic learning methods with neural networks. It is intended to determine the ground state of a particle confined in any two-dimensional potential,…
The recently developed chiral nucleon-nucleon ($NN$) potential by Epelbaum \emph{et al.} has been employed to study the two-nucleon bound and scattering states. Chiral $NN$ potential up to next-to-next-to-next-to leading order (N$^3$LO) is…
Since its formulation by Sir Isaac Newton, the problem of solving the equations of motion for three bodies under their own gravitational force has remained practically unsolved. Currently, the solution for a given initialization can only be…
The challenge posed by the many-body problem in quantum physics originates from the difficulty of describing the non-trivial correlations encoded in the exponential complexity of the many-body wave function. Here we demonstrate that…
We combine density-functional tight-binding (DFTB) with deep tensor neural networks (DTNN) to maximize the strengths of both approaches in predicting structural, energetic, and vibrational molecular properties. The DTNN is used to learn a…
A machine learning technique to obtain the ground states of quantum few-body systems using artificial neural networks is developed. Bosons in continuous space are considered and a neural network is optimized in such a way that when particle…
In this paper, we introduce a novel approach to solve the many-body Schrodinger equation by the tensor neural network. Based on the tensor product structure, we can do the direct numerical integration by using fixed quadrature points for…
A long-standing goal of nuclear theory is to explain how the structure and dynamics of atomic nuclei and neutron-star matter emerge from the underlying interactions among protons and neutrons. Achieving this goal requires solving the…
Recent work in the literature has studied the restricted three-body problem within the framework of effective-field-theory models of gravity. This paper extends such a program by considering the full three-body problem, when the Newtonian…
This paper studies deep neural networks for solving extremely large linear systems arising from highdimensional problems. Because of the curse of dimensionality, it is expensive to store both the solution and right-hand side vector in such…
The three-neutron ($3n$) system is studied by numerical calculations with the Faddeev three-body formalism for a realistic nucleon-nucleon (NN) potential. A response function for the transition from ${}^3\mathrm{H}$ to $3n$ continuum states…
Deep neural network (DNN) and auto differentiation have been widely used in computational physics to solve variational problems. When DNN is used to represent the wave function to solve quantum many-body problems using variational…
We solve the Faddeev bound-state equations for three particles with simple two-body nonlocal, separable potentials that yield a scattering length twice as large as a positive effective range, as indicated by some lattice QCD simulations.…
We develop a computationally and numerically efficient method to calculate binding energies and corresponding wave functions of quantum mechanical three-body problems in low dimensions. Our approach exploits the tensor structure of the…
Machine learning techniques have proven to be effective in addressing the structure of atomic nuclei. Physics$-$Informed Neural Networks (PINNs) are a promising machine learning technique suitable for solving integro-differential problems…