scholarly journals Ab initio solution of the many-electron Schrödinger equation with deep neural networks

2020 ◽  
Vol 2 (3) ◽  
Author(s):  
David Pfau ◽  
James S. Spencer ◽  
Alexander G. D. G. Matthews ◽  
W. M. C. Foulkes
Keyword(s):  
Neural Networks ◽  
Schrödinger Equation ◽  
Ab Initio ◽  
Schrodinger Equation ◽  
Deep Neural Networks ◽  
The Many

scholarly journals Quantum Lattice-Gas Models for the Many-Body Schrödinger Equation

1997 ◽  
Vol 08 (04) ◽  
pp. 705-716 ◽  
Author(s):  
Bruce M. Boghosian ◽  
Washington Taylor
Keyword(s):  
Schrödinger Equation ◽  
Arbitrary Number ◽  
Schrodinger Equation ◽  
Lattice Gas ◽  
Quantum Computer ◽  
Many Body ◽  
Lattice Gas Models ◽  
Many Body Systems ◽  
The Many ◽  
Classical Computer

A general class of discrete unitary models are described whose behavior in the continuum limit corresponds to a many-body Schrödinger equation. On a quantum computer, these models could be used to simulate quantum many-body systems with an exponential speedup over analogous simulations on classical computers. On a classical computer, these models give an explicitly unitary and local prescription for discretizing the Schrödinger equation. It is shown that models of this type can be constructed for an arbitrary number of particles moving in an arbitrary number of dimensions with an arbitrary interparticle interaction.

scholarly journals Hybrid nature of the abnormal solutions of the Bethe–Salpeter equation in the Wick–Cutkosky model

2021 ◽  
Vol 81 (1) ◽  
Author(s):  
J. Carbonell ◽  
V. A. Karmanov ◽  
H. Sazdjian
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Fock Space ◽  
Form Factors ◽  
Massless Particle ◽  
Ladder Approximation ◽  
Many Body ◽  
Relativistic Limit ◽  
Elastic Form ◽  
The Many

AbstractIn the Wick–Cutkosky model, where two scalar massive constituents interact by means of the exchange of a scalar massless particle, the Bethe–Salpeter equation has solutions of two types, called “normal” and “abnormal”. In the non-relativistic limit, the normal solutions correspond to the usual Coulomb spectrum, whereas the abnormal ones do not have non-relativistic counterparts – they are absent in the Schrödinger equation framework. We have studied, in the formalism of the light-front dynamics, the Fock-space content of the abnormal solutions. It turns out that, in contrast to the normal ones, the abnormal states are dominated by the massless exchange particles (by 90 % or more), what provides a natural explanation of their decoupling from the two-body Schrödinger equation. Assuming that one of the massive constituents is charged, we have calculated the electromagnetic elastic form factors of the normal and abnormal states, as well as the transition form factors. The results on form factors confirm the many-body nature of the abnormal states, as found from the Fock-space analysis. The abnormal solutions have thus properties similar to those of hybrid states, made here essentially of two massive constituents and several or many massless exchange particles. They could also be interpreted as the Abelian scalar analogs of the QCD hybrid states. The question of the validity of the ladder approximation of the model is also examined.

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