The Steepest Slope toward a Quantum Few-body Solution - SCOOL
Pré-Publication, Document De Travail Année : 2024

The Steepest Slope toward a Quantum Few-body Solution

Résumé

Quantum few-body systems are deceptively simple. Indeed, with the notable exception of a few special cases, their associated Schr\"{o}dinger equation cannot be solved analytically for more than two particles. One has to resort to approximation methods to tackle quantum few-body problems. In particular, variational methods have been proposed to ease numerical calculations and obtain precise solutions. One such method is the Stochastic Variational Method, which employs a stochastic search to determine the number and parameters of correlated Gaussian basis functions used to construct an ansatz of the wave function. Stochastic methods, however, face numerical and optimization challenges as the number of particles increases. We introduce a family of gradient variational methods that replace stochastic search with gradient optimization. We comparatively and empirically evaluate the performance of the baseline Stochastic Variational Method, several instances of the gradient variational method family, and some hybrid methods for selected few-body problems. We show that gradient and hybrid methods can be more efficient and effective than the Stochastic Variational Method. We discuss the role of singularities, oscillations, and gradient optimization strategies in the performance of the respective methods.
Fichier principal
Vignette du fichier
main.pdf (743.5 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04672894 , version 1 (19-08-2024)

Licence

Identifiants

Citer

Paolo Recchia, Debabrota Basu, Mario Gattobigio, Christian Miniatura, Stéphane Bressan. The Steepest Slope toward a Quantum Few-body Solution. 2024. ⟨hal-04672894⟩
18 Consultations
4 Téléchargements

Altmetric

Partager

More