Morphology of three-body quantum states from machine learning

Huber, David; Marchukov, Oleksandr V.; Hammer, H.-W.; Volosniev, A. G.

doi:10.1088/1367-2630/ac0576

Cited by 6 publications

(2 citation statements)

References 79 publications

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“…There are theoretical examples in the literature of quantum systems with only 3 or 4 interacting particles that already exhibit chaotic properties. They include the cesium atom, which has 4 valence electrons [33]; systems composed of 4 particles of unequal masses in a harmonic trap [49] and 3 particles with unequal masses on a ring [54]; 3 or 4 excitations in spin-1/2 chains with short-range [94] or long-range couplings [115]; and even spin-1/2 chains with only 3 sites [77]. In the context of thermalization due to chaos, we also find works that obtained the Fermi-Dirac distribution in systems with only 4 particles [31,32,34,57,97].…”

Section: Introductionmentioning

confidence: 99%

Probing the edge between integrability and quantum chaos in interacting few-atom systems

Fogarty

García-March

Santos

et al. 2021

Quantum

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Interacting quantum systems in the chaotic domain are at the core of various ongoing studies of many-body physics, ranging from the scrambling of quantum information to the onset of thermalization. We propose a minimum model for chaos that can be experimentally realized with cold atoms trapped in one-dimensional multi-well potentials. We explore the emergence of chaos as the number of particles is increased, starting with as few as two, and as the number of wells is increased, ranging from a double well to a multi-well Kronig-Penney-like system. In this way, we illuminate the narrow boundary between integrability and chaos in a highly tunable few-body system. We show that the competition between the particle interactions and the periodic structure of the confining potential reveals subtle indications of quantum chaos for 3 particles, while for 4 particles stronger signatures are seen. The analysis is performed for bosonic particles and could also be extended to distinguishable fermions.

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Section: Introductionmentioning

confidence: 99%

Probing the edge between integrability and quantum chaos in interacting few-atom systems

Fogarty

García-March

Santos

et al. 2021

Quantum

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“…In other few-body calculations, ANNs were used to determine the deuteron wave function using variational optimization (Keeble and Rios, 2020). Three-body Efimov bound states were studied using ANNs (Saito, 2018), and CNNs were used to classify states of a three-body system (Huber et al, 2021). Variational Monte Carlo calculations optimized with ANNs have been performed for light nuclei with up to six nucleons (Adams et al, 2021;Gnech et al, 2022); see Fig.…”

Section: Effective Field Theory and A-body Systemsmentioning

confidence: 99%

Colloquium: Machine learning in nuclear physics

et al. 2022

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TABLE I. Table of ML methods discussed in this Colloquium with an indication of the main type of learning (S, supervised; U, unsupervised; semi-S, semisupervised). Acronym Method Description Learning type AE, VAE Autoencoders, Variational autoencoders ANN capable of learning efficient representations of the input data without any supervision U ANN Artificial neural network Models for learning defined by connected units (or nodes) and hidden layers with well-defined inputs and outputs S BED Bayesian experimental design Bayesian inference for experimental design S BM Boltzmann machine Generative ANN that can learn a probability distribution from sets of changing inputs U BMA, BMM Bayesian model averaging, Bayesian model mixing Bayesian inference applied to model selection or the combined estimation, or performed over a mixture model S BNN Bayesian neural network ANN where the parameters of the network are represented by probabilities learned by Bayesian inference S BO Bayesian optimization Optimization of functions without an a priori knowledge of functional forms. S and semi-S CNN Convolutional neural network ANN where convolution is used to reduce dimensionalities S EMB Ensemble methods and boosting Methods based on collections of decision trees as simple learners S GAN Generative adversarial network System of two ANNs where a generative network generates outputs while a discriminative network evaluates them U GP Gaussian process Collection of random variables that have a joint Gaussian distribution used in Bayesian inference Semi-S KNN k-nearest neighbors Nonparametric method where inputs consist of the k closest training examples in a dataset S KR Kernel regression Extension of linear regression methods to include nonlinear function kernels S LR Logistic regression Convex optimization method based on maximum likelihood estimate for classification problems S LSTM Long short-term memory RNN capable of learning long-term dependencies S PCA Principal component analysis Dimensionality reduction technique based on retaining the largest eigenvalues of the covariance matrix U REG Linear regression Linear algebra methods used for modeling continuous functions in terms of their explanatory variables S RL Reinforcement learning Learning achieved by trial and error of desired and undesired events Neither S nor U RNN Recurrent neural network ANN where connections between nodes allow for temporal dynamic behavior S SVM Support vector machine Convex optimization techniques with efficient ways to distinguish features in datasets S

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