Morphology of three-body quantum states from machine learning

Abstract

The relative motion of three impenetrable particles on a ring, in our case two identical fermions and one impurity, is isomorphic to a triangular quantum billiard. Depending on the ratio $\kappa$ of the impurity and fermion masses, the billiards can be integrable or non-integrable (also referred to in the main text as chaotic). To set the stage, we first investigate the energy level distributions of the billiards as a function of $1/\kappa \in [0,1]$ and find no evidence of integrable cases beyond the limiting values $1/\kappa =1$ and $1/\kappa =0$. Then, we use machine learning tools to analyze properties of probability distributions of individual quantum states. We find that convolutional neural networks can correctly classify integrable and non-integrable states.The decisive features of the wave functions are the normalization and a large number of zero elements, corresponding to the existence of a nodal line. The network achieves typical accuracies of 97%, suggesting that machine learning tools can be used to analyze and classify the morphology of probability densities obtained in theory or experiment.

arXiv commentversion accepted for publication in New Journal of Physics (Focus Issue on Machine Learning Across Physics)

References in corpus (39)

• Intriguing properties of neural networks
• Decoherence, einselection, and the quantum origins of the classical
• Machine learning and the physical sciences
• Understanding Black-box Predictions via Influence Functions
• Discovering Phase Transitions with Unsupervised Learning
• Fermi gases in one dimension: From Bethe Ansatz to experiments
• Machine learning quantum phases of matter beyond the fermion sign problem
• Discovering Phases, Phase Transitions and Crossovers through Unsupervised Machine Learning: A critical examination
• Remarks on the notion of quantum integrability
• Identifying Quantum Phase Transitions using Artificial Neural Networks on Experimental Data
• Machine Learning in Electronic Quantum Matter Imaging Experiments
• Linear and Nonlinear Theory of Eigenfunction Scars
• Machine learning meets quantum physics
• Classifying Snapshots of the Doped Hubbard Model with Machine Learning
• Experimental Characterization of Two-Particle Entanglement through Position and Momentum Correlations
• Analytical approach to the Bose polaron problem in one dimension
• 100 years of Weyl's law
• Effective approach to impurity dynamics in one-dimensional trapped Bose gases
• Quantum Lissajous Scars
• Nodal portraits of quantum billiards: Domains, lines, and statistics
• Strong-coupling Bose polarons in 1D: Condensate deformation and modified Bogoliubov phonons
• A variational approach to repulsively interacting three-fermion systems in a one-dimensional harmonic trap
• Impenetrable Mass-Imbalanced Particles in One-Dimensional Harmonic Traps
• Extreme gaps between eigenvalues of random matrices
• Revealing quantum chaos with machine learning
• Mean-field construction for spectrum of one-dimensional Bose polaron
• Phase Detection with Neural Networks: Interpreting the Black Box
• Diffractive scattering of three particles in one dimension: a simple result for weak violations of the Yang--Baxter equation
• Integrable families of hard-core particles with unequal masses in a one-dimensional harmonic trap
• Infinite Barriers and Symmetries for a Few Trapped Particles in One Dimension
• Contact and Structure Factor for Bosonic and Fermionic Mixtures
• Statistical properties of spectra in harmonically trapped spin-orbit coupled systems
• Resonant Population Transfer in the Time-Dependent Quantum Elliptical Billiard
• Exactly solvable quantum few-body systems associated with the symmetries of the three-dimensional and four-dimensional icosahedra
• Exact eigenfunction amplitude distributions of integrable quantum billiards
• Shear induced ordering in systems with competing interactions: A machine learning study
• Detecting composite orders in layered models via machine learning
• Mass-imbalanced atoms in a hard-wall trap: an exactly solvable model with emergent $D_6$ symmetry
• A Neural Network Perturbation Theory Based on the Born Series

Cited by in corpus (5)

• Machine Learning in Nuclear Physics
• Few-body Bose gases in low dimensions -- a laboratory for quantum dynamics
• Probing the edge between integrability and quantum chaos in interacting few-atom systems
• Unravelling quantum chaos using persistent homology
• Effective theory for strongly attractive one-dimensional fermions