Isospin composition of the high-momentum fluctuations in nuclei from asymptotic momentum distributions

Background: High-momentum nucleons in a nuclear environment can be associated with short-range correlations (SRC) that primarily occur between nucleon pairs. Observations and theoretical developments have indicated that the SRC properties can be captured by general quantitative principles that are subject to model dependence upon quantification. The variations in the aggregated effect of SRC across nuclei, however, can be quantified in an approximately model-independent fashion in terms of the so-called SRC scaling factors that capture the aggregated effect of SRC for a specific nucleus A relative to the deuteron (A-to-d). Purpose: We aim to provide predictions for the SRC scaling factors across the nuclear periodic table and determine the relative contribution of the different nucleon pair combinations to this quantity. We will also determine the SRC scaling factors for both bound protons and bound neutrons and study how these quantities evolve with the neutron-to-proton (N/Z) ratio in asymmetric nuclei. Methods: We employ the low-order correlation operator approximation (LCA) to compute the SRC contribution to the single-nucleon momentum distribution and ratios of A-to-d momentum distributions. We do this for a sample of fifteen nuclei from He to Pb, thereby gaining access to the evolution of the SRC scaling factor with the nuclear mass 4 <= A <= 208 and the neutron-to-proton ratio 1.0 <= N/Z <= 1.54. Results: We provide evidence for approximate A-to-d scaling of the single-nucleon momentum distribution at nucleon momenta exceeding about 4 fm(-1). For the studied sample of fifteen nuclei, the total SRC scaling factor is in the range 4.05-5.14, of which roughly 3 can be attributed to proton-neutron (pn) correlations. The SRC scaling factors receive sizable contributions from pp and nn correlations. They depend on the (N/Z) ratio reflecting the fact that the minority species (protons) becomes increasingly more short-range correlated with increasing (N/Z). We compare the computed SRC scaling factors in the LCA with those of ab initio calculations and with measured quantities from SRC-sensitive inclusive electron-scattering data. Conclusions: It is shown that the LCA provides predictions for the SRC scaling factors across the nuclear table that are in line with measured values. In asymmetric nuclei there are sizable differences between the SRC scaling factors for protons and neutrons. It is suggested that this phenomenon may impact the variations of the magnitude of the European Muon Collaboration (EMC) effect across nuclei. Our results corroborate the finding that SRC physics can be qualitatively understood by universal principles that build on local modifications of mean-field wave functions of nucleon pairs

Dynamical large deviations of two-dimensional kinetically constrained models using a neural-network state ansatz

We use a neural network ansatz originally designed for the variational optimization of quantum systems to study dynamical large deviations in classical ones. We obtain the scaled cumulant-generating function for the dynamical activity of the Fredrickson-Andersen model, a prototypical kinetically constrained model, in one and two dimensions, and present the first size-scaling analysis of the dynamical activity in two dimensions. These results provide a new route to the study of dynamical large-deviation functions, and highlight the broad applicability of the neural-network state ansatz across domains in physics

The isospin and neutron-to-proton excess dependence of short-range correlations

We provide a systematic study of the isospin composition and neutron-to-proton $\left( \frac{N}{Z} \right)$ ratio dependence of nuclear short-range correlations (SRC) across the nuclear mass table. We use the low-order correlation operator approximation (LCA) to compute the SRC contribution to the single-nucleon momentum distributions for 14 different nuclei from $A=4$ to $A=208$. Ten asymmetric nuclei are included for which the neutrons outnumber the protons by a factor of up to 1.54. The computed momentum distributions are used to extract the pair composition of the SRC. We find that there is a comprehensive picture for the isospin composition of SRC and their evolution with nucleon momentum. We also compute the non-relativistic kinetic energy of neutrons and protons and its evolution with nuclear mass $A$ and $\frac{N}{Z}$. Confirming the conclusions from alternate studies it is shown that the minority species (protons) become increasingly more short-range correlated as the neutron-to-proton ratio increases. We forge connections between measured nucleon-knockout quantities sensitive to SRC and single-nucleon momentum distributions. It is shown that the LCA can account for the observed trends in the data, like the fact that in neutron-rich nuclei the protons are responsible for an unexpectedly large fraction of the high-momentum components.Comment: 8 pages, 7 figure

Restricted Boltzmann machines for quantum states with non-abelian or anyonic symmetries

Although artificial neural networks have recently been proven to provide a promising new framework for constructing quantum many-body wave functions, the parametrization of a quantum wave function with non-abelian symmetries in terms of a Boltzmann machine inherently leads to biased results due to the basis dependence. We demonstrate that this problem can be overcome by sampling in the basis of irreducible representations instead of spins, for which the corresponding ansatz respects the non-abelian symmetries of the system. We apply our methodology to find the ground states of the one-dimensional antiferromagnetic Heisenberg (AFH) model with spin-1/2 and spin-1 degrees of freedom, and obtain a substantially higher accuracy than when using the s(z) basis as an input to the neural network. The proposed ansatz can target excited states, which is illustrated by calculating the energy gap of the AFH model. We also generalize the framework to the case of anyonic spin chains

Optical lattice experiments at unobserved conditions and scales through generative adversarial deep learning

Machine learning provides a novel avenue for the study of experimental realizations of many-body systems, and has recently been proven successful in analyzing properties of experimental data of ultracold quantum gases. We here show that deep learning succeeds in the more challenging task of modelling such an experimental data distribution. Our generative model (RUGAN) is able to produce snapshots of a doped two-dimensional Fermi-Hubbard model that are indistinguishable from previously reported experimental realizations. Importantly, it is capable of accurately generating snapshots at conditions for which it did not observe any experimental data, such as at higher doping values. On top of that, our generative model extracts relevant patterns from small-scale examples and can use these to construct new configurations at a larger size that serve as a precursor to observations at scales that are currently experimentally inaccessible. The snapshots created by our model---which come at effectively no cost---are extremely useful as they can be employed to quantitatively test new theoretical developments under conditions that have not been explored experimentally, parameterize phenomenological models, or train other, more data-intensive, machine learning methods. We provide predictions for experimental observables at unobserved conditions and benchmark these against modern theoretical frameworks. The deep learning method we develop here is broadly applicable and can be used for the efficient large-scale simulation of equilibrium and nonequilibrium physical systems

Social Stability and Extended Social Balance - Quantifying the Role of Inactive Links in Social Networks

Structural balance in social network theory starts from signed networks with active relationships (friendly or hostile) to establish a hierarchy between four different types of triadic relationships. The lack of an active link also provides information about the network. To exploit the information that remains uncovered by structural balance, we introduce the inactive relationship that accounts for both neutral and nonexistent ties between two agents. This addition results in ten types of triads, with the advantage that the network analysis can be done with complete networks. To each type of triadic relationship, we assign an energy that is a measure for its average occupation probability. Finite temperatures account for a persistent form of disorder in the formation of the triadic relationships. We propose a Hamiltonian with three interaction terms and a chemical potential (capturing the cost of edge activation) as an underlying model for the triadic energy levels. Our model is suitable for empirical analysis of political networks and allows to uncover generative mechanisms. It is tested on an extended data set for the standings between two classes of alliances in a massively multi-player on-line game (MMOG) and on real-world data for the relationships between countries during the Cold War era. We find emergent properties in the triadic relationships between the nodes in a political network. For example, we observe a persistent hierarchy between the ten triadic energy levels across time and networks. In addition, the analysis reveals consistency in the extracted model parameters and a universal data collapse of a derived combination of global properties of the networks. We illustrate that the model has predictive power for the transition probabilities between the different triadic states.Comment: 21 pages, 10 figure

Statistical physics of balance theory

Triadic relationships are accepted to play a key role in the dynamics of social and political networks. Building on insights gleaned from balance theory in social network studies and from Boltzmann-Gibbs statistical physics, we propose a model to quantitatively capture the dynamics of the four types of triadic relationships in a network. Central to our model are the triads’ incidence rates and the idea that those can be modeled by assigning a specific triadic energy to each type of triadic relation. We emphasize the role of the degeneracy of the different triads and how it impacts the degree of frustration in the political network. In order to account for a persistent form of disorder in the formation of the triadic relationships, we introduce the systemic variable temperature. In order to learn about the dynamics and motives, we propose a generic Hamiltonian with three terms to model the triadic energies. One term is connected with a three-body interaction that captures balance theory. The other terms take into account the impact of heterogeneity and of negative edges in the triads. The validity of our model is tested on four datasets including the time series of triadic relationships for the standings between two classes of alliances in a massively multiplayer online game (MMOG). We also analyze real-world data for the relationships between the “agents” involved in the Syrian civil war, and in the relations between countries during the Cold War era. We find emerging properties in the triadic relationships in a political network, for example reflecting itself in a persistent hierarchy between the four triadic energies, and in the consistency of the extracted parameters from comparing the model Hamiltonian to the data