arXiv subjects

Xilin Zhang

Publications and source records attributed to Xilin Zhang.

At least 19 recordsLinked to original sources

arXiv2026

Reduced-basis method for linear response within nuclear density functional theory

Background: The quasiparticle random-phase approximation (QRPA) within nuclear density functional theory provides a powerful framework for describing collective excitations. Although the finite-amplitude method (FAM) efficiently solves the QRPA problem, repeated calculations for different external-field parameters remain computationally demanding. Purpose: We construct a reduced basis method (RBM)-based emulator for the FAM that treats the complex energy of the external field as a model parameter to efficiently reproduce FAM amplitudes and QRPA eigenmodes. Methods: High-fidelity FAM calculations are performed at a small set of training points in the complex-energy plane. The resulting FAM amplitudes form a non-orthogonal reduced basis. A variational equation yields an emulator that can predict the response at arbitrary complex energies and QRPA eigensolutions without additional full FAM calculations. Results: The RBM emulator accurately reproduces FAM strength distributions in both giant-resonance and low-energy regions when the relevant energy domain is covered by the training set. It also reproduces imaginary QRPA modes associated with shape instabilities of the HFB state. Applied to the $K^π=0^+$ mode of rare-earth Dy isotopes in a realistic model space, the emulator reproduces strength distributions and the lowest $0^+$ collective states with precision comparable to full FAM calculations, reducing the computational cost by more than an order of magnitude. Conclusions: The RBM provides an efficient and accurate FAM emulator. Its ability to reproduce giant-resonance, low-energy, and imaginary-energy modes at drastically reduced computational cost makes it promising for density-functional optimization, calculations of collective inertia, and large-scale surveys of nuclear collective excitations.

nucl-th↗

arXiv2026

LLM Biases

Transformer-based agentic AI is rapidly being deployed on major platforms to help users shop, watch, and navigate content with less effort. While these systems can deliver impressive performance, a key concern is whether they may be less reliable than they appear. We ask a simple but fundamental question: whether the mechanisms that make transformer-based agents effective can also induce systematic biases or distortions? We study this question through a theoretical analysis of transformer-based generative recommenders, in which the next user interaction is generated sequentially from the user history. Focusing on how the model allocates attention across historical evidence, we identify four bias channels: (i) Positional bias: stronger positional encoding shifts influence toward recent history, improving responsiveness but potentially reducing stability and long-term diversity; (ii) Popularity amplification: small frequency differences in data can be magnified into disproportionate exposure, contributing to Matthew effects and echo chambers; (iii) Latent driver bias: when important drivers of user choices are not directly observed, the model can place overly concentrated weight on a small subset of past events, creating overconfident attributions. (iv) Synthetic data bias: when users increasingly follow AI suggestions and platforms retrain on model-shaped synthetic logs, outputs can concentrate over time, and long-tail alternatives can disappear first. Our analysis highlights mechanism-level reliability risks that may not be visible in offline performance metrics. The four bias channels indicate that large-scale deployment may systematically distort exposure and choice. For managers, the immediate implication is to treat these as operational risk factors and to monitor concentration and drift over time, rather than assuming that performance gains alone guarantee reliability.

cs.CY↗

arXiv2025

Controlled Gate Networks: Theory and Application to Eigenvalue Estimation

We introduce a new scheme for quantum circuit design called controlled gate networks. Rather than trying to reduce the complexity of individual unitary operations, the new strategy is to toggle between all of the unitary operations needed with the fewest number of gates. We present the general theory of controlled gate networks and show that, under quite general conditions, it can significantly reduce the number of two-qubit gates needed to produce linear combinations of unitary operators. The first example we consider is a variational subspace calculation for a two-qubit system. The second example is estimating the eigenvalues of a two-qubit Hamiltonian via the rodeo algorithm using operators that we call controlled reversal gates. We use the Quantinuum H1-2 and IBM Perth devices to realize the quantum circuits. The third example is the application of controlled gate networks to the controlled time evolution of a free nucleon on a three-dimensional lattice. For all of the examples, we show very substantial reductions in the number of two-qubit gates required. Our work demonstrates that controlled gate networks are a useful tool for reducing gate complexity in quantum algorithms for quantum many-body problems such as those relevant to nuclear physics.

quant-ph↗

arXiv2025

Emulation of Proton-Deuteron Scattering via the Reduced Basis Method and Active Learning: Detailed Description

Nucleon-deuteron ($Nd$) scattering can be used to constrain three-nucleon forces in chiral effective field theory ($χ$EFT). However, high-fidelity calculations, such as the Hyperspherical Harmonic (HH) method, are computationally expensive, making it difficult or even prohibitive to explore the vast parameter space of $χ$EFT\xspace. To address this challenge, specifically for proton-deuteron ($pd$) scattering below the deuteron breakup threshold, we developed model-driven emulators based on the Reduced Basis Method (RBM) and active learning techniques, as presented in \href{https://arxiv.org/abs/2511.01844}{arXiv:2511.01844}. The method exploits the similarities between solutions at different parameter points to significantly reduce computational costs. In this companion paper, we provide a comprehensive description of our HH-based high-fidelity calculations and implementation of both variational-method-based and Galerkin-projection-based scattering emulators. We demonstrate the effectiveness of active learning in the form of greedy algorithms for selecting optimal training points in the parameter space, and the high accuracy and speed of the emulators, for two different nucleon forces and two scattering channels (${1/2}^+$ and ${1/2}^-$). For example, in a two-dimensional parameter space, the relative emulation errors can be reduced to $10^{-7}$ with fewer than 10 training points. Our work paves the way for the efficient calibration of $χ$EFT\xspace nucleon interactions using Bayesian statistics, and the methodology can be applied to other nuclear scattering processes (including neutron-deuteron scattering), as well as other finite quantum systems.

nucl-th↗

arXiv2025

Non-Hermitian quantum mechanics approach for extracting and emulating continuum physics based on bound-state-like calculations: Detailed description

This work applies a reduced basis method to study the continuum physics of a finite quantum system -- either few or many-body. Specifically, I develop reduced-order models, or emulators, for the underlying inhomogeneous Schrödinger equation and train the emulators against the equation's bound-state-like solutions at complex energies. The emulators rapidly and accurately interpolate and extrapolate the matrix elements of the Hamiltonian resolvent operator (Green's function) across a parameter space that includes both complex energy and other real-valued physical inputs in the Schrödinger equation. The spectra, discretized and compressed as the result of emulation, and the associated resolvent matrix elements (or amplitudes), have the defining characteristics of non-Hermitian quantum mechanics calculations, featuring complex eigenenergies with negative imaginary parts and branch cuts moved below the real axis in the complex energy plane. Therefore, one now has a method that extracts continuum physics from bound-state-like calculations and emulates those extractions in the input parameter space. Building on a prior Letter [arXiv:2408.03309], this article provides the full theoretical details, a comprehensive analysis of the method's performance, and a brief discussion of how it can be coupled with existing continuum approaches to perform emulations in their input parameter spaces.

nucl-th↗

arXiv2025

Non-Hermitian Quantum Mechanics Approach for Extracting and Emulating Continuum Physics Based on Bound-State-Like Calculations

This work introduces a unified emulation framework for studying continuum physics in finite quantum systems. Using a reduced basis method, we construct powerful emulators for the inhomogeneous Schrödinger equation that operate in a combined parameter space of complex energy ($E$) and other inputs ($\bmθ$). Within the space, the emulators simultaneously perform analytical continuation in $E$ -- extracting continuum physics from numerically simpler bound-state-like calculations -- and interpolate this entire process across $\bmθ$. This yields a small, non-Hermitian system whose properties (e.g., resonances and scattering observables) can be rapidly predicted for any $\bmθ$. Crucially, the complex-$E$ emulation provides a pathway to compute continuum observables for complex systems where advanced bound-state methods exist but direct continuum calculations are yet to be developed, while the $\bmθ$-emulation enables rapid parameter-space exploration and can be adapted to accelerate other existing continuum calculations. Demonstrations with two- and three-body systems highlight the method's effectiveness and suggest its connection to (near-)optimal rational approximation. This Letter presents the key results, with further details reserved for a companion paper.

nucl-th↗

arXiv2025

Accurate and Efficient Emulation of Proton-Deuteron Scattering via the Reduced Basis Method and Active Learning

We introduce highly accurate and efficient emulators for proton-deuteron scattering below the deuteron breakup threshold. We explore two different reduced-basis method strategies: one based on the Kohn variational principle and another on Galerkin projections of the underlying system of linear equations. We use the adaptive greedy algorithm previously developed for two-body scattering for optimal selection of high-fidelity training points in the input parameter space. We demonstrate that these emulators reproduce ab initio hyperspherical harmonics calculations of $R$-matrix elements with remarkable precision, achieving relative errors as low as $10^{-7}$ with a small number of training points, even in regions of strong nonlinear parameter dependence. They also dramatically accelerate the exploration of the scattering predictions in the parameter space, a capability highly desired for calibrating (chiral) three-nucleon forces against scattering measurements. Our formalism can be further generalized to handle nucleon-deuteron scattering above the breakup threshold. These emulator developments will provide valuable tools to accelerate uncertainty quantification and rigorous parameter inference in the study of nuclear forces.

nucl-th↗

arXiv2025

Data-driven trap theory for nuclear scattering

We present a novel data-driven trap theory (abbreviated as DDTT) for nuclear scattering, which aims to overcome the limitations of the traditional trap method in dealing with narrow potential wells, while also providing a more efficient framework for handling long-range Coulomb interactions. As proof-of-concept examples, we employ this unified theory to analyze the elastic scattering of nucleon-nucleon and nucleon-α systems. DDTT can successfully produce results consistent with those from traditional approaches, highlighting its significance for ab initio light nuclei scattering studies and potential for applications in the heavier mass region.

nucl-th↗

arXiv2025

Alter-magnetic properties in the perovskite compounds

Our high-throughput computational screening of the Materials Project database has identified 140 candidate materials exhibiting antiferromagnetic behavior in the $Pnma$ space group. Through systematic density functional theory calculations comparing various magnetic configurations, we demonstrate that 91 of these compounds preferentially stabilize in altermagnetic ground states, with 20 adopting the perovskite structure. Using NaCoF$_3$ as a prototypical example, we perform a comprehensive investigation of its electronic structure, magnetic ordering, and orbital configurations. Our analysis reveals that the magnetic Co$^{2+}$ ions occupy the 4c Wyckoff position and support three distinct antiferromagnetic (AFM) phases, among which the $G$-AFM configuration emerges as the ground state. Detailed symmetry analysis uncovers that the inter-sublattice coupling in the $G$-AFM phase is mediated by the combined time-reversal and rotation operation $\hat{T}\{R_{2x}|\frac{1}{2}\frac{1}{2}0\}$. This unique symmetry protection gives rise to several remarkable physical phenomena: (i) anisotropic optical conductivity, (ii) prominent anomalous transport effects including the anomalous Hall effect (AHE), Nernst effect (ANE), and thermal Hall effect (ATHE), and (iii) strong magneto-optical responses manifested through both Kerr and Faraday effects.

cond-mat.mtrl-sci↗

arXiv2025

Nuclear responses with neural-network quantum states

We introduce a variational Monte Carlo framework that combines neural-network quantum states with the Lorentz integral transform technique to compute the dynamical properties of self-bound quantum many-body systems in continuous Hilbert spaces. While broadly applicable to various quantum systems, including atoms and molecules, in this initial application we focus on the photoabsorption cross section of light nuclei, where benchmarks against numerically exact techniques are available. Our accurate theoretical predictions are complemented by robust uncertainty quantification, enabling meaningful comparisons with experiments. We demonstrate that a simple nuclear Hamiltonian, based on a leading-order pionless effective field theory expansion and known to accurately reproduce the ground-state energies of nuclei with $A\leq 20$ nucleons also provides a reliable description of the photoabsorption cross section.

nucl-th↗

arXiv2024

Motivations for Early High-Profile FRIB Experiments

This white paper is the result of a collaboration by those that attended a workshop at the Facility for Rare Isotope Beams (FRIB), organized by the FRIB Theory Alliance (FRIB-TA), on Theoretical Justifications and Motivations for Early High-Profile FRIB Experiments. It covers a wide range of topics related to the science that will be explored at FRIB. After a brief introduction, the sections address: (II) Overview of theoretical methods, (III) Experimental capabilities, (IV) Structure, (V) Near-threshold Physics, (VI) Reaction mechanisms, (VII) Nuclear equations of state, (VIII) Nuclear astrophysics, (IX) Fundamental symmetries, and (X) Experimental design and uncertainty quantification.

nucl-th↗

arXiv2024

The lowest-radiation environments in the Solar System: new opportunities for underground rare-event searches

We study neutrino, muon, and gamma-ray fluxes in extraterrestrial environments in our Solar System via semi-analytical estimates and Monte Carlo simulations. In sites with negligible atmosphere, we find a strong reduction in the cosmic-ray-induced neutrino and muon fluxes relative to their intensities on Earth. Neutrinos with energies between 50 MeV and 100 TeV show particularly strong suppression, by as much as 10$^3$, even at shallow depths. The solar neutrino suppression increases as the square of the site's distance from the Sun. Natural radiation due to nuclear decay is also expected to be lower in many of these locations and may be reduced to effectively negligible levels in the liquid water environments. The sites satisfying these characteristics represent an opportunity for greatly extending the physics reach of underground searches in fundamental physics, such as searches for WIMP Dark Matter, neutrinoless double-beta decay, the diffuse supernova neutrinos, and neutrinos from nearby supernova. As a potential near-term target, we propose a measurement of muon and gamma-ray fluxes in an accessible underground lunar site such as the Mare Tranquillitatis Pit to perform a first measurement of the prompt component in cosmic-ray-induced particle production, and to constrain lunar evolution models.

hep-ex↗

arXiv2023

Online Stochastic Allocation of Reusable Resources

We study a multi-objective model on the allocation of reusable resources under model uncertainty. Heterogeneous customers arrive sequentially according to a latent stochastic process, request for certain amounts of resources, and occupy them for random durations of time. The decision maker's goal is to simultaneously maximize multiple types of rewards generated by the customers, while satisfying the resource capacity constraints in each time step. We develop models and algorithms for deciding on the allocation actions. We show that when the usage duration is relatively small compared with the length of the planning horizon, our policy achieves $1-O(ε)$ fraction of the optimal expected rewards, where $ε$ decays to zero at a near optimal rate as the resource capacities grow.

math.OC↗

arXiv2023

Wave-function-based emulation for nucleon-nucleon scattering in momentum space

Emulators for low-energy nuclear physics can provide fast & accurate predictions of bound-state and scattering observables for applications that require repeated calculations with different parameters, such as Bayesian uncertainty quantification. In this paper, we extend a scattering emulator based on the Kohn variational principle (KVP) to momentum space (including coupled channels) with arbitrary boundary conditions, which enable the mitigation of spurious singularities known as Kohn anomalies. We test it on a modern chiral nucleon-nucleon (NN) interaction, including emulation of the coupled channels. We provide comparisons between a Lippmann-Schwinger equation emulator and our KVP momentum-space emulator for a representative set of neutron-proton (np) scattering observables, and also introduce a quasi-spline-based approach for the KVP-based emulator. Our findings show that while there are some trade-offs between accuracy and speed, all three emulators perform well. Self-contained Jupyter notebooks that generate the results and figures in this paper are publicly available.

nucl-th↗

arXiv2022

BUQEYE Guide to Projection-Based Emulators in Nuclear Physics

The BUQEYE collaboration (Bayesian Uncertainty Quantification: Errors in Your EFT) presents a pedagogical introduction to projection-based, reduced-order emulators for applications in low-energy nuclear physics. The term emulator refers here to a fast surrogate model capable of reliably approximating high-fidelity models. As the general tools employed by these emulators are not yet well-known in the nuclear physics community, we discuss variational and Galerkin projection methods, emphasize the benefits of offline-online decompositions, and explore how these concepts lead to emulators for bound and scattering systems that enable fast & accurate calculations using many different model parameter sets. We also point to future extensions and applications of these emulators for nuclear physics, guided by the mature field of model (order) reduction. All examples discussed here and more are available as interactive, open-source Python code so that practitioners can readily adapt projection-based emulators for their own work.

nucl-th↗

arXiv2022

Online Resource Allocation for Reusable Resources

We study a general model on reusable resource allocation under model uncertainty. A heterogeneous population of customers arrive at the decision maker's (DM's) platform sequentially. Upon observing a customer's type, the DM selects an allocation decision, which leads to rewards earned and resources occupied. Each resource unit is occupied for a random duration, and the unit is available for another allocation after the usage duration. Our model captures numerous applications involving admission control and assortment planning. The DM aims to simultaneously maximize multiple types of rewards, while satisfying the resource constraints and being uncertain about the customers' arrival process. We develop a near-optimal algorithm that achieves $(1-ε)$ fraction of the optimal expected rewards, where the error parameter $ε$ decays to zero as the resource capacity units and the length of the horizon grow. The algorithm iteratively applies the Multiplicative Weight Update algorithm in a novel manner, which balances the trade-off among the amounts of rewards earned, resources occupied and usage durations.

math.OC↗

arXiv2022

Model reduction methods for nuclear emulators

The field of model order reduction (MOR) is growing in importance due to its ability to extract the key insights from complex simulations while discarding computationally burdensome and superfluous information. We provide an overview of MOR methods for the creation of fast & accurate emulators of memory- and compute-intensive nuclear systems. As an example, we describe how "eigenvector continuation" is a special case of a much more general and well-studied MOR formalism for parameterized systems. We continue with an introduction to the Ritz and Galerkin projection methods that underpin many such emulators, while pointing to the relevant MOR theory and its successful applications along the way. We believe that this will open the door to broader applications in nuclear physics and facilitate communication with practitioners in other fields.

nucl-th↗

arXiv2022

Nuclear Forces for Precision Nuclear Physics -- a collection of perspectives

This is a collection of perspective pieces contributed by the participants of the Institute of Nuclear Theory's Program on Nuclear Physics for Precision Nuclear Physics which was held virtually from April 19 to May 7, 2021. The collection represents the reflections of a vibrant and engaged community of researchers on the status of theoretical research in low-energy nuclear physics, the challenges ahead, and new ideas and strategies to make progress in nuclear structure and reaction physics, effective field theory, lattice QCD, quantum information, and quantum computing. The contributed pieces solely reflect the perspectives of the respective authors and do not represent the viewpoints of the Institute for Nuclear theory or the organizers of the program.

nucl-th↗