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At least 901 records · Page 50

Theory and applications of parton pseudodistributions

We review the basic theory of the parton pseudodistributions approach and its applications to lattice extractions of parton distribution functions. The crucial idea of the approach is the realization that the correlator $M(z,p)$ of the parton fields is a function $M(ν,-z^2)$ of Lorentz invariants $ν=-(zp)$, the Ioffe time, and the invariant interval $z^2$. This observation allows to extract the Ioffe-time distribution $M(ν,-z^2)$ from Euclidean separations z accessible on the lattice. Another basic feature is the use of the ratio $M(ν,-z^2)≡M(ν,-z^2)/M(0,-z^2)$, that allows to eliminate artificial ultraviolet divergence generated by the gauge link for spacelike intervals. The remaining $z^2$-dependence of the reduced Ioffe-time distribution $M(ν,-z^2)$ corresponds to perturbative evolution, and can be converted into the scale-dependence of parton distributions $f(x,μ^2)$ using matching relations. The ν-dependence of $M(ν,-z^2)$ governs the x-dependence of parton densities $f(x,μ^2)$. The perturbative evolution was successfully observed in exploratory quenched lattice calculation. The analysis of its precise data provides a framework for extraction of parton densities using the pseudodistributions approach. It was used in the recently performed calculations of the nucleon and pion valence quark distributions. We also discuss matching conditions for the pion distribution amplitude and generalized parton distributions, the lattice studies of which are now in progress.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Giallar: push-button verification for the qiskit Quantum compiler

This paper presents Giallar, a fully-automated verification toolkit for quantum compilers. Giallar requires no manual specifications, invariants, or proofs, and can automatically verify that a compiler pass preserves the semantics of quantum circuits. To deal with unbounded loops in quantum compilers, Giallar abstracts three loop templates, whose loop invariants can be automatically inferred. To efficiently check the equivalence of arbitrary input and output circuits that have complicated matrix semantics representation, Giallar introduces a symbolic representation for quantum circuits and a set of rewrite rules for showing the equivalence of symbolic quantum circuits. With Giallar, we implemented and verified 44 (out of 56) compiler passes in 13 versions of the Qiskit compiler, the open-source quantum compiler standard, during which three bugs were detected in and confirmed by Qiskit. Furthermore, our evaluation shows that most of Qiskit compiler passes can be automatically verified in seconds and verification imposes only a modest overhead to compilation performance.

automated verification↗

Topological order of the Rys F-model and its breakdown in realistic square spin ice: Topological sectors of Faraday loops

Both the Rys F-model and antiferromagnetic square ice possess the same ordered, antiferromagnetic ground state, but the ordering transition is of second order in the latter, and of infinite order in the former. To tie this difference to topological properties and their breakdown, we introduce a Faraday lines representation where loops carry the energy and magnetization of the system. Because the F-model does not admit monopoles, its Faraday loops have distinct topological properties, absent in square ice, and which allow for a natural partition of its phase space into topological sectors. Then, the Néel temperature corresponds to a transition from topologically trivial to non-trivial Faraday loops. Because magnetization is a homotopy invariant of the Faraday loops, and it is zero for topologically trivial ones, the susceptibility is zero below a critical field. In square spin ice, instead, monopoles destroy the homotopy invariance and the parity distinction among loops, thus erasing this rich topological structure. Consequently, even trivial loops can be magnetized in square ice, and their susceptibility is never zero.

36 MATERIALS SCIENCE↗

Quantum phase transition in CeCoIn 5 : Experimental facts and theory

Abstract The condensed-matter community is involved in a hot debate on the nature of quantum critical points (QCP) governing the low-temperature properties of heavy fermion metals. The smeared jump-like behavior revealed both in the residual resistivity and the Hall resistivity R H , along with the violation of the time invariance symmetry and the charge invariance , include the violation of quasiparticle-hole symmetry, and provide vital clues on the origin of both the non-Fermi-liquid behavior and QCP. For the first time, based on a number of important experimental data, we show that these experimental observations point out unambiguously that QCP of is accompanied by the symmetry violation, and QCP itself is represented by the topological fermion-condensation quantum phase transition (FCQPT) connecting two Fermi surfaces of different topological charges.

Physics↗

Semi-Analytical Hierarchical Bayesian Inference of Nonlinear Model Structure in Stochastic Dynamics: Applied to Compartmental Models of Infectious Diseases

A Bayesian computational framework for parsimonious inference in stochastic nonlinear dynamical systems is presented. This framework enables the concurrent estimation of system states, time-varying parameters, time-invariant parameters, and the optimal sparsity structure of the model parameters. Because differential equation-based models are often simplified mechanistic or phenomenological representations, robust inference from noisy measurement data requires explicit treatment of model error and uncertainty. Model error and time-varying parameters can be represented as random processes, enabling inference while making minimal assumptions about the underlying sources of discrepancy and variability. Adopting stochastic differential equation representations affords the model significant flexibility, but can also render it susceptible to overfitting during statistical inversion, where the inferred model may track noise rather than the underlying signal. To alleviate the effects of overfitting and to enable the discovery of the optimal sparse representation of the time-invariant parameters, a Bayesian sparse learning algorithm is embedded within the framework. This sparse learning framework adopts an approximate hierarchical Bayesian setting defined by a series of semi-analytical expressions. The model structure inference framework is validated using a stochastic compartmental model for tracking and forecasting active cases of an infectious disease. Compartmental models describe population-level infectious disease dynamics through interactions among population fractions grouped by disease state. Mathematically, such models consist of a system of coupled ordinary differential equations. This example adopts an expressive compartmental model that includes multiple possible interactions between disease states, motivated by early uncertainty surrounding COVID-19 reinfection dynamics and their implications for long-term epidemic forecasting. The sparse learning exercise permits the inference of a priori unknown epidemiological dynamics from simulated public health data, discovering the nested compartmental model that optimizes the trade-off between average data-fit and model complexity. It is shown that inducing sparsity among the model parameters eliminates redundant interactions between compartments, equivalently revealing the optimal coupling structure between differential equations.

97 MATHEMATICS AND COMPUTING↗

Tensor Basis Gaussian Process Models of Hyperelastic Materials

In this study, we develop Gaussian process regression (GPR) models of isotropic hyperelastic material behavior. First, we consider the direct approach of modeling the components of the Cauchy stress tensor as a function of the components of the Finger stretch tensor in a Gaussian process. We then consider an improvement on this approach that embeds rotational invariance of the stress-stretch constitutive relation in the GPR representation. This approach requires fewer training examples and achieves higher accuracy while maintaining invariance to rotations exactly. Finally, we consider an approach that recovers the strain-energy density function and derives the stress tensor from this potential. Although the error of this model for predicting the stress tensor is higher, the strain-energy density is recovered with high accuracy from limited training data. The approaches presented here are examples of physics-informed machine learning. They go beyond purely data-driven approaches by embedding the physical system constraints directly into the Gaussian process representation of materials models.

36 MATERIALS SCIENCE↗

Experimental verification of integrability in a Danilov-Nagaitsev lattice using machine learning

In non-linear optics, achieving integrability can enhance the dynamic aperture in storage rings. We analyze turn-by-turn phase-space data from our Danilov-Nagaitsev lattice implementation at Fermilab's Integrable Optics Test Accelerator using machine learning. AI Poincaré estimates conserved quantities from experimental data without prior knowledge of the invariant structure, showing qualitative agreement with theoretical predictions. Additionally, one of the two learned invariants exhibits comparable or better conservation compared to known theoretical expressions.

43 PARTICLE ACCELERATORS↗

A model of persistent breaking of continuous symmetry

We consider a UV-complete field-theoretic model in general dimensions, including d=2+1, which consists of two copies of the long-range vector models, with O(m) and O(N-m) global symmetry groups, perturbed by double-trace operators. Using conformal perturbation theory we find weakly-coupled IR fixed points for N\geq 6 N ≥ 6 that reveal a spontaneous breaking of global symmetry. Namely, at finite temperature the lower rank group is broken, with the pattern persisting at all temperatures due to scale-invariance. We provide evidence that the models in question are unitary and invariant under full conformal symmetry. Furthermore, we show that this model exhibits a continuous family of weakly interacting field theories at finite N.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Lattice regularization of reduced Kähler-Dirac fermions and connections to chiral fermions

We show how a path integral for reduced Kähler-Dirac fermions suffers from a phase ambiguity associated with the fermion measure that is an analog of the measure problem seen for chiral fermions. However, unlike the case of chiral symmetry, a doubler free lattice action exists which is invariant under the corresponding onsite symmetry. This allows for a clear diagnosis and solution to the problem using mirror fermions resulting in a unique gauge invariant measure. By introducing an appropriate set of Yukawa interactions which are consistent with ’t Hooft anomaly cancellation we conjecture the mirrors can be decoupled from low energy physics. Moreover, the minimal such Kähler-Dirac mirror model yields a light sector which corresponds, in the flat space continuum limit, to the Pati-Salam GUT model.

Physics↗

Conformal geometry from entanglement

In a physical system with conformal symmetry, observables depend on cross-ratios, measures of distance invariant under global conformal transformations (conformal geometry for short). We identify a quantum information-theoretic mechanism by which the conformal geometry emerges at the gapless edge of a 2+1D quantum many-body system with a bulk energy gap. We introduce a novel pair of information-theoretic quantities (\mathfrak{c}_{\textrm{tot}}, \eta) ( 𝔠 tot , η ) that can be defined locally on the edge from the wavefunction of the many-body system, without prior knowledge of any distance measure. We posit that, for a topological groundstate, the quantity \mathfrak{c}_{\textrm{tot}} 𝔠 tot is stationary under arbitrary variations of the quantum state, and study the logical consequences. We show that stationarity, modulo an entanglement-based assumption about the bulk, implies (i) \mathfrak{c}_{\textrm{tot}} 𝔠 tot is a non-negative constant that can be interpreted as the total central charge of the edge theory. (ii) \eta η is a cross-ratio, obeying the full set of mathematical consistency rules, which further indicates the existence of a distance measure of the edge with global conformal invariance. Thus, the conformal geometry emerges from a simple assumption on groundstate entanglement. We show that stationarity of \mathfrak{c}_{\textrm{tot}} 𝔠 tot is equivalent to a vector fixed-point equation involving \eta η , making our assumption locally checkable. We also derive similar results for 1+1D systems under a suitable set of assumptions.

Kim, Isaac H.↗

Multipartite edge modes and tensor networks

Holographic tensor networks model AdS/CFT, but so far they have been limited by involving only systems that are very different from gravity. Unfortunately, we cannot straightforwardly discretize gravity to incorporate it, because that would break diffeomorphism invariance. In this note, we explore a resolution. In low dimensions gravity can be written as a topological gauge theory, which can be discretized without breaking gauge-invariance. However, new problems arise. Foremost, we now need a qualitatively new kind of “area operator,” which has no relation to the number of links along the cut and is instead topological. Secondly, the inclusion of matter becomes trickier. We successfully construct a tensor network both including matter and with this new type of area. Notably, while this area is still related to the entanglement in “edge mode” degrees of freedom, the edge modes are no longer bipartite entangled pairs. Instead they are highly multipartite. Along the way, we calculate the entropy of novel subalgebras in a particular topological gauge theory. We also show that the multipartite nature of the edge modes gives rise to non-commuting area operators, a property that other tensor networks do not exhibit.

Akers, Chris (ORCID:0000000227929827)↗

Gluon pseudo-distributions at short distances

We present the results that are necessary in the ongoing lattice calculations of the gluon parton distribution functions (PDFs) within the pseudo-PDF approach. We identify the two-gluon correlator functions that contain the invariant amplitude determining the gluon PDF in the light-cone z^2 \to 0 z 2 → 0 limit, and perform one-loop calculations in the coordinate representation in an explicitly gauge-invariant form. Ultraviolet (UV) terms, which contain \ln (-z^2) ln ( − z 2 ) -dependence cancel in the reduced Ioffe-time distribution (ITD), and we obtain the matching relation between the reduced ITD and the light-cone ITD. Using a kernel form, we get a direct connection between lattice data for the reduced ITD and the normalized gluon PDF.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

New Laboratory and Astrophysical Probes of Physics Beyond the Standard Model (Final Technical Report)

The first of these directions centers on new ideas in dark matter detection. As experimental scrutiny narrows the window for new physics at the weak scale, it has become apparent that the solution to the dark matter mystery may not reside there. Theoretical developments such as the hidden sector/valley paradigm have, at the same time, shown that compelling theories of dark matter reside below the weak scale. Searching for dark matter at lower mass scales requires looking beyond the current paradigm of dark matter direct detection based on nuclear recoils. It is the goal of this project to provide new ideas to guide the experimental program looking for light dark matter. I am actively proposing ideas for detecting dark matter as light as a meV, well beyond the current focus of GeV-TeV scale dark matter. Some of the ideas I have proposed, such as superconducting, superfluid, and polar material targets, are actively being developed into experiments. My group will provide the relevant calculations to determine dark matter reach, providing crucial input to experiment on which targets should be developed. We will also provide an effective field theory framework to understand which types of experiments are most sensitive to each interaction type. The second of these directions is on probes of dark matter substructure as a mean to constrain, or observe, models of dark matter. The standard ΛCDM paradigm assumes that the dark matter density perturbations are adiabatic, scale invariant, and produced during inflation. However, many standard models of dark matter will produce modifications of this prediction, such as axion models with symmetry broken below the inflationary scale. Remarkably, we have limited direct measurements of the dark matter clumpiness at mass scales below dwarf galaxies. This allows for the possibility of observing modifications from vanilla ΛCDM due to particle dynamics. In many cases, simulations of dark matter structure in the presence of non-scale invariant fluctu- ations are understudied or completely lacking. I plan to develop both theoretical predictions for small scale structure in models with additional matter power on small scales, as well as observa- tional probes of small scale halos or clumps. One idea I have been recently focused on is pulsar timing, though my group will pursue a variety of lensing and astrometric probes. Lastly, the most risky direction involves spacetime fluctuations from quantum gravity. I showed that if one assumes that metric fluctuations in the Minkowski vacuum, at a surface separating a region in and out of causal contact (which we call a “horizon”), are determined by standard thermodynamic considerations at horizon, these metric fluctuations are large enough to observe in an interferometer with similar sensitivity to LIGO. In a follow-up paper we showed that these assumption holds for the vacuum in AdS/CFT. In future work, I plan to connect this work to recent soft graviton results, to frame this work in a concrete Randall-Sundrum model, and to work out concrete phenomenological predictions from the model. This work unquestionably takes a less trodden path, and works well as part of a well-rounded portfolio of less and more risky ideas. Particle physics is currently at a juncture which requires bold exploration of qualitatively new directions. This proposal outlines some of my plans over the coming years in these directions, leaving room also for surprises.

79 ASTRONOMY AND ASTROPHYSICS↗

Electron Drift Kinetics in Space and in the Lab [Slides]

In a magnetized plasma, dynamics are fundamentally split between the directions parallel and perpendicular to the magnetic field. Generally, gyration about the magnetic field will occur on smaller spatial and time scales than the bulk dynamics of the system. From Hamiltonian mechanics, a periodic motion on a time scale much shorter than the other system dynamics leads to an adiabatic invariant. The adiabatic invariant for this motion is the magnetic moment $\mu=\frac{mv⟂^2}{2B}$, which will be approximately conserved.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Permutation-adapted complete and independent basis for atomic cluster expansion descriptors

In many recent applications, particularly in the field of atom-centered descriptors for interatomic potentials, tensor products of spherical harmonics have been used to characterize complex atomic environments. When coupled with a radial basis, the atomic cluster expansion (ACE) basis is obtained. However, symmetrization with respect to both rotation and permutation results in an overcomplete set of ACE descriptors with linear dependencies occurring within blocks of functions corresponding to particular generalized Wigner symbols. All practical applications of ACE employ semi-numerical constructions to generate a complete, fully independent basis. While computationally tractable, the resultant basis cannot be expressed analytically, is susceptible to numerical instability, and thus has limited reproducibility. Here we present a procedure for generating explicit analytic expressions for a complete and independent set of ACE descriptors. The procedure uses a coupling scheme that is maximally symmetric w.r.t. permutation of the atoms, exposing the permutational symmetries of the generalized Wigner symbols, and yields a permutation-adapted rotationally and permutationally invariant basis (PA-RPI ACE). Theoretical support for the approach is presented, as well as numerical evidence of completeness and independence. A summary of explicit enumeration of PA-RPI functions up to rank 6 and polynomial degree 32 is provided. The PA-RPI blocks corresponding to particular generalized Wigner symbols may be either larger or smaller than the corresponding blocks in the simpler rotationally invariant basis. Finally, we demonstrate that basis functions of high polynomial degree persist under strong regularization, indicating the importance of not restricting the maximum degree of basis functions in ACE models a priori.

74 ATOMIC AND MOLECULAR PHYSICS↗

Unraveling the Wrinkle in Time-Variable Sources with Lunes and Synthetic Seismic Data

In this report, we describe how to estimate the time-variable components of the seismic moment tensor and compare these estimates to the more conventional analysis that incorporates an assumption of the source time function (STF) across all components of the seismic moment tensor. The advantage of our method is that we are able to independently estimate the time-evolution of each component of the seismic moment tensor, which may help to resolve the complex source phenomena associated with buried explosions. By performing an eigen decomposition of the time-evolving seismic moment tensor components, we are able to plot the seismic mechanism as a trajectory on a lune diagram. This technique enables interpretation of the seismic mechanism as a function of time, as opposed to the more conventional analysis which assumes that the seismic mechanism is time invariant. Finally, we describe the differences between the seismic moment and the seismic moment rate STFs, how to implement each one in inversion schemes, and the relative strengths/weaknesses of each. Our key take-away is that we are able to distinguish nearly-overlapping sources with highly different mechanisms, such as an explosion immediately following an earthquake, by estimating moment rate from seismic data through a STF-invariant inversion for the full time-variable moment tensor.

58 GEOSCIENCES↗

Scattering Amplitudes and QFT Insight (Final Scientific Report)

The calculation of scattering amplitudes provides an invariant window into the physical dynamic content of relativistic quantum field theory. Yet with traditional methods, for empirically relevant theories, these calculations scale with a factorial complexity in external particles and precision. If we aspire to collapse the theoretical uncertainty obscuring new physics hidden at all scales from the microscopic probed at high energy colliders to the largest effective field theory in the universe governing the evolution of large scale structure, this complexity challenge necessitates new ideas and methods in calculation. Novel approaches like the color-kinematics duality and the associated double-copy construction have drastically simplified the situation, relating both gauge and gravity theory predictions to a much smaller kernel of invariant kinematic data. This project supporting research by the PI's Amplitudes and Insights group at Northwestern University looked to push insight deep into both the IR and the UV by establishing how novel structures must constrain the predictions of counterterms in both gauge and gravity theories, setting the groundwork to exploring the high energy behavior of particular gravity theories via constituent gauge-theory calculations, and confronting fundamental challenges at the interface between QFT amplitudes analysis and next generation gravitational wave science as well as well as inflationary and large scale structure cosmology.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Universal Fourier Attack for Time Series

A wide variety of adversarial attacks have been proposed and explored using image and audio data. These attacks are notoriously easy to generate digitally when the attacker can directly manipulate the input to a model, but are much more difficult to implement in the real-world. In this paper we present a universal, time invariant attack for general time series data such that the attack has a frequency spectrum primarily composed of the frequencies present in the original data. The universality of the attack makes it fast and easy to implement as no computation is required to add it to an input, while time invariance is useful for real-world deployment. Additionally, the frequency constraint ensures the attack can withstand filtering. We demonstrate the effectiveness of the attack in two different domains, speech recognition and unintended radiated emission, and show that the attack is robust against common transform-and-compare defense pipelines.

97 MATHEMATICS AND COMPUTING↗