Momentum Space Research Articles

Negative moments as the signature of the radial density at small distances

The present paper proposes a robust evaluation of any radial density at small distances using negative-order radial moments evaluated in momentum space. This evaluation provides a valuable insight into the behavior of a given radial density in the vicinity of r=0, and puts strong emphasis on the importance of measuring form factors at large squared four-momentum transfer, a domain essential for the determination of negative order moments. A specific attention is paid to the regularization scheme directly affecting the numerical determination of the radial density’s parametrization. The proposed method is applied to non-relativistic study cases of the nucleon electric (GEn,GEp), and proton magnetic GMp form factors. The validation is performed through comparison of the results of the approach to the analytically determined Maclaurin expansion - in the vicinity of r=0 - of the radial density function. The method is also applied to the relativistic Dirac form factor F1p of the proton. In such a non-trivial case, the Maclaurin development might not exist for the radial density, rendering the determination from the proposed method extremely important.

Superfluid stiffness of twisted trilayer graphene superconductors.

The robustness of the macroscopic quantum nature of a superconductor can be characterized by the superfluid stiffness, ρs, a quantity that describes the energy required to vary the phase of the macroscopic quantum wavefunction. In unconventional superconductors, such as cuprates, the low-temperature behaviour of ρs markedly differs from that of conventional superconductors owing to quasiparticle excitations from gapless points (nodes) in momentum space. Intensive research on the recently discovered magic-angle twisted graphene family has revealed, in addition to superconducting states, strongly correlated electronic states associated with spontaneously broken symmetries, inviting the study of ρs to uncover the potentially unconventional nature of its superconductivity. Here we report the measurement of ρs in magic-angle twisted trilayer graphene (TTG), revealing unconventional nodal-gap superconductivity. Utilizing radio-frequency reflectometry techniques to measure the kinetic inductive response of superconducting TTG coupled to a microwave resonator, we find a linear temperature dependence of ρs at low temperatures and nonlinear Meissner effects in the current-bias dependence, both indicating nodal structures in the superconducting order parameter. Furthermore, the doping dependence shows a linear correlation between the zero-temperature ρs and the superconducting transition temperature Tc, reminiscent of Uemura's relation in cuprates, suggesting phase-coherence-limited superconductivity. Our results provide strong evidence for nodal superconductivity in TTG and put strong constraints on the mechanisms of these graphene-based superconductors.

Local-photon model of the momentum of light

Recently we introduced a local photon approach for modeling the quantized electromagnetic field in position space. Using this approach, we define the momentum of light in this paper as in quantum mechanics as the generator for spatial translation. Afterward, we analyze the momentum dynamics of photonic wave packets which transition from air into a denser dielectric medium. Our analysis shines new light onto the Abraham-Minkowski controversy, which highlights the intricacies involved in the characterization of the momentum of the electromagnetic field. Although our results align with Minkowski's theory and with the definition of the canonical momentum of light in quantum electrodynamics, there are also some crucial differences. Published by the American Physical Society 2025

All Next-to-Next-to-Extremal One-Loop Correlators of AdS Supergluons and Supergravitons

We bootstrap all of the next-to-next-to-extremal one-loop four-point correlators of supergravitons and supergluons in AdS5 using a differential representation, and obtain closed formulas that are valid in both position space and Mellin space simultaneously. Published by the American Physical Society 2025

CoReSi: a GPU-based software for Compton camera reconstruction and simulation in collimator-free SPECT

Objective.Compton cameras (CCs) are imaging devices that may improve observation of sources ofγphotons. The images are obtained by solving a difficult inverse problem. We present CoReSi, a Compton reconstruction and simulation software implemented in Python and powered by PyTorch to leverage multi-threading and to easily interface with image processing and deep learning algorithms. The code is mainly dedicated to medical imaging and near-field experiments where images are reconstructed in 3D.Approach.The code was developed over several years in C++, with the initial version being proprietary. We have since redesigned and translated it into Python, adding new features to improve its adaptability and performances. This paper reviews the literature on CC mathematical models, explains the implementation strategies we have adopted and presents the features of CoReSi.Main results.The code includes state-of-the-art mathematical models from the literature, from the simplest, which allow limited knowledge of the sources, to more sophisticated ones with a finer description of the physics involved. It offers flexibility in defining the geometry of the CC and the detector materials. Several identical cameras can be considered at arbitrary positions in space. The main functions of the code are dedicated to the computation of the system matrix, leading to the forward and backward projector operators. These are the cornerstones of any image reconstruction algorithm. A simplified Monte Carlo data simulation function is provided to facilitate code development and fast prototyping.Significance.As far as we know, there is no open source code for CC reconstruction, except for MEGAlib, which is mainly dedicated to astronomy applications. This code aims to facilitate research as more and more teams from different communities such as applied mathematics, electrical engineering, physics, medical physics get involved in CC studies. Implementation with PyTorch will also facilitate interfacing with deep learning algorithms.

A new twist on spinning (A)dS correlators

Massless spinning correlators in cosmology are extremely complicated. In contrast, the scattering amplitudes of massless particles with spin are very simple. We propose that the reason for the unreasonable complexity of these correlators lies in the use of inconvenient kinematic variables. For example, in de Sitter space, consistency with unitarity and the background isometries imply that the correlators must be conformally covariant and also conserved. However, the commonly used kinematic variables for correlators do not make all of these properties manifest. In this paper, we introduce twistor space as a powerful way to satisfy all kinematic constraints. We show that conformal correlators of conserved currents can be written as twistor integrals, where the conservation condition translates into holomorphicity of the integrand. The functional form of the twistor-space correlators is very simple and easily bootstrapped. For the case of two- and three-point functions, we verify explicitly that this reproduces known results in embedding space. We also perform a half-Fourier transform of the twistor-space correlators to obtain their counterparts in momentum space. We conclude that twistors provide a promising new avenue to study conformal correlation functions that exposes their hidden simplicity.

Scaling theory for non-Hermitian topological transitions

Understanding the critical properties is essential for determining the physical behavior of topological systems. In this context, scaling theories based on the curvature function in momentum space, the renormalization group (RG) method, and the universality of critical exponents have proven effective. In this work, we develop a scaling theory for non-Hermitian topological states of matter. We utilize the curvature function renormalization group (CRG) method, incorporating biorthonormal vectors for a one dimensional2×2non-Hermitian Dirac model. This approach allows us to analyze the Wannier state correlation function (WCF) and determine the corresponding localization critical exponent. The CRG method successfully identifies topological phase transitions and locates stable and unstable fixed points. To account for non-Hermitian effects, we construct the curvature function in the generalized Brillouin zone using non-Bloch wave functions, enabling a comprehensive WCF and CRG analysis.

The hierarchical three-body problem at OG2

Employing techniques from scattering amplitudes and effective field theory, we model the dynamics of hierarchical triples, which are three-body systems composed of two bodies separated by a distance r and a third body a distance ρ away, with r ≪ ρ. We apply the method of regions to systematically expand in the small ratio r/ρ and illustrate this approach for evaluating Fourier transform integrals, which have been the bottleneck for deriving complete results in position space. In the limit where the distant third body is much heavier than the other two, we derive new analytic results in position space for the three-body conservative potential at OG2 and at leading and next-to-leading order in r/ρ. We also derive new results for arbitrary masses in the rest frame of the distant particle. Our results are exact in velocity, and can be used in analyses involving both bound and unbound hierarchical triples in astrophysical systems.

Twist corrections to exclusive vector meson production in a saturation framework

We develop a framework combining the higher-twist formalism of exclusive processes in the s channel with the semiclassical effective description of small-x physics in the t channel. We apply it to transversely polarized light vector meson production, γ*p→V(ρ,φ,ω)p, which starts at the next-to-leading power and for which a purely collinear treatment leads to end-point singularities. The result is obtained in the most general kinematics, including both forward and nonforward cases by preserving the full impact parameter dependence in the nonperturbative correlators, in both momentum and coordinate space representations. A systematic expansion of the Wilson lines in terms of Reggeized gluon fields is performed in order to obtain the results in the weak-field BFKL approximation. These new results will allow for investigating the dilute-to-dense regime transition of quantum chromodynamics for a wide class of observables. Published by the American Physical Society 2025

Carrollian partition functions and the flat limit of AdS

The formulation of the S-matrix as a path integral with specified asymptotic boundary conditions naturally leads to the realization of a Carrollian partition function defined on the boundary of Minkowski space. This partition function, specified at past and future null infinity in the case of massless particles, generates Carrollian correlation functions that encode the S-matrix. We explore this connection, including the realization of symmetries, soft theorems arising from large gauge transformations, and the correspondence with standard momentum space amplitudes. This framework is also well-suited for embedding the Minkowski space S-matrix into the AdS/CFT duality in the large radius limit. In particular, we identify the AdS and Carrollian partition functions through a simple map between their respective asymptotic data, establishing a direct correspondence between the actions of symmetries on both sides. Our approach thus provides a coherent framework that ties together various topics extensively studied in recent and past literature.

Holographic Carrollian currents for massless scattering

We show that the Ward identities of a Carrollian CFT stress tensor at null infinity reproduce the leading and subleading soft graviton theorems for massless scattering in the bulk. We deduce the expressions of the stress tensor components in terms of the bulk radiative modes, and these components turn out to be local at I in terms of the twistor potentials. This analysis makes the correspondence between the large-time limit of Carrollian amplitudes and the soft limit of momentum space amplitudes manifest. We then construct Carrollian CFT currents from the ascendants of the hard graviton operator, which satisfy the Lw1+∞ algebra. We show that the large-time limit of their Ward identities implies an infinite tower of projected soft graviton theorems in the bulk, while their finite-time OPEs encode the collinear limit of scattering amplitudes.

Testing the Universality of Quantum Gravity Theories with Cosmic Messengers in the Context of DSR Theories

Recently there have been several studies devoted to the investigation of the fate of fundamental relativistic symmetries at the foreseen unification of gravity and quantum regime, that is the Planck scale. In order to preserve covariance of the formulation even if in an amended formulation, new mathematical tools are required. In this work, we consider DSR theories that modify covariance by introducing a non-trivial structure in momentum space. Additionally, we explore the possibility of investigating both universal quantum gravity corrections and scenarios where different particle species are corrected differently within the framework of these models. Several astroparticle phenomena are then analyzed to test the phenomenological predictions of DSR models.

Ray–Wave Correspondence in Anisotropic Mesoscopic Billiards

Mesoscopic billiard systems for electrons and light, realized as quantum dots or optical microcavities, have enriched the fields of quantum chaos and nonlinear dynamics not only by enlarging the class of model systems, but also by providing access to their experimental realization. Here, we add yet another system class, two-dimensional billiards with anisotropies. One example is the anisotropic dispersion relation relevant in bilayer graphene known as trigonal warping, and another is the birefringent closed optical disk cavity. We demonstrate that the established concept of ray–wave correspondence also provides useful insight for anisotropic billiard systems. First, we approach the dynamics of the anisotropic disk from the ray-tracing side that takes the anisotropy in momentum space into account, based on the non-spherical index ellipsoid. Second, we use transformation optics to solve the wave problem and find the resonances to be those of the isotropic elliptical cavity. We illustrate ray–wave correspondence and mark differences in the description of optical and electronic anisotropic systems.

Flat Band Generation Through Interlayer Geometric Frustration in Intercalated Transition Metal Dichalcogenides.

Electronic flat bands can lead to rich many-body quantum phases by quenching the electron's kinetic energy and enhancing many-body correlation. The reduced bandwidth can be realized by either destructive quantum interference in frustrated lattices, or by generating heavy band folding with avoided band crossing in Moiré superlattices. Here a general approach is proposed to introduce flat bands into widely studied transition metal dichalcogenide (TMD) materials by dilute intercalation. A flat band with vanishing dispersion is observed by angle-resolved photoemission spectroscopy (ARPES) over the entire momentum space in intercalated Mn1/4TaS2. Polarization-dependent ARPES measurements combined with symmetry analysis reveal the orbital characters of the flat band. Supercell tight-binding simulations suggest that such flat bands arising from destructive interference between Mn and Ta on S through hopping pathways, are ubiquitous in a range of TMD families as well as for different intercalation configurations. The findings establish a new material platform to manipulate flat band structures and explore their corresponding emergent correlated properties.

Winding topology of multifold exceptional points

Despite their ubiquity, a systematic classification of multifold exceptional points, n-fold spectral degeneracies (EPns), remains a significant unsolved problem. In this article, we characterize the Abelian eigenvalue topology of generic EPns and symmetry-protected EPns for arbitrary n. The former and the latter emerge in (2n−2)- and (n−1)-dimensional parameter spaces, respectively. By introducing topological invariants called resultant winding numbers, we elucidate that these EPns are stable due to topology of a map from a base space (momentum or parameter space) to a sphere defined by resultants. In a D-dimensional parameter space (D≥c), the resultant winding numbers topologically characterize (D−c)-dimensional manifolds of generic (symmetry-protected) EPns, whose codimension is c=2n−2 (c=n−1). Our framework implies fundamental doubling theorems for both generic EPns and symmetry-protected EPns in n-band models. Published by the American Physical Society 2025

A Pride of Satellites in the Constellation Leo? Discovery of the Leo VI Milky Way Satellite Ultra-faint Dwarf Galaxy with DELVE Early Data Release 3

Abstract We report the discovery and spectroscopic confirmation of an ultra-faint Milky Way satellite in the constellation of Leo. This system was discovered as a spatial overdensity of resolved stars observed with Dark Energy Camera (DECam) data from an early version of the third data release of the DECam Local Volume Exploration (or DELVE) survey. The low luminosity ( M V = − 3.5 6 − 0.37 + 0.47 ; L V = 230 0 − 700 + 1200 L ⊙ ), large size ( R 1 / 2 = 9 0 − 30 + 30 pc), and large heliocentric distance ( D = 11 1 − 6 + 9 kpc) are all consistent with the population of ultra-faint dwarf galaxies (UFDs). Using Keck/DEIMOS observations of the system, we were able to spectroscopically confirm nine member stars, while measuring a tentative mass-to-light ratio of 70 0 − 500 + 1400 M ⊙ / L ⊙ and a nonzero metallicity dispersion of σ [ Fe / H ] = 0.1 9 − 0.11 + 0.14 , further confirming Leo VI’s identity as a UFD. While the system has a highly elliptical shape, ϵ = 0.5 4 − 0.29 + 0.19 , we do not find any conclusive evidence that it is tidally disrupting. Moreover, despite the apparent on-sky proximity of Leo VI to members of the proposed Crater-Leo infall group, its smaller heliocentric distance and inconsistent position in energy–angular momentum space make it unlikely that Leo VI is part of the proposed infall group.

Unveiling a Tunable Moiré Bandgap in Bilayer Graphene/hBN Device by Angle-Resolved Photoemission Spectroscopy.

Over the years, great efforts have been devoted in introducing a sizable and tunable band gap in graphene for its potential application in next-generation electronic devices. The primary challenge in modulating this gap has been the absence of a direct method for observing changes of the band gap in momentum space. In this study, advanced spatial- and angle-resolved photoemission spectroscopy technique is employed to directly visualize the gap formation in bilayer graphene, modulated by both displacement fields and moiré potentials. The application of displacement field via in situ electrostatic gating introduces a sizable and tunable electronic bandgap, proportional to the field strength up to 100 meV. Meanwhile, the moiré potential, induced by aligning the underlying hexagonal boron nitride substrate, extends the bandgap by ≈20 meV. Theoretical calculations effectively capture the experimental observations. This investigation provides a quantitative understanding of how these two mechanisms collaboratively modulate the band gap in bilayer graphene, offering valuable guidance for the design of graphene-based electronic devices.

Fixation-related potentials during a virtual navigation task: The influence of image statistics on early cortical processing.

Historically, electrophysiological correlates of scene processing have been studied with experiments using static stimuli presented for discrete timescales where participants maintain a fixed eye position. Gaps remain in generalizing these findings to real-world conditions where eye movements are made to select new visual information and where the environment remains stable but changes with our position and orientation in space, driving dynamic visual stimulation. Co-recording of eye movements and electroencephalography (EEG) is an approach to leverage fixations as time-locking events in the EEG recording under free-viewing conditions to create fixation-related potentials (FRPs), providing a neural snapshot in which to study visual processing under naturalistic conditions. The current experiment aimed to explore the influence of low-level image statistics-specifically, luminance and a metric of spatial frequency (slope of theamplitude spectrum)-on the early visual components evoked from fixation onsets in a free-viewing visual search and navigation task using a virtual environment. This research combines FRPs with an optimized approach to remove ocular artifacts and deconvolution modeling to correct for overlapping neural activity inherent in any free-viewing paradigm. The results suggest that early visual components-namely, the lambda response and N1-of the FRPs are sensitive to luminance and spatial frequency around fixation, separate from modulation due to underlying differences in eye-movement characteristics. Together, our results demonstrate the utility of studying the influence of image statistics on FRPs using a deconvolution modeling approach to control for overlapping neural activity and oculomotor covariates.

Band asymmetry–driven nonreciprocal electronic transport in a helimagnetic semimetal α-EuP3

Chiral magnetic textures give rise to unconventional magnetotransport phenomena such as the topological Hall effect and nonreciprocal electronic transport. While the correspondence between topology or symmetry of chiral magnetic structures and such transport phenomena has been well established, a microscopic understanding based on the spin-dependent band structure in momentum space remains elusive. Here, we demonstrate how a chiral magnetic superstructure introduces an asymmetry in the electronic band structure and triggers a nonreciprocal electronic transport in a centrosymmetric helimagnet α-EuP3. The magnetic structure of α-EuP3 is highly tunable by a magnetic field and closely coupled to its semimetallic electronic band structure, enabling a systematic study across chiral and achiral magnetic phases on the correspondence between nonreciprocal transport and electronic band asymmetry. Our findings reveal how a microscopic change in the magnetic configuration of charge carriers can lead to nonreciprocal electronic transport, paving the way for designing chiral magnets with desirable properties.

The role of patterning skills in early mathematical development: an analysis of all dimensions of visual perception

ABSTRACT In the early stages of mathematical development, the primary objective is to develop pattern recognition skills by mastering fundamental techniques like sorting and comparison. Numerous pattern structures, such as visual, auditory and spatial patterns, can be created. In this study, we examined the effects of PO-MEP, a pattern-focused mathematics education program for preschool children, on children’s visual perception. The “Pattern-Oriented Mathematics Education Program (PO-MEP)” was developed, and compatible original materials were designed. The program is structured around repeating and growing patterns. Its impact was assessed using a quasi-experimental design, including a pretest, posttest and follow-up test, and a control group. The results show that it had a statistically significant impact on the development of all sub-dimensions of visual perception: hand-eye coordination, figure-ground perception, form constancy, position in space, and spatial relationships. In sum, the program developed the children’s visual perception. Further research may be conducted using different methodologies and age groups to strengthen these findings.