Cold-atom experiments based on alkali-like atoms provide us with a tool to experimentally realize Hubbard models with a large number $N$ of components. The value of $N$ can be seen as a new handle to tune the properties of the system, leading to new physics both in the case of fully SU($N$) symmetric systems, or in the presence of controlled symmetry breaking. We focus on the Mott transition at global half filling and we characterize local correlations between particles through the \emph{inter-flavor mutual information}, an experimentally accessible quantity that rigorously measures the distance from the closest gaussian state, unveiling features that cannot be accessed by conventional probes of Mottness. We prove that these correlations are fully independent from local entanglement and quantum discord, and, using Dynamical Mean-Field Theory, we show that the SU(4) system has significantly smaller correlations than the SU(2) counterpart. In the atomic limit we prove that increasing $N$ further decreases the strength of the correlations. This suggests that a controlled reduction of the symmetry, reducing the number of effective components, can be used to enhance the degree of correlation. We confirm this scenario solving the model for $N=4$ and gradually breaking the symmetry via a Raman field, revealing an evolution from the SU(4) to the SU(2) Mott transition as the symmetry-breaking term increases, with a sudden recovery of the large correlations of the SU(2) model at weak Raman coupling in the Mott state. By further exploring the interplay between energy repulsion and the Raman field, we obtain a rich phase diagram with three different phases -- a metal, a band insulator, and a Mott insulator -- all coexisting at a single tricritical point.

We study the influence of positrons on the outer crusts of neutron stars and the interiors of white dwarfs, introducing them as a novel component in both the composition of matter and in transport processes. We solve a system of coupled Boltzmann kinetic equations for the electron and positron distribution functions in the relaxation-time approximation, taking into account electron-ion, positron-ion, and electron-positron collisions. The relevant scattering matrix elements are calculated from one-plasmon exchange diagrams, with in-medium polarization tensors derived within hard-thermal-loop effective theory. Numerical results are obtained for matter composed of carbon nuclei. We find that the conductivity rises with temperature, following a power law sigma proportional to the 4th power of T in the semi-degenerate regime and sigma proportional to T in the nondegenerate regime, due to the intense creation of thermal electron-positron pairs and the resulting collisions among them. These results highlight the importance of including positrons in the transport properties of heated, dense astrophysical plasmas.

In the 1970s, Serre proved that the adelic index of a non-CM elliptic curve over a number field is finite. More recently, Zywina conjectured the complete set of adelic indices for such curves over $\mathbb{Q}$. In this article, we prove that Zywina's conjecture is true for the family of non-CM elliptic curves over $\mathbb{Q}$ that admit a nontrivial rational cyclic isogeny. This strengthens a result of Lemos that resolved Serre's uniformity question for the same family of curves. Our proof proceeds by analyzing a collection of modular curves associated with each prime isogeny degree, using recent advances on $\ell$-adic images, isogeny-torsion graphs, and computations of models and rational points.

Inspired by recent observations of the $1/3$ magnetization plateau in kagome-based magnets, we investigate the $J_1-J_2$ Heisenberg model on the kagome lattice under the influence of an external magnetic field. Although the classical ground state at zero field depends on the sign of $J_2$, we find a robust $1/3$ semiclassical magnetization plateau in both cases. The mechanism that stabilizes this plateau is analogous to that observed in the triangular lattice, where quantum fluctuations select a collinear state from the degenerate classical manifold. We calculate the plateau width, which shows a weak dependence on $J_2$, using nonlinear spin-wave theory. Additionally, we find that a straightforward approach based on linear spin-wave yields quantitatively accurate results even for $S=1/2$. Furthermore, we identify a magnetization jump at the saturation field when $J_2=0$; this jump is related to the presence of a flat band and disappears for $J_2 \neq 0$. Our study demonstrates that a semiclassical approach effectively captures the $1/3$ plateau in the kagome lattice and serves as a valuable tool for interpreting experimental and numerical results alike.

Magnetic particle imaging reconstructs tracer distributions using a system matrix obtained through time-consuming, noise-prone calibration measurements. Methods for addressing imperfections in measured system matrices increasingly rely on deep neural networks, yet curated training data remain scarce. This study evaluates whether physics-based simulated system matrices can be used to train deep learning models for different system matrix restoration tasks, i.e., denoising, accelerated calibration, upsampling, and inpainting, that generalize to measured data. A large system matrices dataset was generated using an equilibrium magnetization model extended with uniaxial anisotropy. The dataset spans particle, scanner, and calibration parameters for 2D and 3D trajectories, and includes background noise injected from empty-frame measurements. For each restoration task, deep learning models were compared with classical non-learning baseline methods. The models trained solely on simulated system matrices generalized to measured data across all tasks: for denoising, DnCNN/RDN/SwinIR outperformed DCT-F baseline by >10 dB PSNR and up to 0.1 SSIM on simulations and led to perceptually better reconstuctions of real data; for 2D upsampling, SMRnet exceeded bicubic by 20 dB PSNR and 0.08 SSIM at $\times 2$-$\times 4$ which did not transfer qualitatively to real measurements. For 3D accelerated calibration, SMRnet matched tricubic in noiseless cases and was more robust under noise, and for 3D inpainting, biharmonic inpainting was superior when noise-free but degraded with noise, while a PConvUNet maintained quality and yielded less blurry reconstructions. The demonstrated transferability of deep learning models trained on simulations to real measurements mitigates the data-scarcity problem and enables the development of new methods beyond current measurement capabilities.

Bulk meteoritic data show isotopic variability of $slow$-neutron-capture ($s$-process) origin in a several elements heavier than Fe. One peculiar feature is that the lighter $s$-process elements (e.g., Zr and Mo) present larger anomalies than the heavier $s$-process elements (e.g., Nd and W). To address this observation, we compared Zr and Nd data to model predictions of the s-process abundances at the surface of low-mass asymptotic giant branch (AGB) stars of initial metallicity from solar to twice solar. We found that the relative magnitude of the isotopic variability between these two elements can be matched by models of AGB stars of super-solar metallicity. The match is favoured by stronger convective overshoot, leading to a deeper dredge-up of the H-rich envelope into the He-rich region, and/or a smaller (~ half than standard) mass of the region rich in the $^{13}$C nuclei that produce free neutrons via the $^{13}$C($α$,n)$^{16}$O reaction. We conclude that nucleosynthesis in AGB stars can match the difference in the magnitude of the bulk meteoritic variations in Zr and Nd, provided that super-solar metallicity stars are the original site of these signatures. The AGB stars that produced such variations could have belonged to the current population of old, super-solar metallicity stars seen in the galactic solar neighbourhood.

While supervised fine-tuning of adult pre-trained models for children's ASR has shown promise, it often fails to capture group-specific characteristics and variations among children. To address this, we introduce GRoup-Aware PARtial model Merging, a parameter-efficient approach that combines unsupervised clustering, partial fine-tuning, and model merging. Our approach adapts adult-pre-trained models to children by first grouping the children's data based on acoustic similarity. Each group is used to partially fine-tune an adult pre-trained model, and the resulting models are merged at the parameter level. Experiments conducted on the MyST children's speech corpus indicate that GRAPAM achieves a relative WER improvement of 6%, using the same amount of data, outperforming full fine-tuning while training fewer parameters.

The present work contains a comprehensive treatment of Weyl eigenvalue and singular value distributions for single-axis quaternion block multilevel Toeplitz matrix sequences generated by $s\times t$ quaternion matrix-valued, $d$-variate, Lebesgue integrable generating functions. Furthermore, in view of concrete applications, we are interested in preconditioning and matrix approximation results. To this end, a crucial step is the extension of the notion of an approximating class of sequences (a.c.s.) to the case of matrix sequences with quaternion entries, since it allows us to decompose the difference between a matrix and its preconditioner into low-norm plus (relatively) low-rank terms. As a specific example, we consider classes of quaternion block multilevel circulant matrix sequences as an a.c.s. for quaternion block multilevel Toeplitz matrix sequences. These approximation results lay the foundations for fast preconditioning methods when dealing with large quaternion linear systems stemming from modern applications. We conclude our study with numerical experiments and directions for future research.

We review the theoretical modelling of moiré materials, focusing on various aspects of magic-angle twisted bilayer graphene (MA-TBG) viewed through the lens of Hartree-Fock mean-field theory. We first provide an elementary introduction to the continuum modelling of moiré bandstructures, and explain how interactions are incorporated to study correlated states. We then discuss how to implement mean-field simulations of ground state structure and collective excitations in this setting. With this background established, we rationalize the power of mean-field approximations in MA-TBG, by discussing the idealized "chiral-flat" strong-coupling limit, in which ground states at electron densities commensurate with the moiré superlattice are exactly captured by mean-field ansätze. We then illustrate the phenomenological shortcomings of this limit, leading us naturally into a discussion of the intermediate-coupling incommensurate Kekulé spiral (IKS) order and its origins in ever-present heterostrain. IKS and its placement within an expanded Hartree-Fock manifold form our first "case study". Our second case study involves time-dependence, and focuses on the collective modes of various broken-symmetry insulators in MA-TBG. As a third and final case study, we return to the strong-coupling picture, which can be stabilized by aligning MA-TBG to an hBN substrate. In this limit, we show how mean field theory can be adapted to the translationally non-invariant setting in order to quantitatively study the energetics of domain walls in orbital Chern insulating states. We close with a discussion of extensions and further applications. Used either as a standalone reference or alongside the accompanying open-source code, this review should enable readers with a basic knowledge of band theory and many-body physics to systematically build and analyze detailed models of generic moiré systems.

We derive an intensity doubling feature of critical Brownian loop-soups on the cable-graphs of ${\mathbb Z}^d$ for $d \ge 7$ that can be described as follows: In the box $[-N, N]^d$ (and with a probability that goes to $1$ as $N$ goes to infinity), the set of all clusters of Brownian loops that do contain proper self-avoiding cycles of diameter comparable to $N$ can be decomposed into two identically distributed families: (a) The collection of clusters that do contain a large Brownian loop from the loop-soup (and therefore do automatically contain such a large cycle) (b) The collection of clusters that contain no macroscopic loop from the loop-soup (more specifically, no loop of diameter greater than $N^β$ when $β> 4/ (d-2)$ is fixed) but nevertheless contain a large cycle. In particular, due to the fact that these two families are asymptotically identically distributed, large cycles formed in case (b) by chains of small Brownian loops (i.e., all of diameter much smaller than $N$) will look like large Brownian loops themselves, and form a second independent "ghost" critical loop-soup in the scaling limit. Reformulated in terms of the Gaussian free field on such cable-graphs, this shows that large cycles in the collection of its sign clusters will converge in the scaling limit to a Brownian loop-soup with twice the usual critical intensity. This result had been conjectured by the first author in arXiv:2209.07901 [math.PR] ; our proof builds heavily on the second author's switching property for such loop-soups from arXiv:2502.06754 [math.PR] .

This paper is a finishing touch to the (over 200 years) {\em classical} `Galois Theory' of {\em arbitrary} finite field extensions, i.e. the goal of it is to describe intermediate subfields of an arbitrary finite field extension via {\em invariants} of `natural/obvious' objects that are associated with subfields via two Galois-type correspondences. The classical Galois Theory covers the case of finite Galois field extensions. For finite Galois field extensions the objects are their Galois groups and their invariants. In \cite{GaloisTh-RingThAp}, we introduce a new (ring theoretic) approach to the Galois Theory which is based on the {\em principle of maximal symmetry}. In \cite{AnGaloisTh-NORMAL-Fields}, the maximal symmetry of {\em normal} finite field extensions yields an analogue of the Galois Theory for them. For a normal finite field extension $L/K$ the `natural/obvious' objects are the subalgebra $\CD (L/K)\rtimes G(L/K)$ of $\End (L/K)$ that is generated by the automorphism group $G(L/K)$ and the algebra $\CD (L/K)$ of differential operators on $L/K$ and its `invariants'. The `maximal symmetry' means the equality $\End (L/K)=\CD (L/K)\rtimes G(L/K)$ which turns out to be a characteristic property of {\em normal} finite field extensions, \cite{AnGaloisTh-NORMAL-Fields}. The aim of this paper is to obtain an analogue of the Galois Theory for {\em arbitrary} finite field extensions based on results and ideas of \cite{GaloisTh-RingThAp} and \cite{AnGaloisTh-NORMAL-Fields}.

We develop a four-dimensional gauge-gravity unification based on the $% SL(2N,C)$ gauge theory taken in a universal Yang--Mills type setting. The accompanying tetrads are promoted to dynamical fields whose length, when projected onto the background Minkowskian spacetime, is restricted by a nonlinear sigma-model type constraint. This triggers tetrad condensation and spontaneous symmetry breaking, $SL(2N,C)\rightarrow SL(2,C)\times SU(N)$, lifting all noncompact directions. A special ghost-free curvature-squared Lagrangian provides a consistent quadratic sector, while an Einstein--Cartan linear curvature term is induced radiatively from fermion loops. Below the breaking scale, only a neutral tetrad associated with graviton and $SU(N)$ vector fields remain massless, whereas axial-vector and tensor fields of the entire gauge multiplet acquire heavy masses. The matter sector clearly points to a deeper elementarity of $SL(2N,C)$ spinors, which can be identified with preon constituents whose bound states form the observed quarks and leptons. Anomaly matching between preons and composites singles out $N=8$. The chain $SL(16,C)\rightarrow SL(2,C)\times SU(8)$ then naturally yields three composite quark--lepton families, while filtering out extraneous heavy states.

This paper develops limit theorems for random variables with network dependence, without requiring the individuals in the network to be located in a Euclidean or metric space. This distinguishes our approach from most existing limit theorems in network statistics and econometrics, which are based on weak dependence concepts such as strong mixing, near-epoch dependence, or $ψ$-dependence. All these weak dependence concepts presuppose an underlying metric. By relaxing the assumption of an underlying metric space, our theorems can be applied to a broader range of network data, including financial and social networks. To derive the limit theorems, we generalize the concept of functional dependence (also known as physical dependence) from time series to random variables with network dependence. Using this framework, we establish several inequalities, a law of large numbers, and central limit theorems. Furthermore, we demonstrate the verifiability of our high-level conditions by deriving primitive sufficient conditions for spatial autoregressive models, which are widely used in network data analysis.

KMOC (Kosower, Maybee, and O'Connell) formalism is an approach to analyze classical scattering in gauge theories and gravity using a class of ``inclusive'' observables which can be computed solely from on-shell amplitudes \cite{Kosower:2018adc}. This formalism has led to striking developments in the context of perturbative scattering, which corresponds to large impact parameter scattering. As a result, in its current form, the KMOC formulae cannot be directly applied to processes for generic values of the impact parameter. However, there is a domain where the relationship between classical radiation and on-shell amplitudes can be stretched beyond large impact parameter scattering. This regime is defined by the soft expansion of outgoing radiation. It is thus natural to ask if such soft radiative fields can be computed using the basic paradigm set by the KMOC formalism. In this short note, we show that this is indeed the case for electromagnetic and gravitational memory. That is, we compute an inclusive observable associated with soft flux at ${\cal I}^{+}$ and show that, irrespective of the details of the hard scattering, this observable defines a non-perturbative formula for the memory in the classical limit. We argue that the result obtained for electromagnetic memory, using the KMOC paradigm, is consistent with those in \cite{Laddha:2018rle}, where the classical limit of the quantum soft theorem was taken using saddle point analysis.

The non-conservation of the energy-momentum tensor in $f(R,T)$ gravity can be interpreted as an effective manifestation of dissipation. Motivated by this, we propose a new formulation of $f(R,T)$ gravity based on the Herglotz variational principle, which extends the usual {Hamilton} variational principle to dissipative systems by allowing the Lagrangian to depend explicitly on the action. The resulting gravitational field equations extend those of $f(R,T)$ gravity by including Herglotz contributions. In the Newtonian limit, these contributions modify the gravitational potential, allowing us to constrain the Herglotz vector through Mercury's perihelion precession and the relativistic light deflection. The Herglotz corrections lead to a scaling law consistent with observations from the Cassini spacecraft. Examining two representative cosmological models, the Herglotz vector effectively reduces to a single function that, under suitable conditions, can play the role of a cosmological constant, providing an alternative mechanism for the Universe's accelerated expansion. Within the Herglotz variational approach, the linear $f(R,T)=R+αT$ model, previously ruled out in the standard formulation due to its fixed deceleration parameter, becomes consistent with observations {for a certain choice of the Herglotz vector.

The main result of this paper is a generalization of the theorem of Chevalley-Shephard-Todd to the rings of invariants of pseudo-reflection groups over regular domains. More precisely, let $A$ be a regular domain and let $K$ be its field of fractions. Let $G\subseteq GL_n(A)$ be a finite group. Let $G$ act linearly on $A[X_1,X_2,\dots, X_n]$ (fixing $A$). Assume that $|G|$ is invertible in $A$. We prove that $G\subseteq GL_n(K)$ is generated by pseudo-reflections if and only if $(A[X_1,X_2,\dots, X_n])^G$ is regular.

The third law of black hole dynamics states that it is impossible, through any classical perturbation of a stationary configuration, to reduce the surface gravity of a black hole to zero. In this work, we examine the validity of this law for static, spherically symmetric charged black holes in the Lovelock theory of gravity. By studying infinitesimal variations in mass and charge, we derive a set of inequalities that constrain these variations. Our analysis shows that as the surface gravity approaches zero ($κ\to 0$), the range of admissible perturbations gradually diminishes, thereby forbidding the attainment of extremality through any finite classical process. The saturation of the inequality is interpreted as the emergence of a dynamical barrier near extremality, which prevents further evolution toward the extremal configuration.

Ultrafast imaging of photon statistics in two dimensions is a powerful tool for probing non-equilibrium and transient optical phenomena, yet it remains experimentally challenging due to the simultaneous need for high temporal resolution and statistical fidelity. In this work, we demonstrate spatially resolved single-shot measurements of photon number distributions using difference-frequency generation (DFG) in a nonlinear BBO crystal. We show that our platform can discriminate between coherent and thermal photon statistics across two spatial dimensions with picosecond resolution. At the same time, we find that the retrieved distributions deviate from the ideal ones, a consequence of vacuum contamination and the multimodal response of the amplifier. To explain this, we develop a temporal mode decomposition framework that captures the essential physics of signal amplification and fluorescence, and quantitatively reproduces the experimental findings. This establishes a robust approach for measuring two-dimensional photon statistics while clarifying the fundamental factors that limit the fidelity of such measurements.

In this paper, we propose a novel blockage-aware hierarchical beamforming framework for movable antenna (MA) systems operating at millimeter-wave (mm-Wave) frequencies. While existing works on MA systems have demonstrated performance gains over conventional systems, they often neglect the design of specialized codebooks to leverage MA's unique capabilities and address the challenges of increased energy consumption and latency inherent to MA systems. To address these aspects, we first integrate blockage detection into the codebook design process based on the Gerchberg-Saxton (GS) algorithm, significantly reducing inefficiencies due to beam evaluations done in blocked directions. Then, we use a two-stage approach to reduce the complexity of the joint beamforming and Reconfigurable Intelligent Surfaces (RIS) optimization problem. The simulations demonstrate that the proposed adaptive codebook successfully improves the Energy Efficiency (EE) and reduces the beam training overhead, substantially boosting the practical deployment potential of RIS-assisted MA systems in future wireless networks.

In this article, we study criteria for producing six-functor formalisms and morphisms between them. One notable application is that the motivic homotopy theory of algebraic stacks is the universal six-functor functor formalism in a strong sense: it is initial in some category whose objects are six-functor formalisms, and whose morphisms commute with all six operations. As a further application, we produce an analytic realization to a complex analytic version of motivic homotopy theory that is compatible with the six operations, and extend Betti realization to a map from this complex analytic version that is also compatible with the six operations. The abstract nature of our results is suitable for applications to many geometric contexts, allowing us to prove a similar result for the motivic homotopy theory of complex analytic stacks as a six-functor formalism defined on complex analytic stacks. Our main general result is a generalized and enhanced version of Voevodsky's geometric criterion for six-functor formalisms, given in terms of localization and duality properties. Our version of Voevodsky's principle makes sense in very general geometric contexts, and provides criteria not only for showing when presheaves extend to six-functor formalism, and when a transformation between six-functor formalisms is compatible with the six operations, but also for when a transformation to an ordinary presheaf extends to a morphism of six-functor formalisms (and therefore establishing the six operations for the codomain).

In altermagnets, the magnon bands are anisotropically spin-split in reciprocal space without relativistic or dipolar spin-spin interactions. In this work, we theoretically study magnons and phonons coupled by spin-lattice interaction in a two-dimensional square-lattice d-wave altermagnet. We show that phonon-chirality-selective magnon-phonon hybridization can be caused by interfacial Dzyaloshinskii-Moriya interaction leading to the emergence of hybrid quasiparticles that possess finite phonon angular momentum. These hybrid quasiparticles are called magnon polarons and consist of spin-polarized magnons and chiral phonons. Their phonon angular momentum texture follows the d-wave character of the magnon spin texture opening up the possibility of phononic counterparts to the electronic response effects in altermagnets, such as a phonon angular momentum splitter effect, i.e., the generation of a transverse phonon angular momentum current induced by a temperature gradient -- the bosonic analogue of the spin-splitter effect.

Quasi-brittle plastic yielding is a salient feature of well-annealed glassy materials. Here we show that the same behavior is characteristic of perfect crystals after they experience mechanically driven elastic instability leading to massive nucleation of dislocations. We argue that such 'preparation' effectively converts an atomic configuration from crystalline to quasi-amorphous. To understand the nature of the subsequent intermittent mechanical response we study a model 2D crystal subjected to AQS driving and show that both pre- and post-yield dislocation avalanches exhibit power law statistics with similar exponents indicative of self-induced marginal stability.

Let $f \in C^n(\mathbb{R})$ be such that $\Vert f^{(n)} \Vert_\infty < \infty$. Let $f^{[n]} \in C(\mathbb{R}^{n+1})$ be the $n$th order divided difference. A special case of our main result states that for $1 < p < \infty$ we have \[\Vert T_{f^{[n]}}: S_{np} \times \ldots \times S_{np} \rightarrow S_{p} \Vert \lesssim p^\ast p^n \Vert f^{(n)} \Vert_\infty, \] where $p^\ast = p/(p-1)$ is the Hölder conjugate of $p$ and $T_{f^{[n]}}$ is the multilinear Schur multiplier with symbol $f^{[n]}$. In case of the generalized absolute value map $f(λ) = λ^{n-1} \vert λ\vert, λ\in \mathbb{R}$, we show that \[p^\ast p^{n} \lesssim \Vert T_{f^{[n]}}: S_{np} \times \ldots \times S_{np} \rightarrow S_{p} \Vert.\] This provides an alternative proof to one of the key theorems in the solution of Koplienko's problem on higher order spectral shift [Invent. Math. 193, No. 3, 501-538 (2013)], which is moreover sharp as $p \searrow 1$ and as $p \to\infty$ for any $n$.

We provide a systematic formula, in terms of integer partitions, that generates perturbation theory explicitly at an arbitrary order. Our approach naturally includes an infinite number of perturbations and uses a single matrix equation that contains the information for both the eigenvalue and eigenvector corrections. The formula reduces to the standard case of one perturbation in the appropriate limit. This formulation streamlines the derivations that are traditionally tedious in perturbation theory, facilitating high-order calculations.

Accurate determination of crystal structures is central to materials science, underpinning the understanding of composition-structure-property relationships and the discovery of new materials. Powder X-ray diffraction is a key technique in this pursuit due to its versatility and reliability. However, current analysis pipelines still rely heavily on expert knowledge and slow iterative fitting, limiting their scalability in high-throughput and autonomous settings. Here, we introduce a physics-guided contrastive learning framework termed as XCCP. It aligns powder diffraction patterns with candidate crystal structures in a shared embedding space to enable efficient structure retrieval and symmetry recognition. The XRD encoder employs a dual-expert design with a Kolmogorov-Arnold Network projection head, one branch emphasizes low angle reflections reflecting long-range order, while the other captures dense high angle peaks shaped by symmetry. Coupled with a crystal graph encoder, contrastive pretraining yields physically grounded representations. XCCP demonstrates strong performance across tasks, with structure retrieval reaching 0.89 and space group identification attains 0.93 accuracy. The framework further generalizes to compositionally similar multi principal element alloys and demonstrates zero-shot transfer to experimental patterns. These results establish XCCP as a robust, interpretable, and scalable approach that offers a new paradigm for X-ray diffraction analysis. XCCP facilitates high-throughput screening, rapid structural validation and integration into autonomous laboratories.

We present a single-shot near-field technique, where the near-field scan is performed on a single sample without repeating measurements or averaging over multiple samples, to reconstruct the isofrequency surfaces of metamaterials in the microwave regime. In our approach, we excite resonant modes using a fixed source in a resonator composed of the material under test and map the in-plane field distribution with a movable probe. Applying a fast Fourier transform (FFT) to the measured field reveals the sample's in-plane dispersion. By extending this analysis over multiple frequencies and comparing the results with Fabry-Pérot resonances, we retrieve the full three-dimensional dispersion relation. When we apply the method to a double non-connected wire metamaterial, it accurately captures the low-frequency hyperbolic isofrequency surface, providing both a precise experimental tool and conceptual insight into spatially dispersive metamaterials.

We study how the inclusion of energy dependence as dictated by quantum chromodynamic (QCD) small-$x$ evolution equations affects key observables in ultra-relativistic heavy-ion collisions. Specifically, we incorporate JIMWLK evolution into the IP-Glasma framework, which serves as the initial condition for a simulation pipeline that includes viscous relativistic hydrodynamics and a hadronic afterburner. This approach enables a consistent modeling of highly energetic nuclei across varying Bjorken-$x$ values, which are relevant for different collision energies and rapidity regions. In comparison to the standard IP-Glasma setup without small-$x$ evolution, we observe pronounced changes in particle multiplicities and spectral distributions, especially in smaller systems and at the highest available energies. We further explore effects on anisotropic flow observables and correlations between mean transverse momentum and elliptic flow. Our findings underscore the critical role of nonlinear QCD evolution in accurately modeling the early stages of heavy-ion collisions, as well as its implications for extracting transport properties of the quark-gluon plasma.

When a hole is introduced into an elastic material, it will usually act to reduce the overall mechanical stiffness. A general ambition is to investigate whether a stiff shell around the hole can act to maintain the overall mechanical properties. We consider this effect from a macroscopic continuum perspective down to atomistic scales. For this purpose, we focus on the basic continuum example situation of an isotropic, homogeneous, linearly elastic material loaded uniformly under compressive plane strain for low concentrations of holes. As we demonstrate, the thickness of the shell can be adjusted in a way to maintain the overall stiffness of the system. We derive a corresponding mathematical expression for the thickness of the shell that conceals the hole. Thus, one can work with given materials to mask the presence of the holes simply by adjusting the thickness of the surrounding shells, with no need to change the materials. Our predictions from linear elasticity continuum theory are extended to atomistic levels using molecular dynamics simulations of a model Lennard-Jones solid. These extensions attest the robustness of our predictions down to atomistic scales. Thus, they open a straightforward possibility to adjust the strategy of mechanical cloaking via atomistic manipulations. From both perspectives, the underlying concept is important in the context of light-weight construction.

The mean squared displacement has been widely used as the primary metric for comparing quantum and classical random walks, with quantum walks showing quadratic scaling versus linear scaling for classical walks. However, this comparison may not capture the full picture: while the mean squared displacement is well-suited for Gaussian distributions, quantum walk distributions exhibit distinctly non-Gaussian features. We propose that the mean hitting time offers a complementary perspective with clear operational meaning for search algorithms. Through analytical calculations, we show that quantum and classical walks yield identical MHT for symmetric initial conditions with two detectors, suggesting that the apparent quantum advantage seen in MSD comparisons may be context-dependent. Interestingly, introducing stochastic resetting reveals new dynamics. We demonstrate analytically that quantum walks can achieve reduced MHT under stochastic reset through quasi-momentum redistribution, while classical walks see no benefit. This quantum advantage naturally degrades with noise, the quantum walk converges to classical behavior. We suggest that MHT reduction under stochastic reset can serve as an additional signature of quantum behavior, particularly useful for characterizing quantum walk implementations on noisy quantum devices. Our results indicate that different metrics can reveal different aspects of quantum-classical comparisons in walk-based algorithms.

Convectively Coupled Equatorial Waves (CCEWs) dominate atmospheric variability on timescales of 2--30 days in the Tropics, bringing episodes of widespread heavy precipitation. This study compares the representation of CCEWs and their connection to upscale energy transfer in two Met Office Unified Model simulations of the full tropical channel with identical km-scale resolution for the DYAMOND Summer period. The principal difference between the simulations is that one parametrizes convection (GAL9), while the other (RAL3) is convection permitting. The GAL9 convection scheme acts to remove vertical instability without explicitly representing the resolved-scale circulation associated with convective plumes. We present the first quantitative diagnosis of interscale energy transfer and its relation to CCEWs. This diagnosis is important because upscale energy transfer between convection and large-scale waves may influence accurate simulation of tropical weather systems. The average upper-tropospheric upscale transfer simulated by RAL3 is approximately 50% higher than GAL9. CCEWs are more coherent in RAL3, with an average phase-speed variability 80% higher than observations, compared with 166% higher in GAL. RAL3 also simulates greater upscale energy transfer within waves than GAL9 with a stronger correlation between the interscale energy transfer and equatorial wave winds. Kelvin and Rossby waves are associated with upscale energy transfer from scales 4-8 times smaller than their wavelength, related to active deep convection within a particular sector of the wave phase. Our findings show that the explicit representation of convection has a significant impact on the simulation of upscale energy transfer, and is very likely to be a significant factor in the faithful simulation of convective coupling within CCEWs.