Altermagnetic magnons in crystalline materials exhibit momentum-dependent splitting whose nodal structure and chiral character are governed by the point-group symmetry of the magnetic sublattice rotation. Here, we demonstrate the first synthetic realization of altermagnetic magnonics in a continuum platform composed of antiferromagnetically coupled ferromagnetic films with alternating in-plane exchange anisotropies, showing that the key signatures of altermagnetic magnonics emerge beyond the crystalline setting. Solving the linearized Landau-Lifshitz equation within a dipole-exchange framework, we show that this architecture reproduces the characteristic momentum-dependent splitting, nodal directions, and anisotropic isofrequency contours of A-type altermagnets. Long-range dipolar interactions qualitatively reconstruct this exchange-driven spectrum by lifting the nominal nodal degeneracy, hybridizing opposite-chirality modes, and producing a finite, thickness-dependent wave-vector splitting along directions that are nodal in the exchange-only limit. Extending the bilayer to finite multilayers reveals that synthetic altermagnetism undergoes a parity-dependent reconstruction that separates surface and bulk altermagnetic excitations. These results establish altermagnetic magnon phenomenology as an engineerable collective response of dipole-exchange multilayers beyond microscopic crystal symmetries.

Background: In pencil beam scanning (PBS) proton therapy, plans are delivered as proton spot maps (PSMs). Although deep learning can rapidly predict 3D dose, direct conversion of dose into deliverable spot patterns remains limited. Purpose: We developed GenSpot, a two stage framework that infers deliverable PSMs from CT and dose, and evaluated it in prostate SBRT by comparing Monte Carlo (MC) doses from GenSpot and clinical PSMs. Methods: GenSpot uses a physics informed projected proton spot map (PrPSM) representation, projecting spots through CT with water equivalent thickness and PDD information to align spots with the CT/dose grid while preserving linearity with spot weights. The dataset included 1,036 fields from 259 prostate SBRT plans, split 80%/10%/10% for training, validation, and testing. A 3D SwinUNETR predicted PrPSMs from CT and dose. Field specific PSMs were reconstructed using column wise nonnegative Lasso regression with precomputed PDD curves. GenSpot and clinical MC doses were compared using MAE, 3D gamma analysis, and composite plan DVH metrics. Results: On the test set, SwinUNETR achieved PrPSM MAE of 0.06 +/- 0.02 with high similarity to clinical PrPSMs. GenSpot MC doses showed low MAE of 0.07 +/- 0.03 Gy in the nonzero dose region and gamma passing rates of 0.90 at the field level and 0.97 at plan level. Composite DVH differences were within 1 Gy for targets and organs at risk, though the CTV showed a modest high dose increase. Spot complexity was similar to clinical plans, with slightly more spots. Prediction and reconstruction averaged 0.02 s and 2.1 s/field. Conclusions: GenSpot generated machine deliverable PSMs from CT and dose whose MC doses closely matched clinical PSM doses in a single institution prostate SBRT cohort. This physics informed dose to spots framework may support automated PBS planning and adaptive replanning, pending broader validation.

Efficiently decomposing finite element stiffness matrices into the Pauli basis is challenging due to the exponential growth of Pauli strings with problem size. A naive Pauli expansion requires $Θ(8^{\lceil \log_2 N \rceil})$ operations, where $N$ denotes the number of degrees of freedom, rendering direct decomposition infeasible for large systems. Existing approaches exploit algebraic sparsity or operator structure but do not incorporate the geometric organization intrinsic to finite element discretizations, and consequently exhibit poor scaling for stiffness matrices. To address this problem, we introduce PHASE, a hierarchical, geometry-aware Pauli decomposition algorithm that leverages recursive mesh partitioning to organize element contributions across multiple spatial scales. PHASE employs a hybrid strategy that combines full- and reduced-space Tensorized Pauli Decomposition with Fast Walsh-Hadamard Transform-based aggregation to assemble global Pauli coefficients efficiently. We show that this approach yields a dimension-dependent reduction in the exponential scaling exponent of Pauli assembly asymptotic complexity relative to existing methods, reducing the cost from $2^{2{\lceil \log_2 N \rceil}}$ to $2^{γ_d{\lceil \log_2 N \rceil}}$ with $γ_d < 2$ under standard mesh regularity and balanced partition assumptions. These results substantially improve the feasibility of quantum-compatible operator synthesis for large-scale finite element models.

Software engineering teams increasingly depend on GitHub issue threads to coordinate work, report bugs, and negotiate technical decisions, yet most repository health tools focus on code metrics and ignore the conversational dynamics that drive or stall development. This paper presents SentTrack, a dual-lens framework for detecting socio-technical bottlenecks from GitHub issue discussions. Applied to the AvaloniaUI open-source repository across approximately 9,000 issue threads, the framework addresses three questions: how to automate workflow-inefficiency detection from real-time conversational data, whether sentiment signals can surface risk earlier than traditional label-based methods, and how to isolate human narrative from machine-generated noise in mixed-media issue text. SentTrack combines two complementary pipelines. A horizontal pipeline translates raw issue reports into clean summaries using a large language model, extracts mid-level concern phrases, and clusters them through UMAP and HDBSCAN, producing 613 semantic clusters from the first 3,608 issues processed. A vertical pipeline applies the ABCDE collaborative interaction framework to classify each comment and infer thread-level outcomes. Across the full corpus, 49\% of threads ended in stagnation and only 13\% reached resolution, with the resolution gap identified as the dominant bottleneck signal. A weighted scoring engine that combines negativity, stagnation, resolution gap, and thread length gives maintainers an interpretable prioritization tool for high-friction discussions before they stall development.

The Linear Combination of Hamiltonian Simulation (LCHS) framework simulates dissipative linear dynamics by representing time evolution as an integral over unitary operators, which is discretized by quadrature and implemented via Hamiltonian simulation. While existing analyses achieve near-optimal scaling in time and precision using norm-based quantities of the dissipative generator, we show that implementing the Hamiltonian simulation steps with Multi-Product Formulas (MPFs) yields commutator-sensitive error and complexity bounds. We demonstrate that the quadrature rule affects not only discretization error but also commutator structure and query complexity. This dependence is quantified through post-quadrature analysis for abstract MPF error profiles and for general time-independent and local Hamiltonians using known commutator-sensitive MPF error estimates. We compare uniform trapezoidal and free-scale sinh--sinh quadrature, showing improved quadrature-cardinality scaling for the latter, and illustrate the framework with applications to fractional diffusion, advection--diffusion, and open quantum systems.

Infinitesimal deformations of $\text{AdS}_5 \times \mathbb{S}^5$ form a representation of the AdS supersymmetry algebra. The structure of this representation has not yet been completely described in the literature. Some information can be obtained just from the fact that the space of deformations is the cohomology of a nilpotent BRST operator. We can consider the bicomplex formed by the BRST operator and the Lie cohomology differential, and its two spectral sequences. Their matching imposes some constraints on the structure of representations, which we start exploring in this paper. In particular, we clarify the structure of ghost number three zero modes.

Entanglement-assisted (EA) quantum QC-LDPC codes offer strong error-correction capabilities with structured parity-check matrices, but their practical use depends on efficient encoder circuits and the availability of pre-shared Bell pairs (ebits). In all encoder implementations based on the stabilizer formalism, the dominant contribution to this complexity comes from the use of controlled gates. In this paper, we adopt the Sharma-Kumar-Garani (SKG) encoder construction. We formulate the encoder optimization as a search over GF(2) row operations that decompose the binary matrix derived from its CNOT sub-sequence. We solve this problem using a beam search algorithm guided by a Hamming-distance heuristic. For the tested EA quantum QC-LDPC code families, the proposed method achieves CNOT-count reductions of 7.3-34.0% relative to the SKG baseline encoder. The optimized circuits also yield lower CNOT counts than Patel-Markov-Hayes synthesis on all tested instances and are verified by stabilizer-tableau simulation. These results show that substantial encoder simplification is possible for structured EA QC-LDPC codes.

We prove a conjecture on the minimal number of generators of licci zero-dimensional ideals that are either monomial or have small Loewy colength.

Background: To our knowledge, no tools have been installed in clinic for delivered and planned dose differences evaluation. This difference could be large for head and neck patients who suffer the most anatomy changes compared with other treatment sites due to long treatment courses and difficulty in eating. At the same time, variable RBE dose is an increasing concern for proton therapy. The constant RBE 1.1 is widely applied in clinics, however, the real RBE is larger than 1.1 especially at the end of beam range. How they are different and what the influence on plan evaluation are an interesting topic to investigate.

Safety assurance cases provide structured justifications that safety-critical systems meet their safety requirements. Recently, the notion of defeaters has emerged as a rigorous means of challenging the validity of safety arguments. Examples of defeaters might include overly strict claims, unreliable evidence, or reasoning gaps. However, defeaters remain ad hoc, lack structured support for critical reflection, are inconsistently described, are difficult to review, and lack documentation standards. To address this, we propose Defeater Cards, a new structured documentation artifact for systematically characterizing, reasoning about, and managing defeaters in safety cases. Drawing on a literature survey and thematic analysis, we identify documentation criteria that inform the card's structure, based on the 5W1H framework. Defeater Cards are designed to support informed analysis and evolution, improve traceability and auditability, and enable the reuse of defeater knowledge across systems and product variants. We demonstrate their applicability through two cross-domain case studies, showing how they expose hidden assumptions, surface reasoning gaps, and support ongoing safety assurance case evolution. To support adoption and community reuse, we also release an open-source repository of defeater cards as a baseline upon which researchers and practitioners can build and describe lessons learned.

Let $G$ be the group of power series $x+a_2x^2+a_3x^3+\cdots\in R[[x]]$ under substitution, where $R$ is a commutative ring with $1\neq 0$ of prime characteristic $p$. Given any $n\geq 1$, the subgroup $K_n=\{x+a_{n+1}x^{n+1}+a_{n+2}x^{n+2}+\cdots\,|\, a_i\in R\}$ is normal in $G$, and the quotient $G_n=G/K_n$ is the group of truncated polynomials over $R$ of degree $\leq n$ under substitution. In this paper, we compute the exponent of the image of $K_r$ in $G_n$, for all $r,n\geq 1$, indicating in every case a family of elements realizing this exponent.

The aim of this note is to present a simple strategy to answer negatively a decomposition question on tori posed by Colliot-Thélène and Sansuc in the article \textit{Principal Homogeneous Spaces under Flasque Tori: Applications} of 1987. We then deduce a torus $T$ over $\mathbb{Q}$ and a prime number $p$ such that $T(\mathbb{Z}_p)\,T(\mathbb{Q})\not=T(\mathbb{Q}_p)$, where $T(\mathbb{Z}_p)$ denotes the maximal compact subgroup of $T(\mathbb{Q}_p)$.

Motivated by forthcoming high-energy experiments at Jefferson Lab and the Electron-Ion Collider, this dissertation develops a novel relativistic formulation of nuclear structure. While previous scattering models were updated to include nucleon-nucleon short-range correlations (SRCs) to explain cross-section plateaus, modern high-kinematics experiments require a relativistic approach. We reformulate conventional tools into a light-front-quantized framework, utilizing density functional theory and similarity renormalization group techniques. Our calculations successfully reproduce nuclear binding energies, shell structure, and SRC physics. However, we show that a purely nucleonic description fails to fully capture inclusive electron-nucleus data or the plateaus at high Bjorken-$x_B$. This demonstrates the critical importance of inelastic final-state interactions currently omitted by standard SRC phenomenology.

Behavioral biometrics offer a promising approach for continuous authentication, but their fairness across demographic groups remains largely unexplored. This paper investigates gender bias in swipe-based authentication using the BBMAS (117 users) and ANTAL (71 users) datasets and evaluates XGBoost and DenseNet classifiers through False Acceptance Rate (FAR) and False Rejection Rate (FRR). XGBoost achieved authentication accuracies of 92% and 94% on the BBMAS and ANTAL datasets, respectively, while statistical tests (Kolmogorov-Smirnov, Mann-Whitney, and Wasserstein permutation) found no significant gender differences in authentication error rates across almost all experimental settings. These findings suggest that swipe-based authentication can achieve high accuracy while maintaining comparable performance for male and female users, supporting its potential as a fair and reliable behavioral biometric modality.

We introduce a construction of Pauli Hamiltonians with exactly known ground-state energies, intended as reference instances for ground-state energy estimation algorithms. The construction embeds a planted block-product state as the simultaneous ground state of a sum of frustration-free local clauses on overlapping supports, exposes the resulting model only as a polynomial-size linear combination of Pauli operators, and admits optional Clifford conjugation that preserves the spectrum. The framework subsumes classical planted constraint-satisfaction problems as a diagonal special case, providing a direct embedding channel through which classical hardness properties can be inherited. Open-source software, certification keys, and example instances are made publicly available.

Finite geometry (FG) codes combine the algebraic properties of classical block codes with the iterative belief propagation (BP) decoding ability of low-density parity-check~(LDPC) codes. However, exploiting both advantages in practice is hindered by the fact that the standard incidence matrix between $(μ+1)$-flats and points is dense and contains many short cycles for any flat dimension $μ\geq 1$. In this work, we propose to sparsify the decoding matrix based on pencil selection, formulated as a constant-dimension subspace packing problem and solved explicitly using lifted Gabidulin codes. For both affine and projective geometries, sparse parity-check matrices are constructed and verified for FG codes of lengths up to $1024$. Simulations on four FG codes show no visible error floor and around $0.5$~dB gain over corresponding 5G LDPC codes at a block error rate of $10^{-7}$.

We perform a Hamiltonian constraint analysis of metric $f(R)$ gravity in the Jordan frame and show that the regular constraint classification degenerates on singular phase-space surfaces located at $f'(R)\!=\!0$ and $f''(R)\!=\!0$. We then study the perturbative implications of these surfaces. For exact backgrounds satisfying $f(R)\!=\!0$ and $f'(R)\!=\!0$, the linearized spectrum is empty; the known pure $R^2$ result is therefore a special case of a more general degeneracy in $f(R)$ gravity. We also show that FLRW trajectories in the Starobinsky model can cross the surface $f'(R)=0$, but that inhomogeneous perturbations develop a degenerate constraint structure at the crossing. The resulting crossing condition is better interpreted as a regularity condition for perturbative evolution than as an ordinary constraint within the Dirac--Bergmann algorithm. Together, these results distinguish backgrounds that lie entirely on a singular surface from backgrounds that cross one dynamically, and show that the two situations lead to different perturbative degeneracies.

This study extends the investigation of rebound outward migration to multi-planet systems near an inner expanding disk cavity driven by stellar X-ray photoevaporation. Using 2D hydrodynamical simulations, we explore how systems of two and three planets that span masses from super-Earths to Jupiters evolve as the disk disperses from the inside out. Our results show that rebound migration can substantially reshape multi-planet architectures in the final stages of disk clearing. Owing to the strong, positive corotation torque exerted onto the planet near the cavity edge, divergent migration of the neighbouring planets can break resonant configurations and trigger dynamical instabilities, producing non-resonant orbits with widened period ratios. However, the outcome depends critically on planet mass and the disk dispersal timescale. In lower-mass disks where cavity expansion is too rapid, rebound migration is suppressed, and systems tend to preserve resonant chains. These findings suggest that the rebound mechanism can provide a compelling pathway to explain the prevalence of widely separated, non-resonant architecture observed in the exoplanet population.

We establish explicit subconvex bounds for central values of Rankin--Selberg $L$-functions $L(1/2,π\timesπ')$ associated with pairs of unitary cuspidal automorphic representations of $\mathrm{GL}_2$ over a number field. Building on the spectral reciprocity framework of Michel and Venkatesh, we develop a refined, fully explicit form of spectral reciprocity that allows for precise control of conductors and local test vectors. As a consequence, we obtain an explicit subconvex bound, which, even over $F=\mathbb{Q}$, improves all previously known results. We further apply these bounds to several arithmetic problems. These include effective equidistribution of CM suborbits on quaternionic Shimura varieties, quantitative equidistribution of totally geodesic submanifolds, a uniform quantitative form of dihedral quantum unique ergodicity over number fields, and an application to distinguishing cuspidal automorphic representations.

This paper investigates coherent multiband orthogonal frequency division multiplexing (OFDM) sensing within an integrated sensing and communication (ISAC) framework. We consider an intra-band configuration in which two sensing subbands of equal width are allocated symmetrically within the same OFDM channel, while the central portion remains available for communication. We address the reconstruction of missing frequency-domain samples induced by the spectral gap and the suppression of the resulting grating lobes in the delay profile. To this end, we propose a low-complexity iterative reconstruction method consisting of an initial delay-domain equalization stage and an iterative apodization-based operator with data-consistency enforcement. Performance results for multi-target scenarios show that the proposed approach remains close to the full-band reference for moderate gap sizes and degrades only for larger gaps because of residual grating lobes. Compared with the compressed-sensing-based orthogonal matching pursuit (OMP) baseline, it exhibits a more favorable performance trend as the number of targets increases, especially in the practically relevant low-signal-to-noise ratio (SNR) regime, while offering a complexity scaling that is independent of the estimated number of targets.

We study the query complexity of Boolean functions $f: \{0, 1\}^n \rightarrow \{0, 1\}$ in the noisy query model introduced by Feige, Raghavan, Peleg and Upfal [SICOMP 1994]. In this model, an algorithm can adaptively query the bits of an input vector, but each query result is independently flipped with constant probability $p \in (0, 1/2)$; repeated queries are allowed. The noisy query complexity $\mathsf{N}_p(f)$ of a function $f$ is defined as the minimum expected number of queries needed to compute $f(x)$ with error probability at most $1/3$, for the worst case input $x$. We prove a general lower bound on $\mathsf{N}_p(f)$ based on degree statistics of certain subgraphs of the Boolean hypercube. This is the first general lower bound beyond those implied by the simple observation that $\mathsf{N}_p(f)$ is lower bounded by the randomized query complexity. We show that this recovers (up to a constant factor) most previously known lower bounds on the noisy query complexity of Boolean functions, providing a unified framework for understanding these results and simplifying the proofs in several cases. Furthermore, this resolves in the affirmative an open problem of Gu, Li and Xu [COLT 2025] that $\mathsf{N}_p(f) = Ω(\mathsf{I}(f) \log \mathsf{I}(f))$, where $\mathsf{I}(f)$ denotes the total influence of $f$. We also apply our general lower bound to obtain tight bounds on the noisy query complexity for several new functions.

We present ALMA high-resolution ($\sim$0.25$^{\prime\prime}$/2 kpc) CO(5-4) and CO(4-3) observations of three $z\sim 3$ submillimetre-selected dusty galaxies from the ALESS survey. These data complement existing [sub]-kpc scale ALMA 870$μ$m continuum imaging and JWST NIRCam and MIRI imaging from the ALESS-JWST program, allowing us to trace the molecular gas, dust-obscured star formation, and stellar populations on similar spatial scales. We spectroscopically confirm that two of the sources lie at the same redshift and are likely interacting. We find that the molecular-gas distribution broadly follows the dusty star-forming structures seen in the 870$μ$m dust continuum imaging, but that the gas reservoirs are significantly more extended than the dust emission with a spatial extent comparable to the rest-frame near-infrared stellar emission. By modeling the kinematics for the two highest signal-to-noise sources, we find that the galaxies are well-fit by rotating disc models with high ratios of ordered to random motion ($V_{\rm{max}}/\overlineσ=5\pm1$ and $6\pm1$), although smaller-scale kinematic deviations cannot be ruled out at the current sensitivity and spatial resolution. Finally, utilizing the high-resolution 870$μ$m dust continuum and CO data, we investigate star-formation scaling relations on kpc-scales in these high-redshift galaxies. Assuming a constant CO-to-H$_{2}$ conversion factor and excitation ratio, we find that the data are offset from theoretical star-formation relation predictions that do not take turbulence into account, but consistent with gravo-turbulent models, thereby suggesting that turbulence plays a central role in regulating star formation at high redshift.

A point of a scheme has an associated tangent cone, the spectrum of a standard graded algebra encoding the local singularity. Its homological complexity can be measured by its graded Betti table: a matrix that records a part of the structure of its graded, minimal free resolution over a polynomial ring. A natural question is whether the homological complexity of the tangent cones varies arbitrarily across a scheme. In this paper, we show that this is not the case for a quasi-excellent Noetherian scheme; over such schemes, only finitely many graded Betti tables can occur. More generally, we show that a coherent sheaf over a quasi-excellent Noetherian scheme admits finitely many graded Betti tables, and that the constancy loci for the graded Betti table are constructible. As an immediate consequence, regularity is bounded on a quasi-excellent Noetherian scheme.

Graphical model editing is shifting from desktop applications to web-based tools. We analyze the characteristics of existing frameworks and, based on this analysis, we derive a set of design principles that imply low-effort generation, extensive customization possibilities, and straightforward deployment of the resulting editors. On these grounds, we introduce EMFular, a purely web-based framework for managing EMF models without any backend. The accompanying EMFular generator maps a given Ecore model (an EMF metamodel) to a ready-to-use and ready-to-customize graphical editor. EMFular editors provide 'EMF consistency', that is, they not only support standard modeling operations such as creation, inspection, navigation, editing, and undo/redo, but they also handle containment and inverse references in close alignment with EMF; they also provide interoperability with existing EMF tooling through compatible de-/serialization. A generated editor is an Angular project with designated extension points, which allows developers to customize and extend all aspects of the editor using the expressive power of Angular and its ecosystem, guided by the extension points of EMFular. We evaluate EMFular in terms of editor adequacy (available editing capabilities), adaptability (customization mechanisms and required effort), and robustness of the generation.

We investigate the electronic screening of long-range Coulomb interactions in carbon nanotubes with different chiralities using first-principles calculations within the random-phase approximation. Depending on their wrapping vector, carbon nanotubes exhibit either metallic or semiconducting behavior, providing an ideal platform to explore how reduced dimensionality and electronic structure govern screening in one-dimensional systems. The strength of on-site Coulomb interactions in these compounds falls within the range of 3.5 to 5 eV, which is approximately 2-3 eV smaller than the corresponding values in nanoribbon compounds. This reduction subsequently affects the value of long-range interactions, consistent with experimental results regarding the smaller binding energy of excitons in nanotubes. Despite their common carbon backbone, we find that the effective interaction landscape depends not only on metallicity but also sensitively on chirality and band topology. In particular, armchair and zigzag nanotubes with similar electronic character exhibit markedly different screening efficiencies. Our results establish a unified microscopic picture of electronic screening in carbon nanotubes and place them in direct context with previous first-principles studies of low-dimensional carbon nanostructures.

Interval-censored data frequently arise in clinical research where event times are only known to fall within specific assessment windows. Although the Cox proportional hazards model is a standard approach for such data, existing Wald-type tests often suffer from instability or poor performance in small samples. In this paper, we propose a robust spline-sieve-based likelihood ratio test for interval-censored data. We develop a computationally efficient estimation framework that ensures numerical stability. Furthermore, we rigorously establish the asymptotic distribution of the proposed likelihood ratio statistic, providing a solid theoretical foundation for statistical inference. Extensive simulation studies demonstrate that our approach achieves superior error control and higher power compared with traditional approaches. The practical utility of the method is further illustrated through the analysis of a real-world clinical dataset.

We show that isotropic random walks on the complex projective space provide a canonical and analytically tractable stochastic-geometric framework for the exploration of quantum-state space. The approach combines harmonic analysis on compact rank-one symmetric spaces with stochastic pure-state evolution and yields explicit analytical expressions for transition kernels, fidelity statistics, and geometric observables associated with the Fubini--Study metric. In particular, the framework provides a solvable reference model for isotropic depolarization and Haar equilibration, reproducing Haar-random fidelity statistics and the invariant measure on projective Hilbert space without specifying a microscopic Lindblad generator. In the short-time regime, the stochastic evolution converges to Brownian diffusion generated by the Fubini--Study Laplace--Beltrami operator, while the long-time limit exhibits concentration-of-measure behaviour characteristic of high-dimensional random quantum states. We further derive analytical and asymptotic results for the first-passage-time problem, including closed-form expressions in the Brownian limit for the mean first passage time and the long-time tail of the first-passage-time distribution. For high-fidelity target states, the mean first passage time exhibits a strong dimension-dependent divergence originating from the concentration properties of the Fubini--Study geometry.

In this paper, we obtain order estimates for the Kolmogorov widths of an intersection of a finite family of Besov classes $SB_{p_j,θ_j}^{\overline{r}_j}(\mathbb{T}^d)$ with dominating mixed smoothness in a Besov space $B_{q,σ}^{\overline{l}}(\mathbb{T}^d)$ in the case $2<q, \, σ<\infty$ when the parameters satisfy certain conditions of general position.

The bulk photovoltaic effect has become a valuable probe of the quantum geometry of Bloch bands. While it is restricted to inversion-broken systems within the dipole approximation, the finite momentum of light is appreciated to give rise to this effect even in centrosymmetric crystals, an effect referred to as "photon drag." In this work, we recast the photon drag effect at leading order in the optical wavevector, highlighting a previously neglected contribution arising intuitively from the electric quadrupole correction to light-matter coupling. In the language of band geometry, we identify this interband quadrupole as a multiband metric tensor that quantifies the variation of two resonantly driven states extrinsic to the subspace they span. We predict that systems in which three or more bands strongly admix in momentum space, such as twisted MoTe$_2$ bilayers, will have anomalously large photon drag due to this quadrupolar effect. Our work provides a conceptual bridge between band-geometric organizing principles and electromagnetic multipole corrections in nonlinear optics.

Let $Δ$ be the Neumann Laplacian on the interval $(0,π)$, and let $T>0$. An integration by parts formula is proven for the spectral fractional Laplacian, $(-Δ)^α$, for $α\in (0,1)$. As an application, we prove well-posedness results for the structurally damped beam equation $$u_{tt}+Δ^2 u+ρ(-Δ)^αu_t=0, x\in (0,π),t>0$$ with various boundary conditions including $$ u_x(0,t)=u_{xxx}(0,t)=0;\ u_x(π,t)=f(t),\ u_{xxx}(π,t)=0, $$ and $f\in L^2(0,T)$ and appropriate initial conditions. Viewing $f$ as a control, we prove null-controllability. Analagous results are proven for higher order controls, and for the Dirichlet Laplacian.