arXiv subjects

Thomas Weber

Publications and source records attributed to Thomas Weber.

At least 19 recordsLinked to original sources

arXiv2026

On Braided Differential Calculi and Quantum G-structures

We develop a theory of first order differential calculi in braided monoidal categories and classify braided covariant and bicovariant calculi on braided Hopf algebras. We show that, under certain conditions, bicovariant calculi can be transmuted to braided bicovariant calculi. For Radford--Majid biproducts, we combine bicovariant calculi on a Hopf algebra and braided bicovariant calculi on the corresponding braided Hopf algebra to covariant smash product calculi. The associated Maurer--Cartan form is shown to decompose into a direct sum of the Maurer--Cartan forms of the structure Hopf algebra of the quantum principal bundle and the braided Hopf algebra on the base. Geometrically, this construction realises the quantum affine extension of a given Hopf algebra, and we prove that the resulting quantum principal bundle is equipped with a frame resolution induced by the quantum Maurer--Cartan form. Building on this correspondence, we introduce and develop the notion of quantum $\textrm{G}$-structure, proving that quantum $\textrm{G}$-structures are quantum frame resolutions on the reduction. The theory is illustrated by examples based on transmutations of higher analogues of Sweedler's Hopf algebra and on the braided quantum plane, seen as a Yetter--Drinfeld module of $O_q(\mathrm{GL}_2)$.

math.QA↗

arXiv2026

An infinitesimal deformation of the post-Lie and post-Hopf algebra correspondence

We describe infinitesimal deformations of post-Lie algebras and post-Hopf algebras and prove that the adjunction given by the universal enveloping algebra and primitive elements functors is compatible with the infinitesimal structure. When restricted to connected and cocommutative infinitesimal post-Hopf algebras, this becomes an equivalence of categories, which constitutes an extension of the Cartier--Milnor--Moore theorem. We classify infinitesimal post-Lie structures on $\mathfrak{sl}(2)$, and discuss a class of infinitesimal post-Lie algebras emerging from flat connections with covariantly-constant torsion. Moreover, we classify infinitesimal post-Hopf structures on Sweedler's Hopf algebra. Cocommutative infinitesimal post-Hopf algebras induce a Hochschild 2-cocycle on the associated subadjacent Hopf algebra. Finally, we prove that the quadratic operad of infinitesimal post-Lie algebras is Koszul, by using a filtered distributive law between the operads of Lie algebras and bi-magmas.

math.QA↗

arXiv2026

Noncommutative vector field calculi

We discuss noncommutative differential geometry from a vector field centric point of view. This is based on the notion of first order vector field calculus (FOVC), which has been previously introduced by Borowiec under the name Cartan pair. We define the universal FOVC and construct an adjunction between the categories of FOVC and that of first order differential calculi, showing that the vector field approach is dual, though not equivalent, to the differential form one. This correspondence is then extended to covariant vector field and differential calculi. On Hopf algebras, (bi)covariant FOVC are in bijection with (bicovariant) quantum tangent spaces. For Hopf--Galois extensions, quantum tangent spaces give rise to vertical vector fields and in this setup we further describe base vector fields and horizontal vector fields and show that they are related via a noncommutative Atiyah sequence. Multiple examples, based on braided derivations, finite groups and the quantum Hopf fibration, are given. The vector field approach is further enriched by a sheaf-theoretic treatment, which recovers the former as a local, or affine, picture.

math.QA↗

arXiv2026

Typing Behavior in Human-LLM Interaction: Keystroke Dynamics Reveal Cognitive Effort During Prompting

As Large Language Models (LLMs) become increasingly integrated into daily routines, understanding how users interact with these systems is crucial for effective human-AI collaboration. This work investigates keystroke dynamics as a behavioral measure of user mental effort and perceived output usefulness in human-LLM interaction. We conducted a user study (N = 36) to examine how task difficulty (easy vs. hard) and device type (desktop vs. mobile) influence typing behavior and workload (NASA-TLX) during interactions. Our results indicate that hard tasks led to significantly more keystrokes, slower typing, increased pauses, and higher self-reported workload. Device type had weaker effects, with mobile use slightly reducing input length and typing speed. While keystrokes captured differences in cognitive effort, they did not predict perceived LLM output usefulness. These findings highlight the potential of keystroke dynamics as real-time indicators of cognitive effort during LLM prompting, while also showing their limitations in capturing perceived collaboration success.

cs.HC↗

arXiv2025

Integration of 2D Materials in Radial van der Waals Heterostructure Metasurfaces

Two-dimensional semiconductors, such as monolayer transition metal dichalcogenides (TMDC), exhibit strong excitonic transitions at room temperature and offer a unique platform for exploring light-matter interactions in nanoscale photonic systems. In this work, we demonstrate a compact and polarization-invariant photonic metasurface, fabricated from hexagonal boron-nitride (hBN) and based on radial bound states in the continuum (BIC), which are formed by radially distributed pairs of structurally asymmetric resonators. The metasurface employs multiple symmetry-breaking perturbations to support high quality-(Q-)factor resonances within a footprint smaller than 8 x 8 $\mu m^2$ - one-sixth of the area of previous approaches. Compared to established hBN metasurface designs, the radial geometry furthermore achieves significantly higher Q-factors with a reduced footprint. By integrating the hBN photonic structure with a WS$_2$ monolayer, we observe enhanced photoluminescence when its resonance is spectrally aligned with the exciton resonance, accompanied by signatures of discrete momentum-space patterns that identify the orbital-angular-momentum-carrying ring eigenmodes. These features persist over a wide range of excitation powers and show minimal linewidth broadening, indicating robust and spatially modulated exciton-photon coupling. This work establishes a scalable approach for generating hybrid photonic-excitonic states with momentum-space structure, offering new opportunities for exciton localization, valley emission, spatially programmable light-matter interaction in two-dimensional material platforms and compact luminescent devices based on 2D material-integrated metasurfaces.

physics.optics↗

arXiv2025

Ultrafast dynamics of coherent exciton-polaritons in van der Waals semiconductor metasurfaces

Enabling coherent light-matter interactions is a critical step toward next-generation quantum technologies. However, achieving this under ambient temperature conditions remains challenging due to rapid dephasing in optically excited systems. Optical metasurfaces based on quasi-bound states in the continuum have recently emerged as a powerful platform for reaching the strong light-matter coupling regime in flat, subwavelength thickness devices. Here, we investigate ultrafast exciton-polariton dynamics in self-hybridized WS$_2$ thin-film metasurfaces. Using hyperspectral momentum-resolved imaging, we reconstruct the highly anisotropic exciton-polariton dispersion, with a transition from positive to negative effective mass along orthogonal symmetry axes. Femtosecond pump-probe and multidimensional spectroscopy reveal detuning-dependent polariton dynamics with a coherence time up to ~110 fs, and allow direct observation of the coherent dynamics through ultrafast Rabi oscillations with ~45 fs period. We describe this behaviour with a three-eigenstate model that couples the photonic resonance with both bright and dark excitons, extending the conventional two-state picture of strong coupling. Our results establish van der Waals metasurfaces as a promising platform for next-generation polaritonic devices, enabling coherent quantum transfer of matter excitations at room temperature.

physics.optics↗

arXiv2025

Topological Control of Polaritonic Flatbands in Anisotropic van der Waals Metasurfaces

Anisotropic van der Waals (vdW) materials exhibit direction-dependent optical and electronic properties, making them valuable for tailoring directional light-matter interactions. Rhenium disulfide (ReS$_2$) stands out for its strong in-plane anisotropy and its thickness-independent direct-bandgap excitons, which can hybridize with light to form exciton-polaritons. In parallel, metasurfaces, engineered arrays of nanoscale subwavelength resonators, can support ultra-sharp photonic modes in the form of quasi-bound states in the continuum (qBICs). Topological transformations of photonic modes can give rise to flatbands, i.e., dispersionless states with quenched kinetic energy and vanishing group velocity. Intrinsic material anisotropy offers an unexplored route to robust far-field flatband formation and control. Here, we demonstrate how structuring an intrinsically anisotropic excitonic material into a resonant metasurface fundamentally transforms its photonic topological features and light-matter coupling behavior, allowing us to drive and topologically control extended far-field flatband formation. To this end, we fabricate C$_4$-symmetric metasurfaces directly from bulk ReS$_2$. The intrinsic anisotropy lifts the initial double degeneracy of the qBIC mode and yields two distinctly polarized resonances. It also reshapes the topological landscape: the integer topological charge of the qBIC mode splits into momentum-separated half-integer singularities, thereby flattening the far-field photonic dispersion. The resulting topologically-controlled photonic flatbands are then tuned in resonance with the linearly polarized excitonic transitions of ReS$_2$, resulting in two distinct, directionally hybridized exciton-polariton flatband regimes. These findings establish anisotropic vdW metasurfaces as a new platform for topologically engineered flatbands and flatband-driven light-matter coupling.

physics.optics↗

arXiv2025

Takeuchi-Schneider equivalence and calculi for homogeneous spaces of Hopf algebroids

We develop a notion of covariant differential calculus for Hopf algebroids. As a byproduct, we prove analogues of the fundamental theorem of Hopf modules and a Takeuchi-Schneider equivalence in the realm of Hopf algebroids. The resulting categorical equivalences enable us to classify covariant calculi on Hopf algebroids and, more in general, covariant calculi on quantum homogeneous spaces in this context, in terms of substructures of the augmentation ideal. This generalises the well-known classification results of Woronowicz and Hermisson. A particular focus is given on examples, including covariant calculi on the Ehresmann-Schauenburg Hopf algebroid of a faithfully flat Hopf-Galois extension, and covariant calculi on scalar extension Hopf algebroids, as well as homogeneous space variants of the latter.

math.QA↗

arXiv2025

A comparative analysis of plasmonic and dielectric metasurface sensing platforms powered by bound states in the continuum

Nanophotonic platforms based on surface-enhanced infrared absorbance spectroscopy (SEIRAS) have emerged as an effective tool for molecular detection. Sensitive nanophotonic sensors with robust resonant modes and amplified electromagnetic near fields are essential for spectroscopy, especially in lossy environments. Metasurfaces driven by bound state in the continuum (BICs) have unlocked a powerful platform for molecular detection due to their exceptional spectral selectivity. While plasmonic BIC metasurfaces are preferred for molecular spectroscopy due to their high surface fields, enhancing the interaction with analytes, dielectric BICs have become popular due to their high-quality factors and, thus high sensitivity. However, their sensing performance has largely been demonstrated in air, neglecting the intrinsic infrared (IR) losses found in common solvents. This study evaluates the suitability of plasmonic versus dielectric platforms for in-situ molecular spectroscopy. Here, the sensing performance of plasmonic (gold) and dielectric (silicon) metasurfaces is assessed across liquid environments with varying losses resembling typical solvents. The results show that dielectric metasurfaces excel in dry conditions, while plasmonic BIC metasurfaces outperform them in lossy solvents, with a distinct crossover point where both show similar performance. Our results provide a framework for selecting the optimal metasurface material platform for SEIRAS studies based on environmental conditions.

physics.optics↗

arXiv2025

Strong coupling and interfering resonances in isolated van der Waals nanoresonators

The study of strong light-matter interaction in van der Waals materials is at the forefront of current research in physics and chemistry, and it can be enhanced dramatically by employing resonances. Here we present the first observation of quasi-bound states in the continuum (qBICs) realized via polaritonic interfering resonances in isolated WS$_2$ nanodisks. We experimentally validate the existence of polaritonic qBICs driven by intrinsic coupling of Mie resonances and excitons. The system exhibits exceptionally strong light-matter interaction with a measured Rabi splitting exceeding 310 meV - the largest reported value among all transition metal dichalcogenide (TMDC) self-hybridized systems to date. The giant coupling strength stems from qBIC-induced in-plane field enhancement, which strongly interacts with in-plane excitonic dipoles while suppressing radiative losses. Polarization-controlled measurements further demonstrate selective excitation of qBIC through switching incident polarization to specific orthogonal configurations. The observed polarization-dependent coupling provides an additional degree of freedom to control over the hybrid states' spectral characteristics and spatial field distributions. Our demonstrations provide a pathway for engineering high-quality light-matter hybrid states in compact nanostructures, with potential applications in on-chip photonics, polaritonics, and quantum optics.

physics.optics↗

arXiv2025

Quantization of infinitesimal braidings and pre-Cartier quasi-bialgebras

In this paper we extend Cartier's deformation theorem of braided monoidal categories admitting an infinitesimal braiding to the non-symmetric case. The algebraic counterpart of these categories is the notion of a pre-Cartier quasi-bialgebra, which extends the well-known notion of quasitriangular quasi-bialgebra given by Drinfeld. Our result implies that one can quantize the infinitesimal $\mathcal{R}$-matrix of any Cartier quasi-bialgebra. We further discuss the emerging concepts of infinitesimal quantum Yang-Baxter equation and Cartier ring, the latter containing braid groups with additional generators that correspond to infinitesimal braidings. Explicit deformations of the representation categories of the gauge deformed quasitriangular quasi-bialgebras $E(n)$ are provided.

math.QA↗

arXiv2025

Gauge transformations on quantum principal bundles

We understand quantum principal bundle as faithfully flat Hopf--Galois extensions, with a structure Hopf algebra coacting on a total space algebra and with base algebra given by the coinvariant elements. To endow such bundles with a compatible differential structure, one requires the coaction to extend as a morphism of differential graded algebras. This leads to an exact noncommutative Atiyah sequence, a graded Hopf--Galois extension of differential forms and a canonical braiding on total space forms such that the latter are graded-braided commutative. We recall this approach to noncommutative differential geometry and further discuss the extension of quantum gauge transformations, in the sense of Brzezi\'nski, to differential forms. In this way we obtain an action of quantum gauge transformations on connections of the quantum principal bundle and their curvature. Explicit examples, such as the noncommutative 2-torus, the quantum Hopf fibration and smash product algebras are discussed.

math.QA↗

arXiv2025

Explainability for Embedding AI: Aspirations and Actuality

With artificial intelligence (AI) embedded in many everyday software systems, effectively and reliably developing and maintaining AI systems becomes an essential skill for software developers. However, the complexity inherent to AI poses new challenges. Explainable AI (XAI) may allow developers to understand better the systems they build, which, in turn, can help with tasks like debugging. In this paper, we report insights from a series of surveys with software developers that highlight that there is indeed an increased need for explanatory tools to support developers in creating AI systems. However, the feedback also indicates that existing XAI systems still fall short of this aspiration. Thus, we see an unmet need to provide developers with adequate support mechanisms to cope with this complexity so they can embed AI into high-quality software in the future.

cs.HC↗

arXiv2025

Ultrafast all-optical switching in nonlinear 3R-MoS$_2$ van der Waals metasurfaces

Second-order nonlinear optical processes are fundamental to photonics, spectroscopy, and information technologies, with material platforms playing a pivotal role in advancing these applications. Here, we demonstrate the exceptional nonlinear optical properties of the van der Waals crystal 3R-MoS$_2$, a rhombohedral polymorph exhibiting high second-order optical susceptibility ($\chi^{(2)}$) and remarkable second-harmonic generation (SHG) capabilities. By designing high quality factor resonances in 3R-MoS$_2$ metasurfaces supporting quasi-bound states in the continuum (qBIC), we first demonstrate SHG efficiency enhancement exceeding 10$^2$. Additionally, by using degenerate pump-probe spectroscopy, we harness the C$_{3v}$ system's symmetry to realize ultrafast SHG polarization switching with near-unity modulation depth. The operation speeds are limited only by the excitation pulse duration, allowing its characterization via the nonlinear autocorrelation function. These findings establish 3R-MoS$_2$ as a transformative platform for nanoscale nonlinear optics, offering large conversion efficiencies and ultrafast response times for advanced pulse measurement devices, integrated photonics, and quantum technologies.

physics.optics↗

arXiv2025

Fabrication Optimization of van der Waals Metasurfaces: Inverse Patterning Boosts Resonance Quality Factor

Van der Waals (vdW) materials have garnered growing interest for use as nanophotonic building blocks that offer precise control over light-matter interaction at the nanoscale, such as optical metasurfaces hosting sharp quasi-bound states in the continuum resonances. However, traditional fabrication strategies often rely on lift-off processes, which inherently introduce imperfections in resonator shape and size distribution, ultimately limiting the resonance performance. Here, an optimized fabrication approach for vdW-metasurfaces is presented that implements inverse patterning of the etching mask, resulting in increased resonator quality solely limited by the resolution of the electron beam lithography resist and etching. Applying this inverse fabrication technique on hexagonal boron nitride (hBN), quality (Q) factors exceeding $10^3$ in the visible spectral range were demonstrated, significantly surpassing previous results shown by lift-off fabricated structures. Additionally, the platforms potential as a biosensor was displayed, achieving competitive sensitivity and figure of merit of 220 in a refractive index sensing experiment. The inverse technique was applied to create chiral metasurfaces from hBN, using a two-height resonator geometry to achieve up to 50 % transmittance selectivity. This inverse lithography technique paves the way towards high-performances vdW-devices with high-Q resonances, establishing hBN as a cornerstone for next-generation nanophotonic and optoelectronic devices.

physics.optics↗

arXiv2025

NVP-HRI: Zero Shot Natural Voice and Posture-based Human-Robot Interaction via Large Language Model

Effective Human-Robot Interaction (HRI) is crucial for future service robots in aging societies. Existing solutions are biased toward only well-trained objects, creating a gap when dealing with new objects. Currently, HRI systems using predefined gestures or language tokens for pretrained objects pose challenges for all individuals, especially elderly ones. These challenges include difficulties in recalling commands, memorizing hand gestures, and learning new names. This paper introduces NVP-HRI, an intuitive multi-modal HRI paradigm that combines voice commands and deictic posture. NVP-HRI utilizes the Segment Anything Model (SAM) to analyze visual cues and depth data, enabling precise structural object representation. Through a pre-trained SAM network, NVP-HRI allows interaction with new objects via zero-shot prediction, even without prior knowledge. NVP-HRI also integrates with a large language model (LLM) for multimodal commands, coordinating them with object selection and scene distribution in real time for collision-free trajectory solutions. We also regulate the action sequence with the essential control syntax to reduce LLM hallucination risks. The evaluation of diverse real-world tasks using a Universal Robot showcased up to 59.2\% efficiency improvement over traditional gesture control, as illustrated in the video https://youtu.be/EbC7al2wiAc. Our code and design will be openly available at https://github.com/laiyuzhi/NVP-HRI.git.

cs.RO↗

arXiv2025

Symmetry breaking in Prussian Blue Analogues via growth--guided local ordering of hexacyanometallate vacancies

We report Growth--Guided Local Ordering, a novel mechanism of symmetry reduction in disordered crystals. This mechanism operates through the directional ordering of point defects during crystal growth, where defect correlations develop preferentially along the growth direction, resulting in reduced symmetry that persists in the final structure through the spatial distribution of defects. We demonstrate this phenomenon in Mn[Co]-Prussian Blue Analogues, disordered cyanide crystals containing numerous Co(CN)$_6$ vacancies. Single crystal diffuse scattering reveals pronounced anisotropy in vacancy distribution: strong correlations along [001] growth direction contrast with weak correlations perpendicular to it. This local ordering reduces the Laue symmetry to tetragonal $4/mmm$, evident in properties such as birefringence, while the average structure retains cubic $m\bar 3m$ symmetry. When growth proceeds along [111] direction, the same mechanism produces domains with trigonal symmetry. Because this mechanism relies on fundamental aspects of crystal growth rather than specific material properties, it offers a general strategy for symmetry control in disordered crystals. Crucially, it transforms the complex task of altering crystal symmetry into the more manageable challenge of controlling growth direction, achievable through various established techniques such as the use of surfactants during crystallization.

cond-mat.mtrl-sci↗

arXiv2025

Temporally symmetry-broken metasurfaces for ultrafast resonance creation and annihilation

Active metasurfaces, compact platforms for nanoscale light manipulation, are transforming technologies like holography, quantum cryptography, and optical computing. Despite their versatility, tunability in metasurfaces has mainly relied on shifting the resonance wavelength or increasing material losses to spectrally detune or quench resonant modes, respectively. However, both methods face fundamental limitations, such as limited Q-factor and near-field enhancement control and the inability to achieve resonance on/off switching by completely coupling and decoupling the mode from the far-field. Here, we demonstrate temporal symmetry-breaking in metasurfaces via ultrafast optical pumping, marking the first experimental realization of radiative loss-driven resonance creation, annihilation, broadening, and sharpening. We introduce restored symmetry-protected bound states in the continuum as a new concept which are central to the realization of temporal symmetry-breaking. These states arise in metasurfaces with geometrically asymmetric unit cells, where the total dipole moment, composed of two antisymmetric dipoles, cancels out. Mie-resonant optical absorption within specific regions of the unit cell locally modifies the refractive index, disrupting the balance between the two dipole moments. A total dipole moment is thereby created or annihilated, and consequently, the radiative loss is tuned. This enables full control over coupling to incoming light, allowing precise adjustment of the resonance linewidth, near-field enhancement, and resonance amplitude. Our work establishes radiative loss-based active metasurfaces with potential applications ranging from high-speed optical and quantum communications to time-crystals and photonic circuits.

physics.optics↗