We determine the exact outer structure of the Abrikosov vortex in the extreme type-II limit, which occurs when the Ginzburg-Landau parameter $κ$ diverges. In this limit, Ginzburg-Landau theory simplifies, outside a shrinking core, to a closed nonlinear theory for the superfluid velocity subject to an algebraic density constraint. The resulting solution is asymptotically exact everywhere outside the vanishing vortex core, demonstrating that both magnetic field and superconducting density vary on the length scale of the London penetration depth. This establishes that the conventional two-length-scale picture of the vortex does not hold in the $κ\gg 1$ limit.

We present the results of a search for diffuse radio emission in a uniformly selected sample of 30 of the most massive Sunyaev-Zel'dovich selected galaxy clusters at $z > 1$, providing the first statistical constraints on the evolution of cluster-scale diffuse emission beyond this redshift. We also analyse the scaling relations between radio power ($P_{1.4\,\mathrm{GHz}}$) and cluster mass ($M_{\rm 500c}$) in this high-redshift sample. It is well established that radio halos are primarily found in the most massive clusters, where turbulent energy from major mergers can re-accelerate relativistic electrons and amplify magnetic fields on megaparsec scales. Deep MeerKAT 1.28 GHz observations reveal diffuse radio halos in eight clusters (27$\%$), while the remaining 21 (70$\%$) show no emission; one additional cluster (3$\%$) was excluded from the radio analysis due to poor data quality. The halo detection rate in this high-redshift sample is lower than at intermediate redshift, but remains higher than the $\lesssim 10\%$ occurrence generally predicted by theoretical models at $z \gtrsim 1$. The detected radio halos scatter around the best-fitting $P_{1.4\,\mathrm{GHz}}$-$M_{\rm 500c}^{\rm {Unc}}$ relation derived for the MMDCS sample, whereas non-detections populate the lower envelope of the radio power-mass plane, similar to trends seen at lower redshift. No cluster-scale radio relics or mini-halos are identified. Our findings highlight MeerKAT's ability to probe non-thermal processes in the most distant clusters and the need for deeper, lower-frequency surveys to uncover faint diffuse emission and test the persistence of the $P_{1.4\,\mathrm{GHz}}$-$M_{\rm 500}$ relation across cosmic time.

Recent observations have revealed intriguing offsets between the UV and FIR emission in high redshift galaxies. In this study, we use the First Light And Reionisation Epoch Simulations (\textsc{Flares}) to compute the spatial offset of ultraviolet (UV) and far-infrared (FIR) centres for a statistical sample (6890) of massive (M$_{\star}\, \gtrsim10^{9} \,{\rm M_{\odot}}$) high redshift galaxies ($z \in [5,10]$). The galaxies are post-processed with the \textsc{skirt} radiative transfer code, to obtain the full spectral energy distribution and surface brightness profile. We simulate \textit{James Webb Space Telescope (JWST)} Near Infrared Camera (NIRCam; rest-frame 1500 Å, $ \approx 0.031 ''$ resolution) and ALMA rest-frame 158 \um\ ($\approx$ $0.3''$ angular resolution) observations of the galaxies and then calculate the distance between the UV-FIR centres to analyse which physical processes drive the observed UV - FIR spatial offset. We find that $\sim16.23\%$ of galaxies exhibit spatial offsets of $\geq 2.5$ kpc between their UV and FIR emission peaks. We establish that the spatial offsets do not correlate with stellar mass, UV/FIR luminosity, and size. Offsets also do not correlate with AGN feedback or with large-scale environment or merger history. Galaxies with significant offsets preferentially have bluer UV slopes ($-2.5<β<-1.5$), consistent with recent star formation and dust-attenuated cores displacing the observed UV centroid. They show an accelerated star formation history, forming half their $z=5$ stellar mass $\sim$0.1 Gyr earlier than galaxies without offsets. These galaxies are enriched earlier than galaxies without an offset and show enhanced stellar metallicities, indicating a transition to an outward growth at higher redshifts ($z \geq 6$).

We introduce a new class of quantum channels, the Generalized Multilevel Amplitude Damping (GMAD) channels, to model noise and decoherence effects in a qudit coupled to a thermal environment. The degradation of energetic resources under GMADs is investigated by evaluating work functionals and ergotropic capacitances, with particular attention to the coherent and incoherent contributions to ergotropy, for which we introduce new quantifiers. Our analysis sheds light on how to optimally prepare a qudit in a thermal environment in order to preserve its value from the perspective of work extraction, and reveals several counterintuitive phenomena: the ergotropic capacitance of a GMAD channel is not monotonic in the temperature of the environment; moreover, iterating the map can lead to crossings between ergotropic functionals at different temperatures, indicating the presence of a Markovian Mpemba effect.

We theoretically investigate the Aharonov-Bohm effect in a thick-walled Weyl semimetal (WSM) cylinder subject to an external axial magnetic field. By employing a low-energy effective Hamiltonian, we analytically solve the eigenvalue problem for both infinite and finite-length cylindrical geometries. We apply infinite-mass boundary conditions at the radial walls and MIT bag boundary conditions at the cylinder caps to properly account for intra-node confinement and inter-valley scattering, respectively. Our numerical results demonstrate that the spatial separation of the Weyl nodes acts as an internal chiral gauge field. This geometric field intrinsically breaks time-reversal (TR) symmetry, lifting the chiral degeneracy even at zero external flux. This symmetry breaking manifests as spontaneous persistent currents and the unfolding of conductance channels. Furthermore, longitudinal confinement induces propagation-direction-dependent energy splitting, altering the partial density of states and causing spatio-chiral current imbalances.

The DECam Rogue Earths and Mars Survey (DREAMS), a NOIRLab survey program, has been conducting a three-year survey covering a 5\,deg$^2$ area in the Galactic bulge since 2025 June. Its primary science goal is to detect low-mass free-floating planets through microlensing, while its minute-level cadence also enables the detection and characterization of rapid phenomena on timescales of minutes to hours such as stellar flares and pulsating stars. Here, we present the data reduction and calibration of the DREAMS observations obtained in 2025 and introduce the first DREAMS data release (DR1). DR1 includes 1,856 $z$-band observations and 325 $r$-band observations for 59,372,789 stars. The DREAMS DR1 catalog contains at least twice as many stars as any previous catalog covering the same 5\,deg$^2$ area. We present DREAMS light curves for a known blue large-amplitude pulsator and a known transiting system to demonstrate the survey's capabilities. We also perform a pilot search for short-duration variables over about 0.4% of the DR1 sample, identifying one new short microlensing event, two stellar flares, and 24 new short variables. This suggests that DREAMS DR1 may contain hundreds of stellar flares and thousands of previously unknown short variables.

We present the first high-resolution near-infrared spectroscopy of the nucleus of the nearby, well-known Seyfert galaxy NGC 4151 (the "Eye of Sauron"). Past studies of this source have revealed that it exhibits a variable absorption feature associated with the He I $λ$10,830 AA emission line, potentially indicative of obscuration events affecting the central engine. Here, we take advantage of the IRTF/iSHELL and TNG/GIANO-B spectrographs to observe this feature with unprecedented spectral resolution ($λ/Δλ> 50,000$), being able to study in detail the structure of the absorption trough and its variations over a time span of $\sim$700 days. In order to infer a connection between the He I absorption variability and that of the X-ray ionising continuum, we also analyse the publicly available data collected by the Swift-XRT instrument over the same period of time, unveiling a potential driving mechanism in the changes of the outflow ionisation state due to the X-ray flux variations. We also derive outflow physical parameters - $\dot{M}_{\rm out} \lesssim 10^{-2}$ M$_\odot$ yr$^{-1}$, $r_{\rm out} \sim 3$ pc, $v_{\rm max} \sim 1000$ km s$^{-1}$ - that are in line with those of comparable ionised winds found in similar targets, where the outflow is not powerful enough to trigger a significant AGN feedback ($\dot{E}_{\rm kin}/L_{\rm bol} \sim 0.001$%). Such findings point at a scenario in which a dusty and clumpy outflow that obscures NGC 4151 up to galactic scales responds to changes in the ionising X-ray flux, similarly to what happens in quasars with broad absorption lines and Seyferts with multiphase outflows such as NGC 5548.

Conventionally, the observed isolation of hot Jupiters, marked by a paucity of nearby low-mass planetary companions, has been interpreted as evidence of high-eccentricity tidal migration for these close-in gas giants. This loneliness is in stark contrast with the compact configurations commonly observed for warm Jupiters, indicating a curious dichotomy in dynamical origins between these two classes of short-period giants. In this study, however, we adopt a unified quiescent framework for both giant populations wherein they emerge from the protoplanetary disk as the sole Jovian planet within a compact multi-super-Earth system. We use long-term numerical simulations to show that post-disk dynamical evolution will naturally result in an observed preferential isolation for hot Jupiters relative to warm Jupiters. Specifically, their companions achieve significantly larger period ratios and mutual inclinations, rendering them more difficult to detect - especially via the transit method. Additionally, we find that this paradigm is consistent with the enigmatic population of longer-period hot Jupiters hosting interior companions on coplanar orbits. Another prediction of this model, best tested through high-precision Doppler campaigns, is the existence of a population of close-in (P<50 days) but mutually inclined outer companions to hot Jupiters.

Matrix string theory (arXiv:hep-th/9703030, arXiv:hep-th/9701025, arXiv:hep-th/9710009) is a conjectured duality between two-dimensional maximally supersymmetric $U(N)$ Yang-Mills theory and type-IIA string theory in ten-dimensional Minkowski spacetime. The IR description of this gauge theory is governed by the symmetric product orbifold $(\mathbb{R}^8)^N/S_N$ CFT. The leading irrelevant deformation from this IR fixed point is the Dijkgraaf-Verlinde-Verlinde operator, which comes with an unknown Wilson coefficient. We determine this coefficient using non-renormalization arguments from the UV gauge theory. The result is consistent with the matrix string theory conjecture and gives a first-principles check of the relation between $g_{\rm YM}$ and the string coupling. We also comment on the prospects for fixing further Wilson coefficients using similar methods.

Future gravitational wave (GW) standard siren catalogues will probe the late-time expansion history of the Universe across redshift ranges largely inaccessible to traditional electromagnetic observations. To determine how effectively this background distance information can distinguish between viable cosmological models, we introduce a model-independent reconstruction framework utilizing Gaussian Process Regression (GPR). Analyzing mock LISA and Einstein Telescope (ET) catalogues across six fiducial cosmological backgrounds-$Λ$CDM, CPL, CPL+$Λ$, interacting dark matter, interacting dark energy and axion inspired early dark energy. We reconstruct the comoving distance and its derivatives. Crucially, we propagated the full GP covariance, including derivative cross-covariances, to robustly evaluate the Hubble parameter $H(z)$ and other diagnostics such as $q(z)$, $\mathcal{O}_{m}(z)$ $w_{\rm total}(z)$ and $κ(z)$. While our analysis demonstrates that GW bright standard sirens faithfully recover fiducial expansion histories, applying pointwise marginal Hellinger distance reveals that background measurements alone do not provide decisive statistical separation among models. Instead, derivative sensitive diagnostics pinpoint specific redshift windows (e.g., $z\simeq1.6-1.8$ for ET and $z\simeq2.6-2.9$ for LISA) where future catalogues will maximize their discriminatory power. As machine learning methodologies become increasingly integral to astrophysics and cosmology, this Bayesian GPR pipeline offers a principled, nonparametric approach to precisely identifying where the most valuable cosmological information lies.

Resistance in standard conductors decreases with increasing cross-section. Yet, in low-dimensional superconductors and superfluids residual resistance arises from topological fluctuations of the order parameter manifesting as phase slips in one-dimensional (1D) and vortices in two-dimensional (2D) systems. How resistance and dissipation evolve as geometry interpolates between these regimes remains an open question. This evolution is masked in solid-state experiments by disorder, impurities, and geometric imperfections, and poses theoretical challenges due to competing dissipative processes and pronounced finite-size effects. Here, we use a defect-free unitary Fermi gas in a digitally programmable transport geometry to isolate geometric effects on superfluid dissipation and discover a paradox: in the crossover from 1D to 2D, the resistance reaches a minimum. There, widening a channel increases its resistance. Narrower, quasi-1D channels show dissipation described by Langer-Ambegaokar-McCumber-Halperin theory of phase slips. In this regime, varying the channel width yields the predicted exponential scaling of the activation factor over more than ten orders of magnitude. Wider, quasi-2D channels show dissipation consistent with a finite-size vortex model. The minimal dissipation in the dimensional crossover reflects a transition in the dominant dissipative mechanism, with both phase slips and vortices simultaneously suppressed. Our measurements suggest a route to minimizing dissipation in superconducting devices and provide a benchmark for theoretical efforts aimed at describing the dimensional crossover.

Sub-Neptunes are among the most common type of close-in planets found in our galaxy, yet their bulk composition remains largely uncertain; H-rich envelopes overlaying rocky cores, volatile-rich planets, and carbon-rich interiors all remain viable configurations for members of this population. Atmospheric characterization has been proposed as a means of distinguishing between these scenarios, but growing evidence suggests that sub-Neptunes may host molten atmosphere-mantle interfaces which could alter the composition of their atmosphere. We use the PICASO 1D climate model, coupled to interior-structure and magma-atmosphere chemistry frameworks to quantify how clouds alter the atmospheric and interior structure of sub-Neptunes. For temperate sub-Neptunes like TOI-270 d, we find that clouds can lead to $\ge{1000}$ K heating at depth (${\sim}10^{4}$ bar) and $\sim{600}$ K cooling at shallow pressures ($\sim$1 bar). This heating is very sensitive to the cloud sedimentation efficiency and, to a lesser extent, to metallicity. Most sub-Neptunes in our sample should have a molten atmosphere-mantle interface, except TOI-1231 b and GJ 1214 b. For these two planets, cloudy models have a molten interface whereas clear models can allow a solid boundary. Clouds can heat the atmosphere-mantle interfaces by a temperature difference between $\sim{1400}-2600$ K for most sub-Neptunes in our sample. Such cloud-driven heating can substantially change the composition of the interface with abundances of O$_2$, SiH$_4$, and SiO showing a $\ge{36}$\% increase between cloudy and clear models of TOI-270 d. We discuss the implications of our results for the thermal evolution and measurements of intrinsic heat flux for this population.

We study spin and entanglement dynamics in spin-1/2 XXZ chains under periodic monitoring and show that this system exhibits two measurement-induced phase transitions: a steady-state entanglement phase transition similar to those in monitored quantum circuits and a ballistic-to-diffusive transition in transient dynamics. Specifically, we discover that at low monitoring rate, an initial configuration containing a domain wall $|\uparrow\uparrow\uparrow\ldots \downarrow\downarrow\downarrow\ldots\rangle$ spreads ballistically while, at large monitoring rates, the domain melting is diffusive. Extensive numerical simulations, supported by theoretical arguments, indicate that the ballistic-diffusive transition is intimately interlinked with the entanglement phase transition. In contrast to the entanglement phase transitions, which require exponentially complex postselection, the ballistic-diffusive transition can be observed without postselection and constitutes an experimentally accessible manifestation of the many-body Zeno effect.

Nuclear quantum effects and non-Born--Oppenheimer effects play a vital role in many chemical and biological processes, motivating the incorporation of such effects into dynamical simulations. In real-time nuclear--electronic orbital time-dependent density functional theory (RT-NEO-TDDFT), the electronic and nuclear densities are propagated numerically in time according to the time-dependent Schrödinger equation. In this framework, specified protons are treated quantum mechanically on the same level as the electrons. The classical nuclei can be propagated on the instantaneous NEO vibronic surface using Ehrenfest dynamics. A traveling proton basis (TPB) can be used to describe the dynamics of moving protons in conjunction with Gaussian-type protonic and electronic basis sets for each quantum proton. Herein, we present a constrained TPB (c-TPB) approach that ensures each protonic basis function center coincides with the corresponding proton position expectation value during the dynamics. This approach produces accurate nuclear--electronic quantum dynamics and rigorously conserves energy. We demonstrate the accuracy and stability of this approach for computing molecular vibrational frequencies as well as simulating excited-state intramolecular proton transfer and double proton transfer in the o-hydroxybenzaldehyde and [2,2$'$-bipyridyl]-3,3$'$-diol molecules. These applications show that the c-TPB method provides accurate dynamics, conserves energy, and is computationally efficient.

Memristive devices have revolutionized non-volatile memory and neuromorphic computing, yet the geometry of their hysteresis loops -- in particular, the occurrence and robustness of multiple self-crossings -- remains poorly understood. Here we introduce a topological and algebraic framework that treats the number of transverse self-intersections of a memristor hysteresis loop as a robust integer-valued invariant. Drawing on differential topology, singularity theory, and cusp catastrophe, we employ discriminants and resultants to stratify the six-dimensional parameter space. This approach partitions the parameter space into structurally stable regions separated by explicitly computable catastrophe surfaces. We demonstrate that the crossing number remains strictly invariant under continuous deformations and changes only at self-tangencies or cusp singularities, thereby providing a complete classification of all multi-lobed hysteresis behaviors. These insights bridge device physics with modern singularity theory and suggest a clear roadmap for exploiting higher-order memory effects in next-generation electronics and brain-inspired hardware.

We discuss a spectral property for the virial operator of the 2D Zakharov-Kuznetsov (ZK) equation. This is a crucial ingredient to establish blow-up or asymptotic stability of solitary waves in higher-dimensional problems. This model in 3D setting was originally introduced by Zakharov and Kuznetsov in plasma physics, and is also a higher-dimensional generalization of the well-known Korteweg-de Vries (KdV) equation. The problem of stability of solitary waves in ZK equation or stable blow-up in modified ZK (or KdV-type) equation is an important physical question, for which virial operators and their spectral properties are the essential elements of the analysis. In this paper we investigate this problem analytically and reduce it to verifying numerically only some signs of inner products and certain eigenvalues.

Silicon photomultipliers (SiPMs) have become the preferred photodetectors in next-generation neutrino experiments, yet no unified closed-form analytical expression free of truncation and numerical convolution has been established for their full charge response spectrum, which must simultaneously capture correlated cross-talk and afterpulsing effects absent in conventional photomultiplier tubes (PMTs). We present a unified closed-form model for the SiPM charge response within the characteristic-function framework, treating pedestal noise, single-electron-response (SER) charge, internal optical cross-talk, and afterpulsing on equal footing. The characteristic-function representation factorises the full charge spectrum into three independent physical components: pedestal, single-electron response (SER), and avalanche count statistics. Prompt internal optical cross-talk is modelled as a Galton-Watson branching process with Poisson offspring; building on the Generalised Poisson count statistics identified by Vinogradov, we derive a Lambert $W$ closed form for the total-progeny PGF via Lagrange-Bürmann inversion, providing the analytical handle needed for efficient event-level reconstruction. Afterpulsing is modelled as a per-avalanche geometric chain, derived as the maximum-entropy Poisson-Gamma mixture: the exponential prior-maximum-entropy for a positive continuous yield with fixed mean-marginalised over a Poisson count yields the geometric per-avalanche distribution, whose $N$-avalanche total is Negative Binomial. This naturally encompasses the Poisson afterpulsing limit and recursive afterpulse chains while preserving analytical closure. The resulting eight-parameter expression is further applied to derive an explicit per-channel charge-time likelihood for event-level energy reconstruction without numerical convolution at inference time.

In this paper, we carry out a numerical study of misaligned accretion disks around spinning supermassive black holes. Here, we conduct a parameter survey covering a range of initial disk misalignment angles ($\mathcal{T}_\mathrm{init}=15^\circ, 45^\circ, 75^\circ$) with either the Magnetically Arrested Disk (MAD) or Standard And Normal Evolution (SANE) magnetic field configurations, using the general-relativistic magnetohydrodynamic (GRMHD) code KHARMA. We find that models in the MAD state can align with the black hole up to $\sim10 \, r_g$, even in extremely misaligned models ($\mathcal{T}_\mathrm{init}=75^\circ$), which has not been seen before. Models without a dynamically important magnetic field remain misaligned up to the black hole, with a maximum disk tilt at $\sim10 \, r_g$, the peak's radial distance from the black hole increases with increasing disk misalignment. However, the maximum disk tilt does not have a linear relationship with the initial disk misalignment, and appears to have a maximum value of $\sim50^\circ$. We also show misaligned disk simulations produced in KHARMA are consistent with other GRMHD codes, for a variety of problems.

Transport-induced self-sustained oscillations in electromechanical systems convert a static electrochemical bias into robust, autonomous oscillatory motion in the absence of any external periodic drive. However, an exact description of such self-oscillations remains challenging in nanoscale electromechanical devices featuring a simultaneously large bosonic Hilbert space, strong interactions, and structured fermionic leads. We formulate a tensor-network framework that combines a binary representation of the vibrational mode with mesoscopic reservoir embeddings that enable controlled access to the self-oscillatory steady states and relevant transport observables without explicit real-time propagation. We demonstrate the emergence of mechanical self-oscillations across a broad set of operating conditions, in which strong electromechanical backaction, nonadiabatic oscillator dynamics, and energy-dependent electronic tunneling processes compete. Furthermore, we observe that for both slow and fast vibrating mechanical modes, suppressed vibrational occupation fluctuations in the self-oscillation window along the electromechanical coupling strength sweep is preceded by a peak in the occupation fluctuations. Collectively, we explore how both intrinsic system properties and environmental parameters govern such autonomous oscillations over a broad range of operating conditions. The generality of our framework will enable the method to be employed straightforwardly to more complicated or experimentally relevant scenarios.

The shock-to-detonation transition in energetic materials is governed by coupled processes spanning Angstroms to millimeters and femtoseconds to microseconds, where traditional multiscale models fail due to the lack of scale separation. We address this grand challenge by directly bridging large-scale molecular dynamics (MD) simulations with continuum finite-element (FE) models using MISTnetX, a convolutional deep neural network. Trained on MD simulations of shock propagation through complex microstructures, MISTnetX captures shock-microstructure interactions, hotspot formation, and the transition to deflagration, supplying critical sub-grid information to FE simulations of mechanics, shocks, thermal transport, and chemistry. Applied to a synthetic but realistic nanostructured plastic-bonded RDX composite, MISTnetX enables parameter-free prediction of the full run-to-detonation transition.

We probe the cosmic expansion scenario within the framework of $f(R, L_{m})$ gravity by employing a well-motivated functional form of $f(R, L_{m}) = \frac{R}{2} + L_{m}^λ$. Specifically, we introduce three novel cosmological models formulated in terms of the redshift-dependent Hubble parameter $H(z)$, offering deeper insights into the underlying cosmic dynamics. The models are further utilized to investigate the expansion history of the universe and the evolution of several cosmological parameters. By using the Bayesian methods based on the $χ^{2}$-minimization technique, the median values of the model parameters are determined for the cosmic chronometer (CC) and joint (CC+Pantheon) datasets. A comprehensive study of the deceleration parameter, energy density, pressure and the equation of state parameter is carried out to understand the universe's evolution. Additionally, the validity of the energy conditions and the behavior of the statefinder diagnostic are thoroughly examined. Finally, the thermodynamic viability of the models is confirmed through the evolution of temperature and entropy density, and the estimated age of the universe further exemplifies good agreement with late-time astronomical observations.

The condensation of photons into a macroscopically populated ground state, a superradiant phase transition (SRPT), is one of the most striking predictions of cavity quantum electrodynamics (cQED), yet has resisted experimental realization in equilibrium for over fifty years. Whether such a transition can survive at all in light-matter coupled systems is still debated, with a widely established \textit{No-Go} theorem ruling it out across several models. Graphene cyclotron transitions ultrastrongly coupled to terahertz (THz) cavities have been at the heart of this debate. At leading order, the linear Dirac dispersion of electrons does not generate the diamagnetic $\vec{A}^2$ term that enforces the theorem, making graphene the cleanest candidate for a No-Go-evading phase transition. Here, we present the first THz spectroscopic measurements of an encapsulated monolayer graphene flake ultrastrongly coupled to a single complementary split-ring resonator. By tuning the carrier density we sweep the system from weak coupling into the ultrastrong regime, reaching a normalized coupling $Ω_\text{R}/ω_\text{cav} \approx 0.4$. This is well into the range where a second order SRPT would manifest by a softening of the lower polariton branch, which we do not observe. The full polariton dispersion is instead quantitatively reproduced by a Hopfield Hamiltonian derived from first principles using a near-field model that accounts for the sub-wavelength character of the cavity. Our results establish an experimental baseline for predictions of cavity-driven phase transitions in two-dimensional Dirac systems, and rule out a No-Go-evading SRPT in graphene Landau polaritons up to the strongest couplings accessible today, with direct implications for proposals invoking vacuum-induced order in solid-state cQED.

Lie algebra $\mathfrak{sl}(2)$ can be realised by vector fields on $\mathbb{R}^1\ni x$ with polynomial coefficients $1$, $-2x$, $-x^2$; their Wronskian determinants yield the Lie bracket. Likewise, the monomials $1$, $\ldots$, $x^k/k!$, $\ldots$, $x^N/N!$ span finite-dimensional strong homotopy (SH) Lie algebras with the Wronskians $\mathbf{1} \wedge \partial_x \wedge \ldots \wedge \partial_x^{N-1}$ as the $N$-ary brackets. Over dimension $d=2$ with $\mathbb{R}^2\ni(x,y)$ and for the generalised complete Wronskian $W^{d=2}_{k=1}=\mathbf{1}\wedge \partial_x \wedge \partial_y$ of differential order $k=1$ as the ternary bracket, the finite-dimensional polynomial SH-Lie algebras are spanned by $\langle 1$, $x$, $y$, $p\rangle$ with $p\in\{x^2$, $xy$, $y^2\}$. We explicitly describe all finite-dimensional polynomial SH-Lie algebras $\Bbbk_k[{\boldsymbol{x}}]\subseteq \mathcal{A} \subseteq \Bbbk[x^1,\ldots,x^d]$ (over $\Bbbk=\mathbb{R}$ or $\mathbb{C}$) with the complete generalised Wronskians $W^{d\geqslant 1}_{k\geqslant 1}$ of order $k$ as $N$-ary bracket: $N=\binom{d+k}{d}$. We obtain a factorisation formula for the generalised Vandermonde determinants which show up in the structure constants of the polynomial algebras $\mathcal{A}$.

We report a comparative analysis of three dynamic neural network (NN) architectures -- NAR, NARX, and NIO -- to evaluate their efficiency in estimating the critical-measurement-strength parameter ($c_{crit}$) characterizing topological phase transitions in geometric phases induced by weak measurements. Our results demonstrate that the NARX architecture achieves superior predictive fidelity, reaching a Mean Squared Error (MSE) of $10^{-27}$ -- the limit of numerical precision -- at an optimal delay of $d=1$. This exceptional performance implies the identification of a perfect functional identity, suggesting that the relationship between winding numbers $W$ and $c_{crit}$ is mathematically deterministic. We observe a "complexity paradox" where the NARX model's accuracy collapses at higher delays ($d=4$), a phase-sensitivity that confirms the model captures a high-precision dynamic mapping rather than a trivial pattern. While the NAR model remains robust for local-trend capture, the NIO architecture fails to accurately resolve the phase transition despite increased neuronal capacity. These findings underscore that both autoregressive feedback and immediate exogenous context are essential for the exact characterization of topological phases, establishing NARX as a robust framework for deriving governing laws in complex quantum systems, where analytical solutions remain elusive.

Disclination lines in three-dimensional nematic liquid crystals generically form closed loops whose topology is classified by homotopy theory. While this classification successfully captures global topological features, it does not encode the geometry of the defect profile along the loop, which can strongly influence defect dynamics. Here, we propose a geometric description of nematic disclination loops using the Clifford algebra Cl(3,0). This approach naturally captures the geometry of the local defect profile, as well as changes along the loop, which is mathematically a SU(2) holonomy. Simulations of the dynamics of defect loops with specified geometries embedded in nematic liquid crystals demonstrate that loops nucleate the growth of "topological blobs" of defects, which later dissipate leaving uniform nematic textures. Self-twist of the defect profile leads to nucleation of additional linking disclination lines, with a simple arithmetic relation between total self-twist and linking number. In contrast, loops with an even number of discrete profile transitions generate patterns with threading between loops, but no linking. These results establish a direct connection between the geometric holonomy of a disclination loop and its subsequent evolution, and may be extendable to more complex order parameter manifolds, such as cholesterics or smectics.

The population of short-period exo-Neptunes is thought to be shaped by an interplay between different dynamical mechanisms, such as orbital migration and tidal effects, and photoevaporation. We can gain insight into these processes by studying observables such as the stellar obliquity. Here we study the Rossiter-McLaughlin (RM) effect and measure the projected obliquity, $λ$, of the Neptunian ridge planet WASP-156 b. We analyse new ESPRESSO and MAROON-X spectroscopic transit observations, and new NGTS photometry simultaneous to the ESPRESSO data. Our analyses show an aligned orbit ($λ=-8\pm16^\circ$, based on the ESPRESSO observations), in contrast to a previous report of a highly misaligned orbit. We also find the star's projected rotational velocity to be $v \sin i_\mathrm{\star}\leq2$ km/s from spectral line modelling and $v \sin i_\mathrm{\star}=0.40\pm0.11$ km/s from the RM modelling. This is lower than the previously reported value of $\sim4$ km/s, which could partly explain the previously derived polar orbit. We also update the system's orbital parameters and rule out Jupiter-mass companions within 5 au using long-term radial velocity data. The planet's aligned and circular orbit ($e<0.16$ at $3σ$), and lack of nearby massive companions, are consistent with in situ formation or early disc-driven migration. Our findings move WASP-156 b from a tentative cluster of close-in Neptunes in polar orbits to the group of aligned Neptunes.

Recent observations, including those by JWST, suggest that the atmospheres of many gas giant exoplanets have super-stellar metallicity that is anti-correlated with planetary mass. Several studies suggest that the super-stellar metallicity can be explained by accretion of vapor-enriched disk gas produced by the sublimation of rapidly drifting icy pebbles. However, recent disk observations and experiments suggest that icy dust is fragile at low temperatures, calling into question the conventional picture that icy grains grow efficiently and drift rapidly. We present a new scenario for heavy-element enrichment in the inner disk by fragile, slowly drifting icy dust, assuming that magnetohydrodynamical disk winds drive gas accretion near the disk surface rather than at the midplane. We simulate the evolution of gas and dust in a surface-accretion disk, taking into account the radial transport of gas and dust, collision growth and fragmentation of fragile dust, and the condensation and sublimation of H2O. Two accretion disk models are presented, in which gas accretion flows are assumed to be either vertically uniform or narrowly concentrated near the disk surface. In the uniform accretion disk model, fragile icy grains enhance the water vapor abundance inside the snow line only by a factor of ${\sim}3$ due to their slow drift. In contrast, in the surface-accretion disk model, the slow drift of icy dust leads to water vapor enrichment that is higher by an order of magnitude, owing to the selective removal of ice-free gas from the disk. Furthermore, surface accretion yields an anti-correlation between the water vapor concentration in the inner disk and the residual disk gas mass, analogous to the anti-correlation between atmospheric metallicity and planet mass observed in extrasolar giant planets.

Classical simulation of many-body quantum systems remains economical only when wavefunction amplitudes stay localized in the working basis. Fixed-basis sparse-state simulators scale memory as $\mathcal{O}(k)$ by keeping the largest computational-basis amplitudes; however, fidelity drops once entanglement or basis rotations spread weight across the Hilbert space. In this work, we introduce an algorithm called Basis-Adaptive Sparse-State Simulation (BASS), which updates each qubit's local representation basis during execution rather than locking the computational basis for the entire circuit. Before truncation, each qubit is rotated into the eigenbasis of its single-qubit reduced density matrix, following the natural-orbital idea from quantum chemistry, so the retained amplitudes stay clustered. We prove that top-$k$ selection is uniquely optimal for one-step truncation in any fixed basis and that the one-body reduced-density-matrix eigenbasis is a stationary product basis for the inverse participation ratio (PR), with a residual bounded by local entanglement coherence. We perform a systematic benchmarking over a variety of quantum circuits and demonstrate that the ratio \(k/\text{PR}_Z\) (sparse budget over computational participation ratio) serves as an indicator for regimes in which adaptive measurement bases provide a performance advantage. On structured brickwork circuits, BASS achieves substantially higher fidelity than the fixed-basis approach, while incurring only a moderate increase in wall-clock time in the memory-limited regime. Moreover, for disordered Ising circuits, BASS systematically provides an improvement of approximately one order of magnitude in state overlap at a fixed computational budget.

The recent development of differentiable simulation codes for particle accelerators has enabled gradient-based workflows that promise finer control and more realistic modeling of accelerator facilities. However, when using reverse-mode automatic differentiation, the memory usage continuously increases during the simulation, and can potentially exceed the available hardware memory -- especially when costly space charge computation is included. To study the memory requirements for differentiable simulations, we have implemented space charge in Cheetah, a PyTorch-based beam tracking code that supports reverse-mode differentiation. We find that the memory usage for reverse-mode differentiation grows linearly with the number of macroparticles and cells, and that it is proportional to the number of space charge kicks involved in the simulation. This general scaling can be used to evaluate whether a given differentiable simulation is feasible given hardware memory constraints.

In noncentrosymmetric metals such as $C_{3v}$ topological-insulator surfaces, moiré heterobilayers, and zincblende crystals, point-group symmetry can forbid the linear and quadratic electric-field-induced orbital magnetization, leaving the cubic response as the leading signal. Using a Ward-complete finite-momentum cubic Kubo kernel with an antisymmetric linear-in-$q$ projection, we show that the dc response separates into three quantum-geometric channels. These are a mixed electric-magnetic positional-shift quadrupole, a quantum-metric drift term, and an orbital-moment octupole. The three contributions share the same point-group symmetry but differ in their lifetime, frequency, and gate fingerprints. For a warped $C_{3v}$ surface the metric channel obeys the cutoff-independent law $\barχ_G \propto μ^{-2}$. We propose third-harmonic magneto-optical Kerr spectroscopy as an experimental route.