In this paper, we give a direct proof of determinantal formulas for connected $k$-point functions for hermitian matrix models. We also give a new proof of KP integrability for them. From the viewpoint of KP hierarchy, we further give a new proof of the explicit formula for the corresponding affine coordinates. Furthermore, duality for some hermitian matrix models is proved.

AlScN wurtzite ferroelectrics are promising candidates for energy-efficient non-volatile memory. However, AlScN suffers from a high coercive field and reduced cycling endurance, and the limited tunability of its properties constrains further optimization. Co-doping AlScN with boron offers the promise of independently tailoring the chemical and structural properties, making AlScBN an attractive quaternary system. This material has already been explored for a few selected compositions, however, no systematic study of the full AlScBN compositional space exists. A combinatorial approach consisting of gradient deposition with HiPIMS at low temperatures of 250°C and automatic analysis of film properties allowed us to analyze a total of 850 unique samples within the AlScBN phase space. In addition to a full screening of the materials' chemical and structural properties, we fabricate and characterize combinatorial device libraries. XPS charge transfer analysis experimentally confirms that bond ionicity correlates with a reduction in the coercive field for AlScN and AlScBN systems, opposite trends are instead observed for AlBN. While the films maintain a high remanent polarization of 130-150 {\mu}C/cm2, Sc and B co-doping reduces the coercive field from 7 MV/cm to 3 MV/cm. Notably, B co-alloying lowers the amount of Sc needed to lower the coercive field, reducing reliance on this scarce element. In addition, we find that co-alloying with B, notably improves cycling endurance, which is related to a reduction in defect density. These results establish AlScBN as a scalable, CMOS-compatible ferroelectric, positioning it as an interesting alternative to AlScN.

The physics of active matter, wherein constituent particles consume energy to generate autonomous motion, has revolutionized non-equilibrium statistical mechanics. While a large body of work has successfully elucidated the behavior of dilute active systems, the dense regime -- characterized by ``active glasses and active solids'' -- presents profound challenges that defy conventional theoretical frameworks. Recent observations reveal two striking features in these dense systems: an apparent enhancement of Mermin-Wagner-Hohenberg (MWH) fluctuations leading to anomalous long-wavelength density fluctuations, and a remarkable correspondence between activity-induced annealing and annealing via oscillatory shear. In this perspective article, we propose a novel approach toward a deeper understanding of dense active matter: by developing active Hamiltonian models as equilibrium reference frameworks, we map out pathways toward non-equilibrium active systems. This strategy allows us to elucidate both the correspondence between driven and active systems and the enhanced MWH fluctuations, which likely arise from a strong coupling between spatially random active forces and long-wavelength density (phonon) modes. We outline a comprehensive roadmap employing complementary approaches, including the active Hamiltonian formalism, comparative studies of oscillatory shear in active and passive solids, and investigations of chiral active matter. Establishing this activity-oscillatory shear correspondence across diverse systems is essential to demonstrate its universality, reveal the underlying large-scale emergent physics, and place our hypothesis on a firmer theoretical ground.

Molecular rare-earth-ion complexes offer unique opportunities for quantum technologies by combining the intrinsic coherence properties of rare-earth ions with chemically tunable molecular environments. A crucial capability is the realization of multi-qubit architectures with defined qubit couplings to enable two-qubit quantum gates. Here, we investigate the optical coherence properties and excitation-induced interactions of two Eu$^{3+}$-based molecular complexes, comparing a mononuclear reference system with a dinuclear analogue in which two Eu$^{3+}$ ions are positioned at a well-defined intramolecular distance of about 7 Angstrom. Using cryogenic ensemble spectroscopy, including spectral hole burning, free-induction decay, and photon echo measurements at temperatures down to 100 mK, we demonstrate long optical coherence times $T_{2,\text{o}}$ of up to 9 $\mu$s. As a key step toward scalable multi-qubit architectures, a control-target sequence was implemented to probe conditional ion-ion interactions, revealing a stronger interaction-induced dephasing in the dinuclear complex. Finally, we show the integration of the dinuclear complex into a fiber-based optical microcavity, and observe an 380-fold emission enhancement of the $\mathrm{}^5\mathrm{D}_0\rightarrow\mathrm{}^7\mathrm{F}_0$ transition. Together, these results position molecular rare-earth complexes as versatile and chemically tunable building blocks for scalable quantum technologies.

Examiner reports from six major UK exam boards published between 2017 and 2025 are analysed using a mixed-methods thematic analysis. Focusing on questions relating to gravity, the objective is to understand where students commonly drop marks. Findings reveal that the source of difficulty is dependent upon topic and question style. Mathematical errors account for the majority of lost marks in calculation-type questions, while a lack of conceptual understanding commonly results in lost marks on questions relating to fields, energy and gravitational potential. Pedagogical strategies for teaching gravity must emphasise algebraic skills for orbital mechanics topics while prioritising qualitative modelling and precise definitions for field theory.

We investigate the critical regime $\kappa(R,T)=0$ in $\kappa(R,T)$ gravity. While most studies assume a non-vanishing effective gravitational coupling, the existence of critical hypersurfaces where $\kappa$ vanishes is a generic feature of many admissible coupling functions. We show that the apparent singularity of the non-conservation equation is an artifact of a rewritten form of the conservation law and that the fundamental equations remain regular at $\kappa=0$. We further analyze the structure of critical hypersurfaces, derive the associated compatibility condition $(\nabla^\mu\kappa)T_{\mu\nu}=0$, and discuss their interpretation as gravitational screening surfaces separating attractive and repulsive gravitational phases. The existence of critical coupling hypersurfaces also obstructs a global Einstein-frame description, distinguishing $\kappa(R,T)$ gravity from theories based solely on algebraic redefinitions of the energy-momentum tensor. Possible cosmological and astrophysical consequences are briefly explored.

The effect of using a graphene layer as a semitransparent contact layer is studied in solar cells based on AlInN on Si (100) substrates. The devices consist of AlxIn1-xN layers deposited on p-type Si (100) substrates incorporating a thin amorphous silicon (a-Si) buffer layer to improve the heterointerface quality. Three aluminum contents are studied, namely: x=0.22, 0.35 and 0.43. Subsequently, a monolayer graphene film was transferred onto the front surface of the devices using a simple and low-temperature transfer process, acting as a semitransparent conductive contact. The photovoltaic characteristics were then evaluated under illumination and dark conditions in devices with and without the graphene layer. The results show that the incorporation of graphene leads to a clear improvement in the short-circuit current density, fill factor, and overall power conversion efficiency for all studied compositions, while the open-circuit voltage remains largely unaffected. These findings demonstrate the potential of graphene as an effective transparent conductive contact for nitride-based solar cells.

The native processing of time-dependent signals from optical sensors by integrated photonic circuits can potentially bring significant advantages in terms of energy consumption, latency and processing power, as it allows skipping or reducing the use of fast digital electronics and directly exploiting optical degrees of freedom and parallelism. However, due to a short memory, optical operations usually struggle to directly process optical signals with relatively slow (<MHz) dynamics from optical sensors. In this work, we experimentally show that these limitations can be overcome by exploiting the self-pulsing dynamics in a microring resonator (MRR) network. In particular, we demonstrate that such dynamics can expand and retain information about perturbations sensed by a fiber sensor. This reduces the minimum sampling rate for the digitization of the sensor signal by at least one order of magnitude. The reduction is achieved by combining fiber sensing measurements at two different perturbation locations and frequencies with MRR network measurements at multiple output ports, input power levels and laser wavelengths. This work represents a first step in bridging time-dependent optical processing and optical sensing at sub-{\mu}s time scales.

Dwarf galaxies, characterized by their low luminosities and masses, are excellent candidates for searches for intermediate-mass black holes (IMBHs), particularly when they show strong accretion and ejection activity. The dwarf galaxy SDSS J101747.09+393207.7 has recently been found to display a very high X-ray luminosity and an X-shaped optical structure, possibly caused by a dwarf--dwarf merger. To explore its potential IMBH ejection activity, we performed very long baseline interferometry (VLBI) observations at 4.9 GHz. In this work, we present the detection of a milliarcsecond-scale, compact, sub-microjansky radio component near the optical centroid. According to some existing radio sky survey data, the radio component was not detected until 2015; it displayed an optically thin steep radio spectrum and declining flux densities across 0.8--5 GHz from 2019 to 2025. Therefore, we identify it as a short-lived and rarely seen ejecta that was produced by unstable accretion onto a massive black hole and likely faded away in a few decades. These results indicate that short-lived, episodic jet activity from accreting IMBHs in dwarf galaxies might exist.

The dynamics of nanoparticles within nanoscale liquid environments exhibit a range of complex phenomena driven by the interplay of processes at varying length scales. While these dynamics have profound technical implications, such as in nanoscale catalytic kinetics, ion-transport pathways in energy storage, and macromolecular crowding in biological systems, real-space imaging of dense, confined nanoparticle assemblies remains a significant challenge. Here, we present a liquid-phase transmission electron microscopy approach in which dense clouds of gold nanoparticles are formed within microfluidic channels, rendering the particle ensemble visible in bright-field electron imaging. This strategy enables direct imaging of different density-dependent particle ordering phenomena, including a local structuring of the colloidal liquid in nanoscale spaces, disordered dynamic clouds at high nanoparticle densities and the reversible formation of superlattice structures. Our results provide a unique window into the complex processes of colloidal self-organization at the nanoscale.

We revisited the singlet fermionic dark matter model in this work, where a Majorana fermion $\chi$ carrying $Z_4$ charge is assumed as the DM candidate. A new singlet scalar $S_0$ with a non-zero vacuum expectation value is also introduced to the SM so that $\chi$ can obtain mass after spontaneous symmetry breaking. We focus on the secluded DM region for the model, where interactions between DM and SM particles can be negligible. We have a new Higgs $h_2$ in the model, and the mixing angle of $h_2$ with the SM Higgs will play an important role in determining DM production, depending on the mass hierarchy between the new Higgs mass and the DM mass. We study DM relic density as a function of the model's four free parameters and estimate the viable parameter space under DM relic density constraint as well as direct detection constraint. We focus on the heavy DM mass region, and our analysis indicates that the mixing angle does not necessarily need to be very small in the secluded dark matter scenario, which offers potential for probing such models in future collider experiments.

We study the effects of dimension-four and dimension-six nonminimal Higgs couplings to the Ricci scalar $R$ in the $R^2$-Higgs inflation model in light of the recent ACT and SPT observations. We show that the dimension-six operators $|\Phi|^2 R^2$ and $|\Phi|^4 R$ can accommodate the enhanced scalar spectral index $n_s$ preferred by the combined CMB+BAO analyses. Using a doubly covariant formalism, we find that the same region of parameter space that explains the observed value of $n_s$ can also induce rapid preheating through the production of the Goldstone modes. If thermalization proceeds efficiently through this preheating mechanism, it may help match the inflationary scale with the CMB reference scale.

Halide double perovskites (A$_2$BB'X$_6$) are a long-known class of materials that has recently been rediscovered for diverse applications, including photovoltaics, photocatalysis, and radiation detection. Their doubled unit cell provides immense chemical tunability, allowing the incorporation of magnetic ions and enabling access to a wide range of electronic-structure features, including different band-edge characters, alignments, and symmetries. Magnetic elements may further introduce spin degrees of freedom and magnetic behaviour, thereby broadening the functional landscape of these compounds. Here, we present the first comprehensive database of spin-polarised electronic-structure data for all halide double perovskites predicted to be stable by the recently introduced $\tau$ tolerance factor by Bartel et al. The dataset focuses on the Cs$_2$BB'X$_6$ family, with X = I, Br, Cl, and F, and includes density of states (DOS) for $>$2,500 compounds, calculated using hybrid-functional density functional theory. Among these, 719 compounds exhibit band gaps in the visible range and 118 display half-metallic character. In addition, we provide chemical-bonding analysis using \textsc{lobster}, which provides insights into orbital interactions across the dataset. To facilitate exploration, we further offer UMAP-based visualisations and an interactive app for systematic investigation of chemical composition, electronic structure, and magnetic properties.

We build a three-dimensional (3D) red supergiant (RSG) stellar model for common envelope evolution (CEE) simulations by transporting a 1D stellar model to a 3D numerical grid, mimicking core nuclear power by depositing energy to an inner shell, and mimicking stellar emission by cooling grid cells with densities below the photospheric density. We do not relax the model; rather, we let it perform its natural pulsation. We find that when we mimic photospheric emission by cooling low-density grid cells, the oscillations slowly decay on a time scale much longer than in the absence of photospheric cooling. When we mimic both nuclear energy production, by depositing the stellar luminosity in an inner shell above the inert core of the stellar model, and the photospheric cooling, the oscillations do not decay and their amplitude slowly increases with time. The main pulsational period is about 1 year, comparable to the stellar dynamical time, suggesting a fundamental radial pulsation mode. The non-spherical structure of the stellar model and rapid low-amplitude temporal variations in the average stellar radius testify to the presence of non-radial oscillation modes on top of the fundamental radial mode. We also obtain vigorous convection, as RSG stars have. We conclude that the best way of preparing a giant star to simulate CEE and grazing-envelope evolution is to deposit energy with the stellar luminosity in an inner shell, and to cool the outer low-density numerical shell. There is no need to relax the model.

The propagation of very-high-energy (VHE; $E_{\gamma} \geq 100$ GeV) gamma rays from extragalactic sources is affected by interactions with photons of the extragalactic background light (EBL), resulting in pair production that attenuates the intrinsic gamma-ray flux. This interaction renders the Universe increasingly opaque to VHE photons at high energies and redshifts. New physics scenarios involving axion-like particles (ALPs) could modify this expected optical depth. In particular, ALPs with masses $m_a \sim 10$ eV can decay into two photons over cosmological timescales, thereby contributing to the diffuse EBL. If such ALPs constitute a significant fraction of the dark matter density, their decay would enhance the EBL intensity and consequently increase the gamma-ray optical depth. In this study, we investigate this scenario using a large sample of gamma-ray spectra observed with the High Energy Stereoscopic System (H.E.S.S.) and the Fermi Large Area Telescope. We model the contribution of decaying ALPs to the EBL and assess their impact on the spectra of blazars across redshifts. By comparing these observations with standard EBL models, we place constraints on the properties of heavy ALPs, specifically their mass and photon coupling, and evaluate their viability as a dark matter candidate capable of modifying the gamma-ray transparency of the Universe. From the combined analysis, and under the assumption that ALPs constitute the entire dark matter density, we derive 95% confidence exclusion limits on the photon-ALP coupling down to $g_{a\gamma} \sim 7 \times 10^{-12}$ GeV$^{-1}$ for masses $m_a\sim 15$ eV. These constraints are competitive with existing astrophysical bounds and provide complementary sensitivity to other techniques, closing a previously unconstrained region of parameter space in the $m_a \sim 2.5$-$20$ eV range.

With the aim to study the spectral properties of some X-ray sources from recently observed {\it Chandra} data, 9 galaxies which have been observed by {\it Chandra} ACIS-S during the year 2018 to 2022 have been considered for the present work. 27 sources with net source counts $ \ge$ 100 have been considered. The spectra of all the sources were fitted using two empirical models -- an absorbed powerlaw and an absorbed disk blackbody. From their estimated bolometric luminosities, the 27 X-ray sources are categorized as 6 X-ray binaries (XRBs) and 21 Ultraluminous X-ray sources (ULXs). All the six XRBs are found to be in the spectrally hard state ($\Gamma \sim$ 1.52-2.29) which indeed may be due to thermal comptonization. Only one ULX, CXOUJ032251.2-370950 (X-5), was found to be spectrally soft while the remaining 20 ULXs were spectrally hard. The spectral parameters of X-5 with an inner disk temperature (kT$_{in}$) $\sim $ 0.5 keV and an estimated bolometric luminosity, L$_X \sim$ 3.26 $\times$ 10$^{39}$ erg s$^{-1} $ requires a black hole of mass, M$_{BH} \sim$ 137.86$^{+66.62}_{-47.41}$ M$_\odot $ accreting at $ \sim$ 0.19 times its Eddington limit. 8 ULXs, X-4, X-8, X-9, X-10, X-11, X-12, X-20 and X-21, were found to be in the Extremely luminous X-ray sources (ELXs) regime with even their lower limit of luminosity $>$ 10$^{40}$ erg s$^{-1}$. Softening/Hardening of spectra with or without changes in the luminosity were also observed in some ULXs/ELXs. In the hard ELX, X-8, spectral softening with almost consistent luminosity was observed. While in the ULXs X-20 and X-25 spectral softening with increasing luminosity was observed. However spectral hardening with increase in luminosity were observed in the ULXs X-21 and X-26.

Angular momentum coupling manifests widely in diverse physical systems, underpinning the emergent properties and collective dynamics across different scales. The tidal locking, which originates from the synchronization of rotational and orbital motions, has far-reaching impacts in celestial mechanics, reflecting fundamental processes of angular momentum transfer, energy dissipation, and evolution toward dynamical equilibrium. However, its counterpart in mesoscopic quantum fluids has remained largely unexplored. Here we demonstrate the emergence of quantum tidal locking in Bose-Einstein condensates undergoing central force motion in an anharmonic potential. The condensate follows a well-defined orbital trajectory in a static trap and experiences an effective rotating potential induced by the trap anharmonicity. The sustained geometric squeezing continuously deforms the condensate and drives a self-organized synchronization process, in which the intrinsic rotation gradually locks to the orbital motion. Numerical simulations further reveal the formation of a ring-shaped vortex array over longer timescales, arising from the coherent evolution of the rotating matter wave during the locking dynamics. Our findings establish quantum tidal locking in mesoscopic systems as a robust self-organized mechanism for generating and stabilizing circulating states.

We present femtoscopy as a new way to search for saturated gluonic matter in inclusive photonuclear processes, such as inclusive ultraperipheral collisions at the Large Hadron Collider (LHC) and the inclusive photonuclear reactions at the Electron-Ion Collider (EIC). As the femtoscopic approaches are sensitive to the space-time structure of the particle emitting source, they are ideal in providing insights also about the initial stage of the collision, where the gluon distributions may impact the effective size of the dipole the quasireal photons oscillate into. This technique demonstrates its capabilities in isolating nuclear shadowing and gluon saturation effects. Finally, we show how a femtoscopic approach is highly sensitive to sub-fermi scale structures typically observed in ultraperipheral collisions, such as gluonic hot spots.

Unconventional magnets combine the vanishing stray fields of antiferromagnets with the strong spin-splitting of ferromagnets, offering a unique material platform for spintronics. However, a critical challenge in realizing functional spin-logic devices lies in preserving long-range spin coherence against momentum-degrading scattering and gate-induced dephasing. Here, we demonstrate that the intrinsic momentum-dependent exchange field of a three-dimensional $p$-wave magnet can be precisely tuned against gate-induced Rashba spin-orbit coupling to establish a \textit{generalized} $\mathrm{SU}(2)$ spin-rotation symmetry. This emergent conservation law generates a symmetry-protected Persistent Spin Helix (PSH), effectively integrating the high energy scales of 3D bulk magnetic exchange with the macroscopic coherence of symmetry protection. By modeling a synergistic $p$-wave magnetic spin field-effect transistor (spin-FET), we reveal high-visibility Datta-Das conductance oscillations controlled purely by electrical gating. Crucially, our quantum transport simulations confirm that this symmetry-engineered transport regime exhibits exceptional resilience against strong non-magnetic Anderson disorder and geometric variations. These results establish a synergistic paradigm for non-magnetized spintronics, demonstrating how the active integration of spin-orbit coupling and unconventional magnetism can yield disorder-resilient spintronic logic.

We investigate two massive young stellar objects (YSOs), IRAS21078+5211 and G035.02+0.35, where evidence for magnetohydrodynamic (MHD) disk winds (DWs) has been obtained at scales of 10-100 au through measurements of the 22GHz water maser velocity distribution within the Protostellar Outflows at the EarliesT Stages (POETS) survey. We employ IRAM Northern Extended Millimeter Array and archival Atacama Large Millimeter Array observations of IRAS21078+5211 and G035.02+0.35, respectively, to study kinematics and physical conditions of the corresponding protostellar winds on scales of 100-1000 au using the same molecular tracers. In IRAS21078+5211, the emissions of several molecules, particularly SO, SO2, CH3CN and CH3OH, are distributed along the axis of the radio jet, and present a LSR velocity (Vlsr) gradient transversal to the jet axis. Position-velocity (PV) plots of the SO lines show patterns consistent with Keplerian rotation. The SO2 emission comes from high velocity gas flowing close to the jet axis, while CH3CN and CH3OH present larger radial extension than the S-bearing species. In G035.02+0.35, the same molecules are instead distributed along the major axis of the rotating disk, and their Vlsr gradients consistently trace the disk rotation. The corresponding PV plots present Keplerian profiles. SO is the only molecular species whose emission extends well outside the disk. In both YSOs, the spatial and velocity distributions of SO are consistent with a rotating wind magneto-centrifugally launched from the YSO disk. The comparison with models of molecule formation and excitation in shocks indicates that the different radial extension of the molecular species observed in the protostellar wind of IRAS21078+5211, as well as the lack of molecules, except SO, in the G035.02+0.35's wind, can be explained in terms of a radially extended MHD DW, rather than a compact X-wind.

We study an electron-phonon interaction driven thermoelectric diode. The nonreciprocity in this diode arises from the asymmetry between the probabilities of phonon emission and absorption in the electron-phonon interaction, as well as the structural reflection asymmetry. We reveal the intrinsic nature of this nonreciprocity, as the forward and backward electron transport remains asymmetric even when the applied temperature difference is not reversed. This intrinsic nonreciprocity gives rise to two novel transport phenomena. One is a novel thermoelectric effect which is driven by the temperature difference between the leads and the central device region, rather than the conventional temperature difference between the two leads. The second, and more significant, phenomenon is the suppression of electronic backscattering in the load resistor. This suppression decreases the resistance of the load resistor, which leads to the breakdown of Ohm's addition law. Under suitable conditions, the presence of electron-phonon interaction can yield a larger thermoelectric current compared to the case without it. This intrinsic nonreciprocity opens up a new pathway for low-power electronics besides topology and superconductivity, and for nonreciprocal thermoelectric devices.

Most galaxies host supermassive black holes (SMBHs) that remain weakly accreting or dormant for much of their lifetimes. At the lowest accretion rates, these systems may represent the transition between active nuclei and dormant black holes, but whether they can still launch collimated jets remains unclear. The nuclei in our Galaxy (\sgra) and M31 are key examples of this regime, although no clear jet structure has yet been detected in either source. Here we report multi-frequency very long baseline interferometric observations of \Msixty\ (NGC~4649), a nearby elliptical galaxy hosting a nearly dormant SMBH with an Eddington ratio of $\sim10^{-8}$. We detect a compact two-sided jet with an unusually steep synchrotron spectrum, demonstrating that collimated outflows can persist even under nearly dormant accretion conditions. The apparent radio core exhibits an unprecedentedly steep frequency-dependent position shift toward the SMBH, locating the central engine only $\sim57\,\mu$as, corresponding to a projected distance of $\sim10$ Schwarzschild radii, upstream of the 8.37-GHz core. The observed jet morphology and steep core-shift behaviour are reproduced by general relativistic magnetohydrodynamic and radiative-transfer simulations, indicating a magnetically dominated, non-equipartition jet-launching region that departs from the standard conical equipartition picture. These results provide direct observational evidence that jet production can survive near the dormant SMBHs and establish \Msixty\ as a unique laboratory for probing jet formation on event-horizon scales in the lowest-accretion SMBH regime.

We study the non-leptonic weak decays of doubly charmed baryons (${\cal B}_{cc}$) into singly charmed baryons (${\cal B}_c$) and vector mesons ($V$), denoted as ${\cal B}_{cc}\to{\cal B}_{c}V$. The short-distance contributions are calculated within the naive factorization hypothesis, while the long-distance final-state interaction effects are modeled via hadronic triangle diagrams. Unlike previous approaches, which compute only the imaginary part using the Cutkosky cutting rule, we evaluate the complete loop integrals to obtain both the real and imaginary parts of the amplitudes. These provide the nontrivial strong phases essential for CP violation. The model parameters are determined using experimental data. With this improved calculation method, we predict the branching ratios and decay asymmetry parameters for various decay channels, as well as $CP$ violations for short-distance dominated and singly Cabibbo-suppressed channels. This strengthens our theoretical framework for future study of doubly charmed baryons. Certain decays, primarily driven by long-distance effects, have been calculated; their observation in future experiments could help clarify the role of final-state interactions in charm baryon decays. Therefore, our calculation of ${\cal B}_{cc}\to{\cal B}_{c}V$ provides crucial predictions for branching ratios, decay asymmetry parameters, and $CP$ violation, which are essential for guiding experimental study at LHCb.

We characterize the quasi-stationary distribution (QSD) of the bond directed-percolation line of the Domany--Kinzel automaton using a matrix-product-state representation of the probability distribution, obtained by projecting out the absorbing state and iterating the transfer matrix. Unlike moment- or sampling-based methods, this yields the full conditional distribution and direct access to information-theoretic diagnostics. The spatial structure of the QSD changes sharply across the transition: the active phase is bulk-like with finite density, whereas in the inactive phase the surviving activity collapses into a single flock occupying a vanishing fraction of the chain, with an internal filling that ranges from a single cluster deep in the inactive phase to a loose, partially filled group near criticality. This picture carries a sharp information-theoretic signature: throughout the inactive phase the bipartite mutual information of the QSD equals the entropy of a single binary choice -- whether the flock lies to the left or right of the cut -- so the surviving clusters together encode just one bit of positional information, corresponding to a single effective cluster. The approach extends matrix-product-state techniques to the projected eigenvector defining a QSD, opening information-theoretic diagnostics for absorbing-state systems that bulk-observable methods cannot reach.

Trace norms are fundamental to quantum information theory, yet in many-body systems their evaluation remains a major computational bottleneck, as it generally requires diagonalizing exponentially large operators. Here, we overcome this bottleneck by introducing a controlled tensor-network algorithm for estimating the trace norm of matrix product operators without full diagonalization. The key idea is to combine Zolotarev's rational approximation to the sign function with a variational formulation solved using a density-matrix-renormalization-group-like algorithm. The resulting approximation is systematically improvable, with its accuracy controlled by the rational approximation parameters and the spectral weight near zero. Beyond the reach of exact diagonalization, we demonstrate controlled trace-norm calculations for entanglement negativity, quantum fidelity and quantum Fisher information, achieving substantially improved accuracy over polynomial-based Lanczos approaches. Our results establish trace-norm-based quantities as practical tensor-network observables, opening a route toward tensor-network studies of quantum information in mixed states.

Thin films draining on top of curved surfaces occur in coating, manufacturing, and geophysical flows, where predicting accumulation and thinning is crucial. Unlike singularities associated with contact lines, boundaries, defects, a smooth saddle alone can produce a locally singular drainage thickness distribution. The singularity stems from competing converging and diverging flow and is regularized within a dynamically selected region where drainage, hydrostatic pressure, and capillarity balance. Saddles thus emerge as generic building blocks for thin-film drainage on complex topographies.

2D electrocatalysts that enable hydrogen evolution at low overpotentials offer an attractive alternative to expensive platinum-based systems. Here, we report the growth of Janus transition metal dichalcogenide (TMD) monolayers (MLs), SeMoS and SeWS, on Au foils using chemical vapor deposition, and systematically compare their catalytic properties in the context of hydrogen evolution reaction (HER) with those of their parent TMDs. The Janus MLs exhibited significantly enhanced catalytic performance relative to the parent TMDs. Furthermore, these MLs on Au foils were subjected to sonochemical treatment in polar and non-polar solvents, in which the treatment with polar solvents led to a substantial improvement in the HER activity of Janus MLs. In particular, SeMoS MLs treated with water showed a low overpotential of ~63 mV, a Tafel slope of ~42 mV/dec, and an exchange current density of ~10$^{-3}$ mA cm$^{- 2}$, approaching that of platinum. Analyses indicate that enhanced electrocatalytic activity is associated with tensile strain induced by Au surface restructuring and the formation of defects in Janus MLs, as shown by experimental observations and by density functional theory calculations. The enhancement in catalytic performance due to sonochemical treatment emphasizes the importance of our results for developing novel catalytic systems for HER based on Janus 2D materials.

The rotational velocity of interstellar gas in the Milky Way, and other galaxies, has been taken to represent the circular velocity of a test particle in the Galaxy gravitational field, and hence an indicator of the Galaxy mass. The derived circular velocity is found to be too high for the gas to be gravitationally bound to the galaxy given the observed Galaxy mass in stars and gas, and consequently an extra component of mass in the Milky Way and other galaxies, namely dark matter, has been postulated. However recently the observational satellite Gaia, has been carrying out ground-breaking astrometric observations to accurately measure, inter alia, the three dimensional velocities of stars in the vicinity of the Sun and beyond. This has revealed that the circular velocity derived from the stellar population is much less than that of the gas, and the rotation curve, circular velocity versus radius, is distinctly declining with radius, whereas the gas rotation curve is not declining. By combining results from multiple observations of the gas velocity, averaging the velocities in radial bins, we establish that there is a grand average rotation curve. This can be compared directly with a grand average of the published Gaia rotation curves, and the confidence level in the difference between the two estimated by statistical analysis. The difference is shown to have a high degree of confidence, and increases with galactocentric radius. The lower circular rotation curve from the stellar velocities has resulted in significantly reduced estimates of the dark matter mass fraction of the Milky Way. The higher rotation of the gas lacks an explanation, but it is unlikely to be an accurate indicator of the kinematic mass of the Galaxy. This also has significant consequences for the mass of external galaxies based on gas rotation curves.

Machine learning is increasingly applied to accelerate the discovery of novel materials by exploring large compositional and structural design spaces. Yet, the scarcity of high-quality data and the frequent need for out-of-distribution prediction introduce substantial uncertainty, making the assessment of model reliability essential. In this work, we investigate uncertainty quantification as a means to evaluate model confidence in the context of permanent magnet research. In a first study, we benchmark classical and modern machine learning models for predicting intrinsic magnetic properties, focusing on the quality of their uncertainty estimates. We apply Gaussian negative log-likelihood loss and dropout-based Bayesian approximation as practical strategies for estimating predictive uncertainty. In a second study, we transfer these architectural features for uncertainty estimation to a more complex task: predicting coercivity from microstructural information using a graph neural network. Together, these studies demonstrate that uncertainty quantification not only enhances the trustworthiness of predictions but is also transferable across different modeling tasks.

Some rocky planets orbit so close to their host stars that stellar heating melts their surfaces. They offer a rare glimpse of planets in a magma-ocean state, providing an observable analogue to processes that likely shaped the early Earth and other terrestrial planets during their infancy. Recent JWST observations of five eclipses of the prototypical lava planet 55 Cnc e have confirmed earlier hints that it exhibits highly variable thermal emission, with low-resolution spectroscopy pointing to a possible volatile-rich atmosphere likely rich in CO and CO2. Here we report on an analysis of the same JWST datasets but at their native spectral resolution, utilizing cross-correlation techniques. An unambiguously strong ~8 sigma signal from CO in emission is recovered during one out of five epochs, with potential ~3 sigma detections during two others. The strongest observed cross-correlation signal is difficult to reconcile with a hydrostatic atmosphere, requiring a steep and strong thermal inversion at the right pressure level (~1-10 mbar) and a relative abundance of CO2 that is at least 3 orders of magnitude lower which would otherwise mask the CO signal. Self-consistent atmospheric modelling indicates that this is most readily achieved in a hydrogen-rich atmosphere, which produces the steepest inversions and highest CO/CO2 ratios. The pronounced epoch-to-epoch variability suggests that the CO signal does not trace a static atmosphere alone, but may reveal a transient, dynamically active component, potentially linked to variable atmospheric outflow.