Papers

We study the dynamics of the cumulants of the entanglement Hamiltonian in interacting integrable models following global quantum quenches. Building on recent results based on space-time duality, we show that these cumulants are exactly given by the cumulants of currents of suitable conserved charges evaluated in the macrostate selected by the initial state. This establishes a direct connection between entanglement dynamics and transport, providing a transport counterpart to the quasiparticle picture that successfully describes the evolution of the von Neumann entropy. In the free-fermion and conformal limits, our results reduce to the difference between the current cumulants carried by right- and left-moving excitations, recovering previously known expressions. In interacting integrable models, where a decomposition into independent right and left movers is no longer meaningful at the operator level, a similar structure survives at the level of the entanglement spectrum, yielding a unified description of entanglement Hamiltonian fluctuations across free, conformal, and interacting integrable systems.

In low-regularity spacetimes and Lorentzian length spaces, achronal causal curves play the role of null (pre-)geodesics. Because of the lack of a geodesic equation, they do not come with a canonical parametrization. In this context, we discuss a notion of affine parametrization via limits of affinely parametrized timelike geodesics. However, we point out a major drawback: an example where this approximation procedures gives a non-unique result, in a way that even completeness or incompleteness of the limit null geodesic is not well-defined. This example involves discontinuous gluing of two Lorentzian metrics across a null hypersurface to give a well-behaved Lorentzian length space and as such is, just like the parametrization problem itself, manifestly Lorentzian. In view of this, we explore possibilities for a Penrose-type singularity theorem using timelike geodesics.

Density matrix renormalization group methods or tensor network methods in general can not only be used to determine ground states but also to evaluate thermal equilibrium properties. Although convergence is superior for one-dimensional quantum spin systems with nearest neighbor exchange and open boundary conditions, the hope is that these methods can as well be employed to approximate magnetic observables of magnetic molecules with more complex interaction patterns. Here, we assume the position of a user and study the accuracy that can realistically be achieved for several archetypical quasi one-dimensional structures using the TenPy suite. In our study, we aim at systems that are too large for exact diagonalization or Krylov space methods.

TiNTaN superlattice coatings were designed to investigate how atomic-scale interface chemistry and defect-stabilized TaN layers govern hardness and fracture toughness. Guided by first-principles predictions identifying TaN-based layers as more damage tolerant than TiN, coherent superlattices with a bilayer period of 6 nm were synthesized by reactive magnetron sputtering and interfacially doped with C, B, or Si. Structural and chemical analyses reveal coherent fcc architectures with well-defined interfaces. Si segregates preferentially to the interfaces while incorporating into both TiN and TaN, whereas C and B predominantly diffuse into the TaN layers, modifying coherency strain, bonding, and defect populations. Consequently, hardness increases from 34 GPa for the undoped superlattice to 41 GPa for the Si-doped architecture, whereas fracture toughness increases from 2.8 to 4.0 MPam0.5 for the B-doped superlattice. First-principles calculations show that vacancy-stabilized TaxNy enhances elastic compliance and elastic contrast rather than intrinsic toughness, while the additional toughening induced by B indicates localized defect-assisted energy dissipation at chemically engineered interfaces. Thus, Si maximizes interface strengthening, whereas B provides the most favourable hardness-toughness balance while preserving high hardness, 38 GPa. These findings establish interface chemistry as an additional design parameter for tailoring the mechanical performance of ceramic nitride superlattices.

Adaptive optimizers retain gradient history in moment variables, allowing a local change in loss weighting to alter later updates. We examine whether this delayed transport is large enough to change prospective short-horizon decisions. On committed future-minibatch sequences, we differentiate eight-step AdamW trajectories through the complete model–optimizer state and select exposure-matched Math–Code loss schedules before independent evaluation. Across 12 unused 0.3M Transformer histories, full transport lowers token-disjoint loss relative to an optimizer-aware immediate derivative in 10/12 histories (mean benefit $4.71\times10^{-4}$; exact one-sided sign test, $p=0.0193$). The two controllers act equally often but select different schedules in 60/96 windows. Crossed checkpoint–future-path tests attribute this reordering to the interaction between optimizer state and near-future data, while an independent Ising–CNN experiment shows that deleting moment-state transport destroys accurate response prediction. Full-transport scores also concentrate exact-rollout winners in larger candidate libraries, focusing finite-amplitude evaluation on a shortlist. On these committed short paths, optimizer memory and near-future data order are therefore actionable components of the training state, providing a mechanism-based criterion for when finite-horizon rather than one-step intervention is required.

As a new probe, the weak lensing (WL) peak steepness statistics is sensitive to the density profile of halos that encodes important information of baryonic feedback and dark matter properties, leading to a promising means to statistically constrain these effects using WL data. In this article, we present its first application to HSC Y1 data to demonstrate the great potential of this new statistics. Within the phenomenological framework of HMcode2016 that attributes the baryonic feedback solely to the reduction of the halo concentration parameter and focusing on high peaks originated dominantly from massive clusters, our analyses by combining WL peak height and steepness statistics resulted in $S_8=0.76^{+0.08}_{-0.07}$ with the maximum-a-posteriori (MAP) of $0.79$ and low concentrations. Taking the form of the concentration-mass relation as $c(M,z)=A(1+z_{\rm f})/(1+z)$ with $z_{\rm f}$ being the formation redshift of halos with mass $M$ at redshift $z$, we obtain $A=1.93^{+1.33}_{-1.16}$ (MAP=$1.70$) in comparison with $A=3.34^{+1.52}_{-1.74}$ (MAP=3.31) from dark matter only simulated mocks. The result tends to support phenomenologically strong baryonic feedback effects at cluster scales.

We study how non-magnetic impurity scattering affects the emergence and possible coexistence of pairing instabilities in a two-node multi-Weyl semimetal. Within an explicitly specified projected impurity kernel—valley diagonal and momentum independent across each Fermi pocket, the leading behaviour of non-magnetic disorder in the small-pocket window $q^{\max}_{\rm intra}\xi_{\rm dis}\ll1\ll|2\mathbf Q|\xi_{\rm dis}$, treated at leading order in Born and Abrikosov–Gor'kov theory—quenched disorder tunes the leading pairing instability from a topologically nontrivial monopole channel to a conventional ($s$-wave) one, extending our earlier clean-system analysis into the disordered regime. A Born self-energy calculation in the chiral band basis then gives: (i) a band-isotropic conventional channel that is Anderson protected against intra-node scalar disorder ($\eta_s=1$), introduced phenomenologically at the projected-band level; solving the competition for arbitrary $\eta_s$ yields the crossing criterion $(1-\eta_s)/(1-\eta_m)<T_{c0}^{(s)}/T_{c0}^{(m)}$, so the mechanism tolerates substantial loss of conventional-channel protection; and (ii) a rank-one monopole sector fixing $f_m$ as the exact eigenfunction with $\eta_m(J)=1/(J+2)$, exact given that kernel. The crossing location in $\Gamma_N/T_{c0}^{(m)}$ is set by $\eta_m(J)$, $\eta_s$, and $r=T_{c0}^{(s)}/T_{c0}^{(m)}$. From the clean projected BdG Hamiltonian the pure monopole nodes carry Berry charge $\pm J$, distinct from the gapped conventional solution; the clean nodal thermodynamics is charge-dependent, $N_{\rm SC}(E)\propto E^{2/J}$ and $C\propto T^{1+2/J}$, and the residual density of states shows a threshold only for $J=1$. The crossing lies in the moderately metallic regime, $\mu/\Gamma_N\simeq11$–$14$ for the illustrative $T_{c0}^{(m)}/\mu=0.133$ used in the figures.

We develop a theoretical framework for intervalley magnetotrions in buckled two-dimensional materials, including silicene, germanene, and stanene, subjected to perpendicular electric and magnetic fields. Within the effective-mass approximation, the three-particle Schrödinger equation is formulated with the Rytova–Keldysh interaction potential and analyzed in the high-magnetic-field regime. We demonstrate that intervalley trions with equal electron and hole effective masses constitute an exceptional case for which the center-of-mass and internal motions separate exactly. The center-of-mass motion is governed by a two-dimensional harmonic-oscillator Hamiltonian, leading to quantized Landau states whose energies form electrically tunable Landau surfaces controlled by the magnetic field and the electric-field dependence of the carrier effective masses. The internal motion is investigated by solving the three-body Schrödinger equation within the framework of the hyperspherical harmonics method. Numerical calculations reveal that the trion binding energy increases monotonically with both magnetic and electric fields owing to the combined effects of magnetic confinement and electric-field-induced enhancement of the effective masses. The strongest binding is obtained for silicene, followed by stanene and germanene. The present work provides a unified description of both the collective center-of-mass motion and the internal dynamics of magnetotrions in Xene monolayers, demonstrating that both degrees of freedom can be independently manipulated by external electric and magnetic fields.

The convective turbulent motion of the fluid below the shock in a core-collapse supernova stretches and amplifies the magnetic field of the progenitor star. The energy contained in the field is sourced from the work done by the fluid on the field which comes at the expense of the fluid's kinetic and internal energy. In addition to the energy exchange with the fluid, the magnetic field also has a back-reaction upon the fluid via a contribution to the baroclinic vector and thus affects the fluid vorticity. In this paper we explore the interaction of the magnetic field with the fluid in core-collapse supernovae using the ELEPHANT code with solar-metallicity stars of 15 and 20 \msun zero-age main sequence mass and purely toroidal initial magnetic fields of $B_0 = 0, 10^{10}, and 10^{12}$~G. We find that the magnetic field in the gain region does not become so large that it alters the global dynamics above the 10% level in the early post-bounce evolution. The turbulent kinetic energy of the fluid in the gain region is smaller in simulations with a strong initial magnetic field, but the exact amount of reduction is uncertain due to limitations of the methods for measuring turbulent kinetic energy. The structure of the field in the simulations quickly becomes a tangled mass of flux ropes as soon as convection begins, which leads to a large magnetic field contribution to the baroclinic vector that dominates over the hydrodynamic contribution. Although governed by very similar transport equations to the magnetic field, the fluid vorticity and magnetic field are always close to being randomly aligned at every stage of the evolution. The enstrophy, which is seen to be closely associated with the turbulent kinetic energy, is found to be reduced in simulations with a strong initial magnetic field supporting the inference that the magnetic field reduces the amount of turbulence in the fluid.

Bondi showed in 1957 that a body of negative active gravitational mass and a positive one should accelerate together without limit while their total momentum stays zero. We test this prediction in full 3+1 numerical relativity, from constraint-satisfying initial data. The matter is two complex scalar fields with identical self-interactions, one of which enters the Einstein equations with the opposite sign; its stars have positive inertial and passive masses but negative active and Arnowitt-Deser-Misner (ADM) masses. To our knowledge, they are the first asymptotically flat bodies of negative ADM mass evolved in numerical relativity. A pair of stars with equal and opposite ADM masses accelerates as a single object at constant separation, and its total momentum stays zero to within 0.5%. The acceleration follows Newton's law of gravitation in both mass and separation, reverses when the stars are exchanged, and is absent in same-sign pairs and isolated stars. We detect no gravitational radiation. The results hold for head-on pairs released from rest, up to a few percent of the speed of light, and in the longest run the pair reaches a tenth of it with both stars intact.

Recent STAR measurements at fixed-target Beam Energy Scan energies have revealed an unexpectedly large directed flow of $\phi$ mesons in Au+Au collisions, comparable to that of protons and $\Lambda$ baryons and much stronger than that of light strange mesons. Since the $\phi$ is a hidden-strangeness meson with relatively weak interactions with non-strange hadrons, this observation has been interpreted as a possible signal of unconventional baryonic dynamics or exotic baryonic resonances coupled to the $\phi$ channel. Within the framework of the Parton-Hadron-Quantum-Molecular-Dynamics(PHQMD) model, we demonstrate that in the high baryon density region, $\phi$ mesons are produced predominantly through multi-step meson–baryon and meson–hyperon reactions, whose transition amplitudes are constrained by a coupled-channel $T$-matrix calculation based on an extended SU(6) chiral effective Lagrangian. Together with the in-medium broadening of the $\phi$ spectral function, these baryon-driven production channels enhance near-threshold $\phi$ production and imprint the collective motion of the baryon-rich source on the produced $\phi$ mesons.

We investigate the diffusiophoretic motion of a chemically isotropic active colloid in a three-dimensional wedge formed by two distinct fluid media, in the limit of vanishing Péclet and Reynolds numbers. The concentration field is obtained using the Fourier-Kontorovich-Lebedev transform, yielding an exact representation for arbitrary wedge opening angles and interfacial contrasts. We introduce the interfacial parameter $\Gamma=(1-\lambda\ell)/(1+\lambda\ell)$, where $\lambda$ denotes the diffusivity contrast and $\ell$ the solute partition coefficient. For $\Gamma=\pm1$ and commensurate wedge angles, the solution reduces to finite image constructions, with distinct structures for even and odd commensurability. The general solution also recovers the planar-interface and semi-infinite-interface limits. The leading-order translational phoretic velocity is derived from the concentration field, revealing a strong interplay between wedge geometry and interfacial properties that governs both the magnitude and direction of particle motion. This work provides a framework for understanding and controlling phoretic transport in confined multiphase environments and offer a basis for extensions to finite-size geometries and mixed fluid–fluid and solid boundary conditions. Our results may find applications in the control of active-particle transport in confined multiphase environments, where interfacial properties and geometry can be exploited to tune phoretic motion.

Electron monochromators are essential components for many applications in electron microscopy but are often large and complex to operate instruments. In prior work, we presented a concept for monochromation using the fringe fields around miniature electrostatic elements. This concept could be realized with a compact monochromator design that requires tuning of only 7 power supplies. In this manuscript, we present the fabrication using MEMS technology and experimental testing of such a miniaturized monochromator. The fabrication scheme involves Bosch deep reactive ion etching to shape lens and deflector electrodes and focused ion beam milling to create nanoscale apertures in a silicon nitride membrane. All elements are then coated, precisely aligned and, after stacking, wire bonded to connect to external power supplies. We use the assembled prototype to measure the electron-beam energy spread in a scanning electron microscope demonstrating the energy filtering capability of the device. These results highlight the possibilities for making miniaturized electron optics instruments using alignment and stacking of different MEMS fabricated elements, representing an important step towards the development of compact, lightweight, high performance electron-beam instrumentation.

We extend the earlier analysis of cosmic censorship and the Weak Gravity Conjecture (WGC) in Einstein–Maxwell-dilaton (EMD) theory by performing a complete higher-order Sorce–Wald gedankenexperiment on the static charged Gibbons–Maeda–Garfinkle–Horowitz–Strominger (GMG) black hole. In the probe limit, an extremal GMG black hole can apparently be overcharged by a test particle, seemingly violating the weak cosmic censorship conjecture (WCCC), which is nothing but first-order variational identity in the Iyer–Wald formalism. This window can be closed by either incorporating backreaction via the Hoop Conjecture or further including second-order variational identities. In this paper, we explicitly compute third-order variational identities. The extremality parameter eta remains non-negative to the third perturbative orders confirming WCCC protection, regardless of the apparent failure of all-order generalization, model-independent proof of Lu, et al.. We further incorporate the Swampland Distance Conjecture (SDC): the resulting infinite tower of light charged states discharges any would-be overcharged configuration on a timescale tau much less than 2M, exponentially faster than a horizon can be destroyed, reinforcing WCCC in dynamical regimes and strongly relaxing the original WGC charge-to-mass bound.

Analyses of Gaia DR3 wide binaries reach opposite verdicts on a claimed low-acceleration anomaly: gamma = Geff/G ~ 1.4 (Chae 2023-2026; Hernandez et al. 2024) versus Newtonian at high significance (Banik et al. 2024; Pittordis et al. 2025), from the same catalogue. We localize the disagreement experimentally. A generative model – Keplerian binaries plus hierarchical triples with photocentre and time-averaging effects – is validated without tuning against Pittordis et al. (2025). Synthetic catalogues of known truth are confronted with three estimator families: a full-median estimator, even with a perfect eccentricity correction, recovers gamma = 1.08-1.13 from purely Newtonian universes containing 20-30% residual triples – half-way to the claimed anomaly – while a tail-truncated estimator and a mixture likelihood recover <= 1.04 and 1.00. An injected MOND-like boost (gamma = 1.4 above 2 kau) is recovered at >= 1.26 by all three: the hypotheses never overlap under robust estimation, so the controversy is decidable. Applying the calibrated estimators to the 81,088-pair Chae (2024) sample we measure gamma = 1.045 [1.025, 1.068] (2-30 kau), and a joint mixture fit gives gamma = 1.05 [1.04, 1.07] with f_trip = 0.15, consistent with the independent 0.17; gamma = 1.4 is rejected at ~16 sigma. We freeze a pre-registered protocol, time-stamped on Zenodo, for Gaia DR4, where sigma_stat(gamma) < 0.005 will make estimator systematics fully dominant.

Parliamentary systems pass more bills than presidential systems at baseline, but collapse to near-zero passage under party-system fragmentation. The literature offers three competing micro-explanations: coalition-formation failure, party discipline, and committee gatekeeping. These operate simultaneously in any real legislature, so observational studies struggle to separate their contributions. We present an agent-based model that compares four democratic institutions: pure parliamentary, pure republican/presidential, premier-presidential (France), and president-parliamentary (Russia). Across four scenarios and N=200 seeds per cell we report bootstrap confidence intervals, Morris screening, Sobol variance decomposition, mechanism ablations, and a hung-parliament variant comparison. Three findings emerge. First, government formation failure alone does not halt legislation: when a fragmented parliament reverts to personal voting, parliamentary passage (46.4%) is statistically indistinguishable from the presidential benchmark (44.8%); collapse requires cohesive opposition obstruction, which drives passage to 0.05%. Second, disabling discipline restores fragmented passage to 46.7%, and the rescue magnitude is monotone across the four institutions in a pattern that survives varying the common discipline level. Third, the passage-representation tradeoff is a single spectrum: parliamentary maximises throughput at the cost of representational fidelity; republican maximises fidelity via the presidential veto; semi-presidential variants split the difference.

The read-out electronics of the ATLAS muon drift-tube chambers will be upgraded for operation at the High-Luminosity Large Hadron Collider. Part of the upgrade is the introduction of new amplifier-shaper-discriminator chips. This note presents the calibration of the discriminator threshold of the new chip in terms of primary electron signals using data from small-diameter muon drift-tube chambers operated in a monoenergetic, high-energy muon beam. The discriminator threshold intended for use in the ATLAS muon spectrometer corresponds to the signal of 20 primary electrons.

Identities asserting that an antisymmetrizer admits a determinantal expression are central to several proofs of counting formulas for alternating sign matrices. Antisymmetrizers appear also frequently in symmetric function theory as, for instance, the Hall-Littlewood polynomials can be realized via antisymmetrizers. In this paper, we establish a new identity of this type, thereby proving a conjecture of Lukas Riegler and one of the authors. We also elaborate on a related antisymmetrizer that may be pivotal in resolving a beautiful conjecture of Colomo and Pronko, and we formulate a version of their conjecture tailored to the suggested approach.

Galactic binaries are expected to be the most numerous long-lived sources in the Laser Interferometer Space Antenna (LISA) data stream and are commonly modeled as quasi-circular, nearly monochromatic systems. In this work we present eGB-multi, a fast time-domain eccentric Galactic-binary waveform package for LISA. The package combines a post-Newtonian-accurate quasi-Keplerian eccentric source model with a time-domain LISA response, evaluating the signal on the retarded one-way links and then constructing time-delay interferometry observables. Its modular implementation allows the user to switch between different levels of orbital description, ranging from Newtonian closed eccentric orbits and relativistically precessing eccentric orbits incorporating the 1PN-accurate periastron advance, to precessing and shrinking eccentric orbits that additionally account for gravitational radiation reaction at leading quadrupolar order. The framework also provides an automatic evolution mode, in which the appropriate level of orbital dynamics is selected based on a pre-defined mismatch tolerance. We employ this framework to quantify the regimes in which orbital eccentricity renders the commonly adopted quasi-circular approximation for Galactic binaries inadequate.

We study a returning quantum change interval in which a source emits $\lvert\psi\rangle$ over one interval and $\lvert0\rangle$ elsewhere. A collective measurement on the full sequence identifies both endpoints with minimum error. We analyze the Gram matrix using Toeplitz comparison and Følner transfer, together with an exact decomposition by excitation number and interval hull. The resulting bounds establish asymptotic Bayes optimality of the square root measurement (SRM). Let $c=\lvert\langle0\vert\psi\rangle\rvert$ and $p_1(x)=4(1-x^2)K^2(x^2)/\pi^2$, where $K$ is the complete elliptic integral of the first kind. For a known interval length $i$, the SRM success probability and the Bayes optimum converge to the same Toeplitz symbol integral as the number $N$ of translations grows. For fixed $i$ and $0<c<1$, their gap is $P_{\mathrm{opt}}(G_{N,i})-P_{\mathrm{SRM}}(G_{N,i})=O_{i,c}(N^{-1/2})$. If $i$ and $N$ both diverge, their common limit is $p_1(c^2)$, with no constraint on their relative growth. For unknown length, the uniform prior over all $M_n=n(n+1)/2$ nonempty intervals gives the common limit $p_1(c)^2$ at fixed overlap. For a varying overlap $c_n$, set $\tau_n=n(1-c_n)(\log n)^2$. Uniformly for $0\leq\tau_n\leq T$, we obtain $M_nP_X=(1+2\sqrt{\tau_n}/\pi+\sqrt{2}\tau_n/\pi^2)^2+O_T(\log\log n/\log n)$, where $X\in\{\mathrm{tr},\mathrm{SRM},\mathrm{opt}\}$. More generally, if $c_n$ approaches one from below and $n p_1(c_n)\to\infty$, the same three quantities satisfy $P_X\sim p_1(c_n)^2$. These asymptotic laws also extend to joint detection and exact localization in the presence of a no change prior.

We present broadband X-ray spectral and timing analysis of the Ultra-luminous X-ray source (ULX) in IC5052 using simultaneous XMM-Newton and NuSTAR observations from 2022, supplemented by archival 2013 XMM-Newton data. A two-thermal component model, often interpreted as radially-segregated emission from a super-Eddington inner disc and its associated wind, provides a statistically acceptable fit but yields an implausibly high inner disc temperature of $k T_\mathrm{in} \approx 6.4$ keV, inconsistent with even super-Eddington disc models. Including an additional continuum component from either an accretion column or a Comptonizing corona, as motivated by high S/N observations from other ULXs, provides comparable goodness of fit while allowing plausible inner disc temperatures. The accretion column model yields $k T_\mathrm{in} \approx 1.2$ keV with the column contributing $F_\mathrm{col} \approx 62\%$ of total flux, while the Comptonizing corona model yields $k T_\mathrm{in} \approx 3.0$ keV with a scattered fraction $\sim 1$, assuming the hotter disc provides the seed photons. Timing analysis initially challenges both scenarios: the accretion column model places IC5052 ULX where prior results suggest pulsations may be detectable ($F_\mathrm{col} \sim 62\%$), yet none were detected, while the corona model appears inconsistent with its lack of observed short-timescale variability. However, incorporating spectral information relaxes these constraints, allowing both models to remain physically plausible for IC5052 ULX. Finally, using improved Chandra astrometry, we identified a candidate optical counterpart consistent with an evolved high mass donor. A discrepancy between the optical extinction and X-ray fitted absorption suggests localised X-ray absorption.

Fu and Nijhoff's direct linearization scheme for the KP hierarchy and its reductions employs a system of evolution equations of an infinite matrix $U$ with quadratic nonlinearity. Part of the matrix elements of $U$ can be identified with affine coordinates $w_{ij}$ of the top cell of the Sato Grassmannian. The evolution equations of these matrix elements are identical to the evolution equations of $w_{ij}$ representing the KP hierarchy in geometric terms. This geometric interpretation can be extended to other matrix elements of $U$ by introducing negative flows to the evolution equations of $U$. The extended system turns out to be substantially equivalent to the two-component KP hierarchy. The Cauchy matrix approach to the KP hierarchy can be explained in this geometric perspective. Multi-component generalizations of Fu and Nijhoff's nonlinear system are related to the AKNS and ASDYM hierarchies. Multi-component Sato Grassmannians show up therein as the relevant geometric structure.

We first present an introduction to the differential geometry of noncommutative algebras that carry a representation of a triangular Hopf algebra. Their noncommutativity is encoded in the universal R-matrix. The differential geometry is canonically constructed from these data. We then develop a new approach to the Bianchi identities for curvature and torsion of arbitrary connections (not necessarily bimodule connections). Using the Cartan calculus for connections, we prove the equivalence of their global formulations in terms of exterior forms and tensor fields. In particular, we obtain the noncommutative analogues of the first and second Bianchi identities familiar from general relativity.

We study electron transport through a monolayer jacutingaite (Pt$_2$HgSe$_3$) tunnel junction in which only the barrier is irradiated by off-resonant circularly polarized light, while the leads remain undriven. In the high-frequency regime, the driven barrier reduces to an effective static Dirac Hamiltonian with a photon-dressed, valley-dependent mass term. A staggered sublattice potential $V_z$ and a substrate-induced exchange field $m_s$ provide additional tunable mass terms. Using scattering theory, we compute spin- and valley-resolved transmission and reflection, as well as the Landauer conductance. Photon dressing shifts the barrier {Dirac masses} with opposite signs in the ($\boldsymbol{K}, \boldsymbol{K}'$) valleys and induces a splitting of the propagation thresholds. The finite barrier then produces channel-dependent Fabry–Pérot-type interference through the phase $q_x^{\eta s_z}L$. We find broad parameter windows with near-perfect valley filtering ($|P_v|\simeq 100\%$) and substantial spin polarization ($|P_s|\sim 70\%$). The dominant spin and valley polarizations can be switched by tuning the drive amplitude $A_0$, $V_z$, and~$m_s$.

A formula for the $\alpha$-K-energy functional for the Kähler-Yang-Mills (KYM) equations is provided in this paper. Using this formula and Chen's $\epsilon$-geodesic equation on the space of Kähler potentials, we prove that if a solution exists to the KYM equations for a simple vector bundle on a Kähler manifold with discrete automorphism group, then it is unique and the $\alpha$-K-energy is bounded from below. Inspired by the study of constant scalar curvature Kähler metrics, we introduce a coupled J-equation to study the $\alpha$-K energy functional.

Iterative diagonalization is the dominant cost of plane-wave density-functional theory (DFT), with search-space orthogonalization scaling particularly quickly with problem size and the number of target states. We present a randomized block Davidson-type eigensolver that replaces Euclidean orthogonalization with randomized Gram-Schmidt in a sketched inner product, requiring only a single pass over the basis while keeping its conditioning bounded independently of the input vectors. This modification changes only the Rayleigh-Ritz step, which becomes a definite generalized Hermitian eigenproblem. Ritz extraction remains exact, preserving true Ritz pairs and the interlacing property that makes each band energy an upper bound on the true one. The method is implemented in mixed precision for CPUs and GPUs from a single Julia code, interfaces matrix-free with DFTK, and is released in the open-source RandESC library. On sparse test problems with a fixed number of eigenpairs, the sketched solver overtakes its deterministic counterpart beyond matrix dimensions of about $2\times 10^4$ and is $25\%$ faster at $5\times 10^5$. In full self-consistent field DFT calculations, however, both Davidson variants outperform the locally optimal block preconditioned conjugate gradient (LOBPCG) reference only by $5$ to $11\%$ in total time, while the additional benefit of sketching is limited. As the number of requested states grows with system size, orthogonalization savings are offset by the generalized eigenproblem. Therefore, the regime in which sketching pays off is set by how the number of wanted states scales with the problem dimension, not by the eigensolver as such.

We prove the first quantum-classical separation for a sampling problem over a continuous domain. For a class of Gibbs states $p\propto e^{-\beta E}$ on the torus $\mathbb{T}^d$ with smooth ($s$-Gevrey) potential and barrier amplitude $\alpha=e^{\beta\Delta}$, where $\Delta = \max E-\min E$, every classical algorithm querying the value, gradient, or any higher-order derivatives of the log-density requires $\Omega(\alpha)$ queries to sample at constant accuracy in total variation distance, while a quantum algorithm based on quantum singular value thresholding and temperature annealing samples with $\tilde{O}\left(\sqrt{\alpha}\right)$ queries to an oracle for the gradient. The advantage is quadratic in the barrier amplitude, which becomes exponential in the dimension, $e^{\Omega(d)}$, at low temperature. The classical bound is information-theoretic, holding for every classical algorithm with query access to the Gibbs potential and its derivatives at any order.

In coupled micro-ring resonator (MRR) systems, the coupling process plays a critical role in determining the optical response, yet models of these structures typically assume this process to be either lossless, or dissipative with either purely real or purely imaginary coupling rate, respectively. Dissipative coupling is contingent on having appropriately phase engineered structures with intricate coupling geometries, but systems exhibiting `lossy coupling', i.e., characterized by complex-valued coupling rates, have received comparatively little attention. In this work, we investigate the effect of such `lossy' coupling, by modelling the optical response of a tri-waveguide coupled MRR system, using Temporal Coupled-Mode Theory (TCMT). The `lossy' coupling occurs via a common bus waveguide, positioned between a pair of MRRs, leading to the emergence of a pair of intrinsic resonances, whose frequency and linewidth may be tailored by controlling the respective coupling rates from either MRR. We develop these ideas, and by connecting the input (driving) waveguides, using a 3dB y-splitter, demonstrate a novel, coherently driven, lossy-coupled MRR, which exhibits either an absorptive or transparent resonance peak on demand by phase-controlled super-modes.

We analyze quasi-periodic oscillation (QPO) candidates in the 0.1-100 GeV Fermi-LAT light curves of 41 TeV blazars with a conservative, multi-stage timing analysis combining FFT power spectra, red-noise Monte Carlo simulations, false-discovery-rate control, bootstrap period uncertainties, split-sample cross-validation, Lomb-Scargle and WWZ diagnostics, a detection-only sensitivity test, observingwindow checks, and injection-recovery experiments. A first-pass FFT search flags 16 sources above a raw 95% level and six strong candidates after data-quality and split-sample filtering, none satisfying a fully automated multi-method tier. Source-level significance is quantified with forward simulations that preserve the observed sampling and non-Gaussian flux distribution, treating the red-noise slope as a nuisance parameter and never assuming independence of periodogram powers. At simulation-selected reference slopes, only two of the 41 sources reach a raw source-level p < 0.05,only J1555.7+1111 reaches Benjamini-Hochberg significance, and none survives Benjamini-Yekutieli correction. No source survives the conservative slope envelope. Even J1555.7+1111, which the first-pass search flagged as significant but did not rank among its strong candidates, has a global p-value that rises to 7.5*10^-3 under the least favorable slope (~ 0.31 after the full-sample search), so it is not a robust detection. With substantial period uncertainties, a weak observing window, and limited injection-recovery sensitivity, we establish no robust gamma-ray QPO detection: a sampling-faithful red-noise treatment substantially contracts the candidate set, providing an explicit assessment of QPO credibility.

In this work, we investigate quantum quenches in the two-leg Creutz model with long-range hopping, where the hopping amplitudes decay with distance as a power law characterized by an exponent $\nu$ and have a finite range $D$. We first obtain the exact solution of a generic two-band model in momentum space. This allows us to compute the Loschmidt amplitude and, consequently, the dynamical free energy $f(\texttt{t})$ of the two-band model. We also show how to determine the Yang-Lee Fisher (YLF) zeros by solving a nonlinear equation. We demonstrate that the two-leg Creutz model in momentum space is a special case of the generic two-band model. Using these results, we identify the non-analyticities in the dynamical free energy $f(\texttt{t})$ at critical times $\texttt{t}_{c}$. We find that the number of nontrivial critical times $N_{s}$ depends on both $\nu$ and $D$. In particular, we show that for small $\nu$ and large $D$ the critical times become increasingly dense, leading, in the appropriate regime, to non-analyticities at an increasingly dense set of times—similar to what was observed by Xavier and Hoyos [Phys. Rev. B, $\textbf{108}$, 214303 (2023)] in the Su-Schrieffer-Heeger (SSH) model with long-range hopping terms.