Papers

Cold collisionless matter is usually described by pressureless fluid equations; this fails in three-dimensional spherical geometry. For the cold spherical case, kinetic and fluid descriptions share the same time-domain dynamics, but if we look at the spectrum, the kinetic system admits one solution the fluid does not: a discrete mode at twice the central orbital frequency, $\omega_0 = 2\Omega(0)$. It is specific to 3D: razor-thin disks reduce to the fluid description. Nonlinear simulations confirm it survives at finite dispersion. Around Sgr~A$^*$ it lies at $\kappa(r_{\rm in})$, with $r_{\rm in}$ the cusp's inner edge; if excited, stars at all radii would oscillate at this one frequency.

Pion exchange plays a fundamental role in nuclear structure and is responsible for tensor correlations and high-momentum components in nuclei. The $(p,p'\pi)$ reaction provides a unique opportunity to investigate pion dynamics under large-momentum-transfer conditions. Its three-body kinematics allows large momentum transfer to be achieved while keeping the excitation energy of the residual nucleus low. We investigate the kinematical properties of the $^{12}\mathrm{C}(p,p'\pi^+)^{12}\mathrm{B}$ reaction using Lorentz-invariant three-body phase-space calculations. The calculations were performed for a 392-MeV proton beam assuming a constant transition amplitude. The resulting momentum-transfer map and phase-space distribution identify experimentally accessible regions of large momentum transfer and provide guidance for optimizing a double-arm spectrometer experiment at RCNP. The present study establishes a model-independent kinematical foundation for future investigations of pion-induced correlations, high-momentum components, and pion dynamics in nuclei.

We investigate nonlinear static screening of a proton in a homogeneous electron gas, focusing on the induced density and contact Hartree potential $V_{\rm H}(0)$, an $r$-weighted moment of the entire screening cloud rather than a strictly local quantity. Thomas–Fermi, RPA, and local-field-corrected linear response are compared with nonlinear DFT-LDA and DFT-PBE calculations. The Estreicher–Meier LDA density fit reproduces the contact Hartree potential closely and resolves its core and Friedel contributions, despite an approximate cusp. Kaplan–Kukkonen and Corradini–Del Sole–Onida–Palummo local-field factors give nearly identical contact predictions for the states examined, without implying general insensitivity to local-field corrections. We extend the variable-phase approach with a companion amplitude equation to reconstruct the quantal induced density from bound and continuum states of constrained screened potentials. Friedel-constrained Yukawa, hydrogenic, and Hulthén potentials satisfy the same total-screening condition but yield different contact densities and Hartree potentials. In the two-parameter Apagyi–Nagy construction, the cusp constrains an auxiliary Poisson density, whereas the reconstructed quantum density obeys the Coulomb cusp automatically; neither the Friedel sum rule nor the cusp uniquely fixes the screening cloud. Model-potential contact results approach nonlinear DFT toward high density but deviate increasingly as $r_s$ grows. By contrast, density-informed Popović–Stott potentials reproduce historical Hartree-only and exchange–correlation-modified contact values within $0.05\%$ without refitting. These findings distinguish global scattering constraints, local cusp behavior, and full-density information, and establish a one-center baseline for future two-center screening calculations.

Non-normality can induce large transient growth in linearly stable systems. Determining whether this growth triggers a transition in the underlying nonlinear system, however, requires understanding the interaction between non-normality and nonlinearity. Here, we develop a weakly nonlinear theory for linearly-stable, non-normal systems subject to harmonic forcing, enabling a systematic analysis of this interaction. Following Ducimetière et al. (J. Fluid Mech., vol. 947, 2022, A43), we define a formal small parameter $\varepsilon$ as the reciprocal of the system's maximum linear amplification. However, we ensure asymptotic consistency by providing a framework that naturally adapts to the underlying structure of the system. The approach is applied to a harmonically forced channel flow and to a two-dimensional model mimicking the structure of the Orr-Sommerfeld-Squire equations. Unlike classical weakly nonlinear analysis near bifurcation points, the resulting amplitude equations are non-universal. In fact, a single linear mode amplified by the non-normality can nonlinearly excite a multi-modal and multi-frequency response at leading-order, which is system- or even regime-specific. Nevertheless, the method yields asymptotically consistent amplitude equations that capture this complexity provided a limit in which $\varepsilon\rightarrow0$ can be identified. As the forcing amplitude increases, the reduced equations capture stable nonlinear states emerging from the laminar flow, their subsequent bifurcations, and their eventual collision with the boundary of their basin of attraction. Thus, the amplitude equations can capture subcritical transitions driven by forcing and varied initial conditions and enable the identification of critical parameters beyond which no stable weakly nonlinear state exists.

We investigate the polarization properties and effective stress–energy tensor of gravitational waves in metric $f(R)$ gravity within the linearized approximation around Minkowski spacetime. Owing to the additional scalar degree of freedom inherent in the theory, gravitational waves exhibit polarization states beyond the two tensor modes predicted by general relativity. Using the electric components of the linearized Riemann tensor, we derive explicit expressions for the polarization amplitudes and show that a massless scalar field excites a transverse breathing mode, whereas a massive scalar field generates both breathing and longitudinal responses through a single propagating scalar excitation. Employing the Isaacson high-frequency averaging formalism, we further derive the effective stress–energy tensor and demonstrate that both tensor and scalar perturbations contribute to the total gravitational-wave energy density. The energy transport associated with the massive scalar mode is reduced by its subluminal group velocity, leading to a frequency-dependent suppression of the scalar energy flux. These results establish a unified connection between gravitational-wave polarization and energy transport in metric $f(R)$ gravity and provide potential observational signatures for testing modified gravity with current and future gravitational-wave detectors.

Understanding the spatial distribution of carriers is important for interpreting transport in nanoscale devices. Here, we apply conductance fluctuation tomography to planar selective-area-grown InAs nanowires in both normal-normal and normal-superconductor device geometries. By tracking the evolution of conductance-interference features as a function of magnetic-field strength and orientation, we extract information about the geometry of phase-coherent transport pathways. Using theory to distinguish between bulk-dominated transport, coherent near-surface transport across facets, and transport confined to individual facets. The measurements are consistent with transport dominated by a near-surface accumulation layer in InAs. Devices with normal contacts show behavior consistent with coherent transport across the nanowire apex, whereas hybrid normal-superconductor devices exhibit signatures of more facet-dependent transport. These results demonstrate how universal conductance fluctuations can be used as a tomographic probe of phase-coherent transport pathways in semiconductor nanostructures.

Predictive modelling of triboelectric nanogenerators (TENGs) remains fragmented across analytical theories, finite-geometry solvers and disconnected simulation workflows. These disparate approaches must be unified into an executable framework to advance quantitative TENG research.Here we introduce a charge-defined modelling framework and implement it as TENG-CLAW, a physics-governed platform for traceable TENG simulation. The framework establishes a self-consistent electrostatic hierarchy in which triboelectric charges, pre-charging charges and compensating electrode charges serve as defining state variables.This hierarchy connects the infinite plate analytical limit for near-uniform fields with finite-geometry numerical formulations required for edge-dominated devices. Built on this basis, TENG-CLAW converts user-defined research requests into physically admissible simulation tasks, so that generated outputs are tied to explicit charge states, boundary conditions, solver routes and reusable artifacts across spatial, temporal, field-level, comparative and reporting workflows. This work establishes a rigorous computational basis for interpreting TENG mechanisms and provides reproducible research infrastructure for simulation and physics-guided device design.

Quantum computers relying on cold atoms are being built and promise a high flexibility in the way information in encoded into the physical system. In particular, the analog mode is spiking interest in the field of optimization as a classically intractable number of configurations can be tackled. In this work, we investigate a problem that requires every-day scheduling of critical tasks involving a large number of actors. Namely, fixing the planning for a Earth Observation satellite fleet composed of several of units exposed to a high density of targets to be scanned. We explore numerical schemes that convert the formulated problem into a cold-atoms friendly setup. We begin by a naive formulation of the Satellite Mission Planning problem without taking account for the agility of the satellites. We then extend the problem to take it into account based on the literature. By formulating the planning problem as a Maximum Independent Set problem, we are able to solve the problem with a QPU based on Rydberg atoms. We explore two ways of solving the MIS problem on the QPU, one relying on the graphs and on the Quadratic Unconstrained Binary Optimization Framework (QUBO). We show that the QUBO methodology is the most relevant and explore it more deeply with numerical experiments. We conclude on the potential utility of using a QPU to solve the Satellite Mission Planning problem in an operational context.

Scale-free temporal organization, in which fluctuations show similar statistical structures across timescales, is a feature of many complex systems considered to support optimal functioning. Alterations of such scaling have been reported in several pathologies, but whether comparable alterations characterize the temporal organization of language remains largely unexplored. We address this question in the domain of psychosis, where language anomalies are pervasively documented. Specifically, we apply detrended fluctuation analysis (DFA) to quantify temporal scaling in Qwen3-derived continuous cosine similarity time series, capturing trajectories through semantic space computed from transcripts of picture descriptions across three independent datasets. DFA scaling exponents {\alpha} were extracted to characterize the strength of long-range temporal correlations. Across all datasets, patients exhibited significantly elevated {\alpha} relative to controls, indicating increased temporal persistence in semantic fluctuations. This analysis opens a window into the multi-timescale organization of meaning as it unfolds in discourse and reveals a signature of altered temporal scaling. This alteration parallels known departures from critical scaling in brain dynamics in psychosis, suggesting the exploration of possible links between these two.

In this article, we define and study the statistical physics of planar Carrollian systems. While it has been shown recently that, for general dimensions, the Carroll limit of Poincaré statistical physics typically does not converge, we show that thanks to the central extensions of the Carroll algebra in the plane, and by considering systems with angular momentum, there exists a well defined notion of planar Carrollian statistical physics. Using Souriau's geometric thermodynamics, we compute the partition function for particles on a uniformly rotating disc, and show that rotation is inevitable for thermal equilibrium of planar Carroll systems, with one of the central charges determining the direction of rotation. We derive thermodynamic quantities in particular entropy, which scales logarithmically with the disc area, and pressure, which follows the two-dimensional ideal gas law. Though all results are obtained from symmetry considerations, we also derive the corresponding effective Hamiltonian.

Advances in gravitational-wave detector sensitivity have increased the rate of transient signal detections, demanding faster automated analysis. We extend MaxWave, a fast maximum likelihood wavelet reconstruction algorithm, to perform coherent multi-detector signal reconstruction and glitch rejection. We coherently search for a common set of wavelets modeling the signal in all detectors. Multi-detector data are aligned using z-statistic time and phase offsets and amplitude scalings relative to the dominant reconstruction, as well as adaptive noise weightings derived from a geometrically averaged noise spectrum. By aligning and weighting individual detectors, we form a synthetic detector that amplifies non-Gaussian features, down-weights noisy detectors, and preserves Gaussian noise statistics. We extract the coherent signal using this synthetic detector, improving sensitivity to weak events while rejecting coincident glitches that lack consistent phase and amplitude evolution. Our algorithm provides real-time, low-latency, model-independent signal reconstructions, safely denoises gravitational wave data without removing transient signals, and can complement existing burst search and reconstruction frameworks through a fundamentally distinct approach, strengthening detection confidence and improving sensitivity to diverse signal morphologies.

The classic Rytova-Keldysh potential describes the non-local dielectric screening of Coulomb interactions in ultrathin two-dimensional (2D) materials. Recently, the corresponding potential for arbitrary in-plane anisotropy was derived in integral form, with numerical studies suggesting that an effective isotropic approximation remains robust for highly directional systems. In this paper we provide the analytical foundation for these observations by mapping the complete spatial landscape of the strongly anisotropic Rytova-Keldysh interaction. By applying the method of steepest descent and momentum-space coordinate scaling to the exact one-dimensional integral representation, we derive closed-form asymptotic expressions for the potential across all spatial regimes. We find that the intermediate-range screening exhibits a non-trivial amplitude scaling driven by the direction of weakest polarizability, while the short-range limit produces an anisotropic logarithmic well governed by the geometric mean of the principal polarizabilities. Finally, utilizing this short-range confinement, we implement an anisotropic Gaussian variational ansatz to solve the Wannier equation, providing a closed-form analytical expression for the exciton ground-state binding energy that explicitly captures the competition between the effective mass and dielectric tensors.

We investigate the interplay between spin-density-wave (SDW) order and superconductivity in the bilayer nickelate La$_3$Ni$_2$O$_7$ using the functional renormalization group~(fRG) applied to multiorbital weak-coupling models of both the ambient- and high-pressure crystal structures. As Hund's coupling increases, the leading instability evolves from superconductivity to an SDW state with ordering vector $\mathbf{Q}_1 \approx (\pi/2,\pi/2)$ (equivalently $\mathbf{Q}_Y \approx (0,\pi)$ in the orthorhombic $Amam$ unit cell), in agreement with experimental observations. Surprisingly, the ambient- and high-pressure structures exhibit nearly identical non-interacting susceptibilities and leading fRG instabilities, indicating that the emergence of superconductivity under pressure cannot be explained solely by changes in the low-energy electronic structure. Instead, our results identify the suppression of orthorhombicity as a key ingredient for superconductivity. As the system approaches the tetragonal limit, symmetry-related SDW fluctuations become nearly degenerate, frustrating long-range magnetic order while enhancing pairing interactions. These findings highlight lattice symmetry as a central tuning parameter of the competing ordered states in bilayer nickelates and suggest that reducing orthorhombicity through uniaxial strain could stabilize bulk superconductivity already at ambient pressure.

We investigate timelike geodesics and gravitational wave signatures of periodic motion around a static magnetically charged black hole arising from nonlinear electrodynamics and immersed in a quintessence background. We analyze the effective potential for massive particles, determine the marginally bound and innermost stable circular orbits, and classify the resulting bound trajectories using the zoom-whirl taxonomy $(\mathit{z},\mathit{w},\mathit{v})$. We show that the quintessence parameter $c_q$ systematically shifts the orbital radii, conserved quantities, and turning-point structure associated with representative periodic families. We then model the gravitational radiation emitted by periodic extreme-mass-ratio inspirals within the numerical kludge approximation. The resulting waveforms exhibit the characteristic burst-like structure of zoom-whirl motion, while variations in the quintessence coupling parameter modify the phase evolution, burst timing, and harmonic content of the signal. The corresponding Fourier spectra display a discrete comb-like structure, and the characteristic strain is concentrated in the millihertz band relevant for space-based detectors such as LISA. These results indicate that a quintessence background can leave systematic imprints on periodic orbit dynamics and on the associated time and frequency-domain gravitational wave observables.

We develop a second-quantization framework for photons based on the optical Dirac equation of source-free Maxwell theory in generic media. In this formulation, the electromagnetic field is recast as a four-component spinor-like wave function that admits both positive-energy and negative-energy solutions, which are naturally interpreted as photon and antiphoton states. By expanding the field in terms of single-photon eigenmodes, we construct a consistent quantization scheme in which the photon field operators obey bosonic commutation relations, in close analogy with the Dirac quantization of electrons. In structured media, the optical Dirac equation acquires effective mass and coupling terms induced by the dielectric tensor, analogous to an electronic Dirac-type structure. This allows photon propagation in media to be interpreted in terms of boosted spinor states and provides a unified description of vacuum and medium-modified dispersion relations. The framework further reveals a natural quantum-mechanical origin of transverse spin in structured electromagnetic fields, including evanescent waves, where spin components perpendicular to the propagation direction emerge from the underlying helicity structure. In the context of optical Dirac theory, this work presents a quantum field-theoretic description of photons in both vacuum and media, offering a new perspective on photon quantization, spin-orbit interaction, and light-matter coupling in structured optical systems.

The assembly history of the central regions of disc galaxies is regulated by dynamical processes that trigger gas infall events, leading to active star formation in nuclear stellar discs (NSD) and in nuclear stellar clusters (NSC). In the Milky Way, recent studies of its nuclear regions have revealed a complex star formation history (SFH), with an initial burst associated to the formation of the Galactic bar, followed by a non-constant star formation rate. In this work, we aim to study the formation and evolution of nuclear structures and their link with the formation of large-scale structures. Our goal is to investigate the effects of the bar and spiral arms on the gas dynamics and, as a result on the SFH of NSDs and NSCs. We run a simulation of an isolated Milky Way-like galaxy with the SWIFT N-Body+hydro simulation code, including star formation and stellar feedback from SNIa & SNII. We start from a live DM halo and a pre-existing stellar & gaseous disc with 20% gas fraction, which form a bar, a boxy/peanut bulge, spiral arms and nuclear structures. We study the SFH of these regions and how they relate to variations in the bar length, strength and pattern speed. We investigate the role of spiral arms and their interaction with the bar. We find that the SFH of the nuclear regions display a main burst at bar formation time, due to bar-driven gas inflows. After bar formation, we find secondary periodic formation bursts, that do not appear in the disc SFH. These bursts occur when the spiral arms and the bar, rotating at different pattern speeds, reconnect, triggering secondary gas inflow events. The interaction of spiral arms and the galactic bar can enhance non-axisymmetric features in the disc, triggering bar-driven gas infall even after the bar has formed. These bar-spiral reconnection events are imprinted into the SFH of the NSCs and NSDs as episodic star formation bursts.

Transverse emittance is one of the central figures of merit for charged-particle beams because it connects the microscopic phase-space distribution to macroscopic accelerator performance. This report introduces the trace-space description of emittance, relates it to the Courant-Snyder formalism and the second-moment beam matrix, and then follows the experimental logic behind common diagnostics. Emphasis is placed on how profile measurements, masks, drifts, quadrupole scans, and transverse deflecting structures convert otherwise inaccessible angular or slice information into measurable beam sizes.

Frustrated magnets host strong quantum fluctuations that can suppress conventional magnetic order and give rise to exotic quantum phases such as spin liquids. In some cases, however, quantum fluctuations lift classical degeneracies and stabilize ordered states via an order-by-quantum-disorder mechanism. The spin-7/2 honeycomb antiferromagnet GdZnPO has recently been proposed as a spiral spin-liquid candidate arising from cooperative fluctuations among a subextensively degenerate manifold of spiral states. Here, we investigate the local magnetization and spin dynamics in GdZnPO using nuclear magnetic resonance. In an intermediate field regime between $\sim$3 T and the saturation field ($\sim$12 T), we observe a spatially uniform magnetization and persistent low-energy spin dynamics down to 0.033 K, with no detectable symmetry breaking, providing spectroscopic evidence for a spin-liquid state. At lower fields below $\sim$3 T, a weak stripe order emerges below $\sim$0.25 K; however, strong fluctuations persist, as indicated by a nearly temperature-independent and unusually large spin-lattice relaxation rate in the low-temperature limit. Our results demonstrate that spin-7/2 quantization weakly lifts the spiral degeneracy, stabilizing subtle magnetic order while preserving robust dynamics and spin-liquid phenomenology. These findings establish GdZnPO as a promising platform for exploring spin liquids in high-spin frustrated magnets down to the lowest accessible temperatures.

The upcoming launch of the PLATO mission will open a new area of exoplanetary research by probing transiting exoplanets at long orbital periods around bright stars. These planets will be amenable to follow-up observations, especially with the ESO telescopes as the first PLATO field is in the southern sky. In this paper we listed the lessons we learned by monitoring the bright HIP41378 multi-planetary system over one decade via both radial-velocity and transit observations. These lessons are important for the follow-up strategy of PLATO transiting exoplanets.

Powder spreading and layer deposition are fundamental stages of Powder Bed Fusion (PBF) technologies and play a critical role in determining process stability and final component quality. This chapter examines the mechanisms governing powder-bed formation, highlighting the interactions between powder characteristics, process parameters, and machine architecture. Particular attention is devoted to the influence of particle size distribution, morphology, cohesion, flowability, layer thickness, recoater velocity, and environmental conditions on powder-bed quality. The resulting powder-bed is discussed as a process state variable whose characteristics, including packing density, surface coverage, effective layer thickness, and spatial homogeneity, directly affect energy absorption, melt-pool stability, defect formation, and mechanical performance. The chapter also reviews the application of the Discrete Element Method (DEM) for modelling powder spreading phenomena and quantifying powder-bed quality metrics. Finally, the role of powder reuse, lifecycle management, and future developments involving process monitoring, digital twins, and data-driven optimization strategies is discussed, emphasizing the growing importance of powder engineering in advanced metal additive manufacturing.

Cross-correlation searches for gravitational-wave backgrounds depend on the geometrical configuration (physical separation and relative orientation) of the detectors comprising the network. Applying standard techniques to a few simple examples, we illustrate how the relative orientation of a pair of Earth-based L-shaped laser interferometers can drastically impact the detectability of both isotropic and anisotropic gravitational-wave backgrounds.

Efficient sampling of the Boltzmann distribution in frustrated spin glasses is central to statistical mechanics and combinatorial optimization. Despite advances in machine-learning-based approaches, two issues persist: limited understanding of why variational models fail to benefit from increased scale, unlike the monotonic scaling law of large language models; and high computational cost on large systems that negates advantages over classical sampling methods. Here, we develop a physics-inspired transformer with interpretable sparse attention and spin-tailored positional embeddings to address these challenges. By further leveraging FlashAttention for parallel ancestral sampling, it achieves up to two orders of magnitude speedup over vanilla variational autoregressive networks, enabling neural-network simulations of spin-glass systems to unprecedented sizes on a single GPU. It can resolve full probability distributions, free energies, and overlap statistics across temperatures, for Sherrington-Kirkpatrick and 2D or 3D Edwards-Anderson models, where existing machine-learning methods encounter limitations at certain temperatures. This framework thus establishes a scalable paradigm for frustrated spin-glass systems.

Reversible control of crystal symmetry offers a powerful route to programmable optical functionality. However, achieving solid-state bistability between centrosymmetric and non-centrosymmetric crystalline phases remains a formidable challenge; examples of materials that enable stable switching of second-order nonlinear optical (NLO) responses are exceptionally rare. Here we report a solar-powered, symmetry-bistable organic material based on the photoisomerizable molecule (E/Z)-2-(4-(4-bromophenyl)thiazol-2-yl)-3-(4- (dimethylamino)phenyl)acrylonitrile (E/Z-BTDPA). The crystallizable E- and Z-isomers adopt distinct molecular packing arrangements that reversibly toggle between these states, controlling second-order NLO activity. The E-form exhibits strong second-harmonic generation (SHG), whereas the Z-form is SHG-inactive and displays twophoton luminescence. This bistable behavior is retained in flexible thin films, where sunlight-driven photoisomerization enables reversible photoswitching of the second-order electric susceptibility (ḩi} 2), large-area optical patterning, and real-time NLO communication via waveform generation and text-string transcription at telecommunication wavelengths. This sustainable strategy bypasses rigid inorganic architectures, establishing photoinduced symmetry bistability as a scalable paradigm for all-optical computing and advanced communication networks.

The Laser Interferometer Space Antenna (LISA) is a space-based gravitational-wave observatory that uses free-falling test masses as inertial references to detect milliHertz frequency signals. Interactions between test masses and galactic or solar energetic particles cause charge buildup and Coulomb forces, source of acceleration noise that must be accurately modeled. LISA Pathfinder measurements showed that the Poissonian test mass charging noise was considerably larger than that in pre launch simulations, indicating missing physical processes in early models. Emission of low energy secondary electrons (LEE) from test mass and housing surfaces has been proposed as a key mechanism affecting charging and the sensor electrostatic response. We report a particle accelerator based experiment that directly tests the LEE hypothesis by measuring proton induced test mass charging in a LISA like Gravitational Reference Sensor geometry as a function of the test mass electrostatic potential.

Predicting the behavior of dynamical systems (DS) beyond the dynamical and parameter regimes observed in training is a pivotal and essentially unresolved problem in scientific ML. It is central to any good scientific theory, which we expect to be able to make predictions about regimes not covered by currently available data. Recent hierarchical and hyper-network guided approaches for DS reconstruction (DSR) enable training on many DS simultaneously, and revealed that extracted latent features are often related to crucial control parameters of the underlying DS that varied across the training corpus. However, true out-of-domain forecasting abilities of these models, e.g., across tipping points, remain limited, and fine-tuning, or even full model retraining, on time series from the new dynamical regime is usually required. Here, we mathematically analyze the root of these limitations in previous model formulations and identify three core shortcomings rooted in a mismatch between structural assumptions of the reconstruction model and typical properties of physical systems. We propose a combination of remedies for these shortcomings, most importantly feature splitting, and furthermore derive a closed-form bound on the reliable extrapolation range. We demonstrate empirically that our techniques allow for accurate zero-shot prediction into new dynamical regimes, outside the observed training regime, as, e.g., encountered across tipping points.

BB84 quantum key distribution derives its security from a physical guarantee that any eavesdropper disturbs the channel in a statistically detectable way. Prior work evaluates this by assuming Eve attacks at a fixed, analytically optimized rate. We examine what happens when Eve is modeled instead as a learning agent. Classical reinforcement learning is used, specifically tabular Q-Learning, SARSA, and Double Q-Learning, to adaptive BB84 eavesdropping. This formulates the attacker's decision as a Markov Decision Process where the agent observes Quantum Bit Error Rate (QBER) feedback and decides, qubit by qubit, whether to intercept or pass. Experiments span three channel noise levels ($\mu_{ch}\in\{1\%,3\%,5\%\}$) and are validated across five independent random seeds (45 training runs per condition, 10,000 episodes each). Against the best non-adaptive analytical baseline, Q-Learning reduces detection from $99.4\%$ to $0.28\%\pm0.27\%$ at $\mu_{ch}=1\%$ while extracting approximately 10.5 correct bits per episode. This is a 355-fold reduction that is statistically significant ($p=0.020$, Mann-Whitney $U$ test). We also report the spontaneous emergence of an end-game burst, where agents independently learn to surge their attack rate at the final block. This exploit vanishes under randomized checkpoint intervals while stealth performance remains statistically indistinguishable. These results motivate the inclusion of adaptive adversary baselines in quantum cryptographic security evaluations.

We introduce and study compatible Lie conformal bialgebras as conformal counterparts of compatible Lie bialgebras. Such a structure consists of two compatible Lie conformal brackets and two compatible conformal cobrackets on the same $\C[\partial]$-module, and every simultaneous linear combination of them is again a Lie conformal bialgebra. We develop representations and matched pairs for compatible Lie conformal algebras, introduce compatible Lie conformal coalgebras, and establish their duality through the conformal dual in the finite case. For $\C[\p]$-modules that are free of finite rank, we prove the equivalence among compatible Lie conformal bialgebras, standard compatible conformal Manin triples and matched pairs. In the coboundary case, we characterize the tensors $r$ that determine compatible Lie conformal bialgebras. The characterization requires the symmetric part of $r$ to be invariant with respect to both brackets and three conformal Yang–Baxter conditions to hold. The first two conditions correspond to the two brackets separately, whereas the third is the compatible conformal Yang–Baxter condition. For comparison, we introduce the compatible conformal classical Yang–Baxter equation (CYBE) and show that each of its solutions satisfies these three conditions, while the converse fails. One explicit example shows that the first two conditions do not imply the third. Another shows that all three conformal Yang-Baxter conditions may hold even though $r$ is not a solution of compatible conformal CYBE.

Nuclei charge radii play an essential role in understanding the fundamental interactions of finite quantum fermion systems. In this work, input-driven Bayesian neural network based on the Monte Carlo dropout approach has been built to characterize the systematic evolution of charge radii of nuclei with proton number $Z\geq20$ and mass number $A\geq40$. The motivated underlying mechanisms have been introduced into the input structures, which contain pairing effect, isospin asymmetry degree, the correlations between the valence nucleons and valence holes for neutron and proton, quadrupole deformation parameter $\beta_{20}$, and the local shape staggering phenomena of $^{181,183,185}$Hg isotopes.In addition, shell quenching effect is also taken into account by incorporating the modified Casten factor $P^{*}$ into the input structure. The quadrupole deformation parameters $\beta_{20}$ derived from finite-range droplet model (FRDM), relativistic mean field (RMF) theory and Weizsäcker-Skyrme (WS) approach are employed to analyze the local variations of nuclear charge radii.The hyperparameter is adjusted automatically in the constructed model.The calibrated results give comparable root-mean-square deviations (RMSD) in the training and validation sets with various shape deformation inputs. The abrupt increase in charge radii around N=60 is well reproduced along Z=37-40 isotopic chains, but this trend is less pronounced along Z=36 and 41 chains. This provides a indicator to confirm the rapid shape-phase transition regions around N=60 from the perspective of finite nuclei size. Shell quenching effect of charge radii along the bismuth isotopes are reproduced well at N=126, but slight deviations can be encountered due to the absence of high-order octupole deformation around N=130 regions and shape-staggering phenomena toward neutron-deficient regions, respectively. This means that...

Nested sampling is a Monte Carlo algorithm for posterior estimation and Bayesian model comparison. It maintains a population of $K$ live points sampled from the prior, and at each iteration discards the lowest-likelihood point and replaces it with a new sample drawn from the prior restricted to exceed the discarded likelihood. Achieving this likelihood-restricted prior sampling efficiently and reliably is the central computational challenge. For low-to-moderate dimensional problems, MLFriends is a general and robust region-based approach that constructs a proposal region by bootstrap aggregation over the current live points and rejects proposals outside this region. We present a self-contained mathematical formulation of MLFriends and derive, under a homogeneous Binomial point process model for the live points, heuristic bounds on the expected fraction of the likelihood-restricted prior not covered by the proposal region. These bounds decay as $(\frac{1}{3}Km)^{-3/2}$, where $m$ is the number of bootstrap rounds, and are negligibly small for practical parameter choices. We show heuristically that the resulting bias in the marginal likelihood estimate is negligible compared to the inherent statistical variance of a nested sampling run. While a fully rigorous treatment remains an open problem, these results provide the first analytical characterisation of a fully specified and practically implementable nested sampling algorithm, without assuming an idealised or asymptotic sampling procedure.

Nested Sampling is a Monte Carlo algorithm enabling posterior estimation and Bayesian model comparison, and is especially robust in multi-modal posteriors. This is because nested sampling maintains a population of live points sampled from the entire prior. In each iteration, the population is advanced above a likelihood threshold, potentially discarding modes ruled out by the data. However, the Monte Carlo nature of point replenishment can also accidentally discard a mode. We draw a connection to the neutral Moran process in genetics, and quantify the occurrence probability of this failure mode of nested sampling with a simple symmetric random walk model on the live point occupancy. We find a simple rule for setting the minimum number of live points so that mode die-out is made unlikely.