Papers

Detector observables pose a fundamental challenge for nonperturbative lattice methods due to their intrinsically real-time and asymptotic nature. We propose quantum simulation platforms as an ideal setting for studying these observables. Using quantum spin systems as a demonstration, we construct lattice detector operators and establish their connection to continuum energy-flow observables. We demonstrate this framework in the $1+1$-dimensional quantum Ising model, where finite lattice calculations show quantitative agreement with conformal field theory expectations at criticality. These results support the interpretation of the lattice flow operators as regulated counterparts of continuum detectors in the scaling and asymptotic limits, providing a concrete route toward realizing high-energy collider physics on table-top quantum platforms.

Using thermal analyticity, we derive directional large-frequency bounds on the smooth functions entering full eigenstate thermalization in continuum quantum field theory. The strongest directions reproduce the scales previously identified for lattice systems, while the complete analyticity domain reveals an asymmetric multifrequency structure. Thermal conformal correlators saturate the second- and third-order bounds, and the leading gravitational Regge contribution saturates the strongest fourth-order direction.

We study how morphology relates to environment from massive to dwarf galaxies using, for the first time, a mass-complete sample of ~13,000 galaxies, in the stellar-mass and redshift ranges 10^8 MSun < Mstar < 10^11.5 MSun and 0.2<z<0.4, respectively. By combining HST-derived visual morphological classifications with local density and galaxy distances from nodes and filaments, we quantify how early-type and late-type galaxies (ETGs and LTGs) differ with respect to environment. The overall ETG fraction decreases from ~65 per cent at Mstar ~ 10^11 MSun to ~20 per cent at Mstar ~ 10^8 MSun. Regardless of morphology, lower stellar mass galaxies lie further away from nodes and filaments than their more massive counterparts. While, at Mstar > 10^9 MSun, ETGs reside further away from nodes and filaments than LTGs, this segregation weakens as stellar mass decreases, with ETGs and LTGs exhibiting similar locations at Mstar < 10^9 MSun. This diminishing difference at lower stellar mass is likely driven by the fact that filaments have a finite extent and lower mass galaxies, of all morphologies, lie further away from filament cores and are therefore confined to a smaller region of the filament itself. For high-mass galaxies (where ETGs and LTGs show strong environmental segregation), greater proximity to nodes likely inhibits coherent angular momentum acquisition, while residing closer to filament cores increases the likelihood of interactions and mergers. Both make it easier to create dispersion-dominated systems, driving the sharp rise of the ETG fraction, in the high-mass regime, close to nodes (and, to a lesser extent) filaments. Our results show that galaxy evolution is increasingly driven by internal processes as stellar mass decreases.

Hard X-rays in persistent magnetar emission originate from radiative processes in pair-loaded magnetospheric plasma, yet self-consistent kinetic simulations of such radiation-rich systems remain limited. We perform 1D particle-in-cell simulations of pair creation mediated by resonant inverse Compton scattering (RICS) along isolated field lines in twisted magnetospheres, capturing particle acceleration and radiative drag from first principles. The drag force, which strongly depends on the particle Lorentz factor and location, plays a key role in the magnetospheric circuit. Strong RICS drag impedes the flow of electrons and positrons, particularly along extended field lines. Nevertheless, the plasma sustains the circuit by self-organizing into a single accelerating gap near the star in one hemisphere. The accelerated plasma flow from the gap becomes loaded with copious electron-positron pairs in extended RICS zones, and also carries ions extracted from the star and accelerated in the gap. When radiative drag stops the pair-loaded flow at the magnetic equator, the ion component transfers momentum through streaming instabilities, delivering a small lepton population into the opposite hemisphere and sustaining the circuit. The gap confined to a single (anode) hemisphere implies asymmetric hard X-ray production, possibly detectable in phase-resolved magnetar spectra.

We develop a method for numerically computing higher genus CFT correlators and string amplitudes based on Kontsevich's ribbon graph parametrization of the moduli space $\mathcal{M}_{g,n}$ of punctured Riemann surfaces. Using this method, we compute the compact boson partition function up to genus 6 as well as the moduli space integrand for bosonic string vacuum amplitudes up to genus 3. Our results pass a number of nontrivial numerical checks. In particular, the moduli space integrand of bosonic string amplitudes reproduce the Igusa cusp forms at genera 2 and 3.

Weakly supervised anomaly detection has been shown to be an effective tool for model-agnostic searches for new physics, especially in the context of resonance searches. However, correlations between the anomaly score and the resonant mass can distort the background distribution after selecting on the anomaly score, complicating background estimation from the sidebands. To mitigate this background sculpting, we propose a domain-adaptation-based decorrelation of the anomaly score from the resonant mass. We study this approach using the LHC Olympics R&D data set and several weakly supervised anomaly detection methods. We find that domain adaptation can substantially reduce background sculpting while largely preserving the anomaly detection performance. When correlations between the input features and the resonant mass degrade the original method's performance, domain adaptation can also recover sensitivity.

We present the public release of OpenGadget3 (OG3), a substantially extended and re-organised version of the widely used Gadget-2/3 family of cosmological simulation codes. Since G2 was made publicly available, the absence of continued official development led to the creation of numerous, mutually incompatible developer versions of G3 across the community. This made it effectively impossible to track bug fixes, reproduce published results, or consistently credit the many individual contributors. OG3 addresses this by consolidating these disparate developments into a single, documented, and continuously maintained code base, released under the GNU GPLv3 through a GitLab repository (with an accompanying wiki), regularly synchronised with the active developer branch, and supported by a dedicated continuous-integration (CI) pipeline. OG3 retains the core algorithmic backbone of its predecessors, a Barnes&Hut oct-tree combined with a Particle-Mesh method for gravity, and a choice of Smoothed Particle Hydrodynamics or Meshless-Finite-Mass solvers for gas dynamics, within a hybrid MPI/OpenMP parallelisation framework, extended with GPU offloading via OpenACC and OpenMP. The code integrates an extensive suite of sub-resolution and physical modules, including primordial chemistry, radiative cooling, star formation, stellar feedback and chemical enrichment, dust formation and evolution, black hole growth and AGN feedback, MHD, thermal conduction, physical viscosity, SIDM, and massive neutrinos. OG3 introduces new features improving robustness, reproducibility, and usability: a flexible mixed-precision framework spanning 16- to 128-bit representations; expert-level tagged parameters with restart-time change log; extensive consistency checks against invalid configurations; and FAIR-compliant reporting of all settings, parameters, and specific publications. (shortened and abridged)

Starting from a general Hamiltonian describing the quantum dynamics of probe particles interacting with a set of environment degrees of freedom, we derive the quantum master equation with which the reduced density matrix of a probe particle evolves, the general equilibration condition that they satisfy when the environment is prepared in a thermal state – encoded in a KMS property for line operators extended in real time – and the Langevin description that emerges. The novelty of our results resides in their generality: We do not assume a specific form of the environment self-coupling, of the environment operator that couples the particle to it, of the statistics of its correlation functions, whether the statistics of the momentum transfer is Gaussian or not, or whether the probe particles move relativistically. Our results only require that spacetime translations, parity and time reversal be symmetries of the Hamiltonian, and that there exists a separation of scales between those characterizing the dispersion relation of the probe particle and those of the environment. We also discuss the limiting case in which Gaussian Brownian motion emerges. Overall, our results constitute a first-principles derivation of what properties of the underlying quantum field theory govern the energy loss and momentum fluctuations of probe particles.

Noether charges in gravity are always defined with respect to a reference metric, but the near-horizon extremal Kerr (NHEK) solution does not come with an obvious choice of reference metric (it is not asymptotically flat, for example). We discuss a one parameter generalization of the NHEK solution due to Kinnersley and Kelley which interpolates between NHEK and an analytically continued version of Minkowski spacetime. We use this interpolating family of solutions to compute the conformal energy of NHEK above the Minkowski reference metric. We find an interesting order of limits issue when computing the conformal energy of the Minkowski vacuum and we discuss a few natural prescriptions for fixing it, including one motivated by the Kerr/CFT correspondence.

This thesis develops robust and efficient AI frameworks for accelerating crystalline materials discovery by addressing both major stages of the materials-design pipeline: crystal property prediction and crystal structure generation. Motivated by the high computational cost of Density Functional Theory (DFT) and the limited availability of labeled materials data, the thesis explores graph representation learning, pretraining, multimodal learning, and generative modeling for scalable materials design. For property prediction, the thesis first introduces CrysXPP, which learns transferable crystal representations through unsupervised graph autoencoding, reducing dependence on large property-labeled datasets. It then proposes CrysGNN, a large-scale self-supervised graph pretraining framework that captures atomic connectivity, chemical attributes, and global structural information and transfers this knowledge to downstream property predictors through knowledge distillation. CrysMMNet further enriches crystal representations by jointly modeling graph structure and textual descriptions, thereby incorporating both local chemical and global structural knowledge. For crystal generation, the thesis introduces TGDMat, a text-guided joint diffusion framework that jointly models lattice parameters, atomic types, and atomic coordinates while incorporating textual structural knowledge during denoising. This enables the generation of more valid and stable periodic materials while also supporting conditional generation from natural-language descriptions. Overall, the thesis establishes a unified AI-based framework for data-efficient property prediction and controllable crystal generation, demonstrating how graph learning, multimodal representations, and generative models can reduce computational cost and improve the scalability of materials

Domain-specialized language models are widely used for scientific question answering, but stronger general-purpose systems raise a sharper question: when does domain-specific fine-tuning remain valuable for open-ended scientific reasoning? We study this in astronomy with a curated QA benchmark from publicly available 2017–2026 Olympiad-style materials. The free-response subset contains 300 questions, including 204 text-only and 96 image-linked examples. We compare open-weight and API-served general-purpose, multimodal, and astronomy-specialized models using judge-based correctness and complementary reference metrics. Strong general-purpose models establish the highest correctness baseline in this testbed, while analyses of metric agreement, judge sensitivity, benchmark composition, and modality reveal variation not captured by a single leaderboard. These results motivate treating domain specialization as a task- and deployment-dependent property and highlight the role of domain-specific evaluation in determining which models, capabilities, and evaluation criteria are appropriate for scientific workflows.

Late-time cosmic acceleration is conventionally ascribed to a cosmological constant, though $\Lambda$CDM continues to face several theoretical difficulties that keep alternative gravity models under active consideration. This work examines the Hu-Sawicki $f(R)$ model in a spatially non-flat background, with the modified-gravity parameter $b$ and the curvature density $\Omega_k$ both treated as free parameters, constrained using DESI-DR2 BAO, BBN, and four Type Ia supernova compilations – PantheonPlus, PantheonPlus+SH0ES, Union3, and DESY5yr. Across all four combinations, $H_0$ and $\Omega_m$ stay close to their $\Lambda$CDM values, with a noticeable shift in $H_0$ appearing only for the SH0ES-calibrated dataset. The parameter $b$ departs from zero at better than $2\sigma$ in three of the four fits, most prominently for DESY5yr, whereas the SH0ES-calibrated combination alone prefers $b<0$. A strong positive correlation among $b$, $H_0$, and $\Omega_k$ underlies this shift, suggesting that curvature signatures obtained under $\Lambda$CDM can be reabsorbed into the modified-gravity sector once this additional freedom is allowed. Statistical model comparison via AIC and BIC gives a mixed picture: AIC leans toward the Hu-Sawicki model in three of the four combinations, while BIC's heavier penalty on the extra parameter favors $\Lambda$CDM in most cases, and only DESY5yr is preferred under both criteria. These findings show that the Hu-Sawicki $f(R)$ scenario with unconstrained curvature is nonetheless a statistically feasible, if not obviously preferred, alternative to $\Lambda$CDM, and that curvature restrictions generated inside $\Lambda$CDM cannot be viewed as independent of the underlying gravity model.

The finite-time blow-up construction for the forced Navier-Stokes equations released by OpenAI in Sep. 2026 (OpenAI 2026) has as its object an axisymmetric swirl core in anisotropic similarity variables. Its geometry is that of an exact steady swirl between rotating porous cylinders found by Gumerov and Duraiswami in 1998 (GD1998). We find that the GD1998 boundary value problem does not recast into the similarity variables and that its generalization is a two-dimensional profile problem between porous walls held at fixed similarity radii, second order in the radial variable X and first order in the time-like axial variable $\eta$. We solve it by tensor Chebyshev collocation with a pinned pressure gauge, complex-step Newton and arclength continuation, verify it three ways, and sweep the radial Reynolds number, the wall swirl and a symmetry-breaking datum. Below inflow 9 the solution is one smooth branch; above it the symmetric branch folds at a critical swirl $F^*=0.41V_0^2$. The Dirichlet axis problem has no resolution-stable solution; the core must be a Cauchy problem from the axis. Its moment identities cannot be met by a core symmetric about the dividing plane: the core is an axial through-flow, as its authors chose it; a non-symmetric core meets them to 0.2%. The cone condition is Rayleigh's criterion with axial shear and requires radii of order $10^{20}$. Dynamic rescaling shows the profile to be an attractor at weak inflow and toward the fold, a saddle-node; at moderate inflow and strong swirl the spectrum does not converge in the axial resolution and is left open. A real fluid cavitates (water) or shocks (air) first; the GD1998 chamber is proposed as the experiment. Nothing found suggests the mechanism is reachable in a flow one computes or builds; the forced theorem, and this study, leave the unforced equations of practice as they were. Code, tests and log accompany the paper.

This is the set of lecture notes for the PhD course \href{https://www.unibz.it/en/faculties/engineering/phd-computer-science/study-course-offering/2025/36967}{Physics Informed Neural Network, held at the University of Bozen/Bolzano} in the academic year 2025/2026. The goal of the course was to introduce the concept of Physics Informed Deep Neural Networks (PINN) and Neural Operators (NOs), discuss their implementation from scratch in PyTorch and using advanced ad-hoc developed open-source libraries such as NVIDia PhysicsNeMo to address real-world problems in various fields (engineering, physics, petroleum reservoir). We discuss recent topics such as Mixture-of-Models, Fourier Neural Operators, Physics-Informed Kolmogorov-Arnold Networks (PIKANs) and Fourier Neural Operators.

Wide-field spectral-line imaging with modern radio interferometers remains challenging when the emission is extended, multiscale, and distributed over many overlapping pointings. Accurate reconstruction requires joint treatment of the calibrated visibilities, control of image-domain regularity, and recovery of missing short spacings from single-dish data. We present IViS (Interferometric Visibility-domain Inversion Software), a GPU-accelerated Python framework for visibility-domain joint deconvolution, and assess its performance for wide-field HI imaging with the Australian Square Kilometre Array Pathfinder (ASKAP). The current model, Classic3D, reconstructs a non-parametric sky cube directly from calibrated visibilities by minimizing a regularized least-squares criterion. The forward model relies on a non-uniform fast Fourier transform (NUFFT), supports joint deconvolution across mosaic pointings and positivity constraints, and can incorporate single-dish data through a fusion term. We validate the method using point-source, noise-only, and multiscale diffuse-emission simulations, and apply it to ASKAP observations toward the Large Magellanic Cloud (LMC). The simulations show that IViS recovers point-source flux accurately without regularization and that regularization sets the trade-off between noise suppression and effective resolution. Joint deconvolution can recover more large-scale power than linear mosaicking of independently deconvolved pointings. With single-dish information, the reconstructed power spectra closely reproduce the input sky statistics. Applied to ASKAP data, IViS yields 10h mosaics with an effective resolution of 22” and reduced residual side-lobe structure. Compared with ASKAPSoft multi-scale CLEAN for a single observing block, Classic3D exhibits fewer residual side-lobes and recovers substantially more power at low spatial frequencies.

It is shown that the second-order Carleman truncation (C2) captures the steady state of the decaying forced logistic with second-order accuracy in the forcing parameter, provided such forcing remains below a critical value of 1/2. We then investigate the extension of these results to spatially extended systems by means of Carleman Lattice Boltzmann simulations of a two-dimensional periodically forced flow. It is found that C2 correctly reproduces the low-Reynolds-number (between 1 and 10) quasi-linear dynamics, well above the critical value of the forced logistic equation. However, C2 fails to capture more complex steady states characterised by persistent vortical structures at Reynolds numbers around 20. Interestingly, the divergence observed in the latter case shows qualitative similarities with the runaway behaviour of the C2 linearization of the growing logistics, suggesting that suitable closures and/or change of variables may improve the convergence of the C2 procedure.

We study uniform high-frequency localization for the Laplacian on compact metric graphs through the least $L^2$-mass that eigenfunctions must place in a prescribed measurable observation set. We first identify this asymptotic localization constant with the minimum of a linear functional over the attainable edge-intensity set; in the generic standard-Kirchhoff setting, this set is governed by the regular Gauss image of the secular manifold. Primitive cycles and exterior-to-exterior paths consequently determine the positivity threshold, but not, in general, the positive numerical value. We introduce a boundary-aware singular-completion cone and prove that it contains all regular secular edge-energy vectors for trees, unicyclic graphs, and closed graphs of cycle rank two. We then construct a cycle-rank-two graph with two Dirichlet leaves for which this completion principle fails. An exact rational separator, combined with a validated Krawczyk enclosure, yields a nonsingular scalar secular state lying outside every boundary-compatible singular sector. A positive radial derivative identity and recurrence in the compact orbit closure convert this local separation into an exact high-frequency eigensequence for a single fixed metric. For a suitable measurable observation set, the true high-frequency localization constant $C_\infty(\omega;\ell)$ and its singular-completion counterpart $C_{\mathrm{sing}}(\omega;\ell)$ satisfy $$C_\infty(\omega;\ell)<1/2<C_{\mathrm{sing}}(\omega;\ell)$$. Thus, singular completion captures the quantitative localization geometry in several low-complexity classes but does not, in general, determine the high-frequency variational problem on a fixed quantum graph.

Population-level heterogeneities, combined with temporal fluctuations in sexual partnerships, shape the structure of sexual contact networks and can substantially influence the spread of sexually transmitted infections (STIs). Traditional static network models, which assume fixed attributes of partnerships, such as count and duration, may not adequately capture the effects of partnerships on STI transmission. In contrast, agent-based dynamic network models offer a flexible framework for incorporating individual and population-level heterogeneities. We developed an agent-based dynamic network model in which partnership formation and dissolution probabilities, stratified by age, sex, and sexual orientation (including bisexual individuals), govern the formation of monogamous and concurrent partnerships and their dissolution via a duration-dependent hazard. Partnership statistics from the National Survey of Sexual Attitudes and Lifestyles (NATSAL-3) were used as model calibration targets, and Latin Hypercube Sampling (LHS) was used to generate candidate parameter combinations. Parameter estimation was performed by selecting the combination that produced the lowest Mean Squared Error (MSE) between the model outputs and the calibration targets. Our study addresses three questions: (1) how well can the observed characteristics of sexual partnerships in NATSAL-3 be reproduced using an agent-based model; (2) how does concurrency shape the structure of dynamic sexual contact networks; and (3) how do concurrent partnerships affect the dynamics of STI transmission. In this study, we find that interactions between individual characteristics such as age, sex, and sexual orientation, and partnership attributes such as count, duration, and concurrency play a critical role in shaping the population-level sexual contact network and, in turn, the dynamics of STI transmission.

Galactic foregrounds represent a major contamination to the measurement of primordial $B$-modes from observations of the Cosmic Microwave Background polarisation. Even after the application of component separation algorithms, foreground residuals may potentially still bias the estimate of the tensor-to-scalar ratio $r$, causing a false detection. In this work, we present the methodology of a robustness test for the validation of an eventual detection of primordial $B$-modes, as obtained by a future, LiteBIRD-like satellite experiment. The goal of the test is to identify the foreground residuals contamination by looking for non-Gaussian properties in the CMB $B$-modes map, recovered through blind component separation algorithms. We adopt scattering transforms (ST) as our summary statistics sensitive to the non-Gaussian features of foreground residuals and to their correlation with foregrounds tracer maps. We characterise and validate the methodology on realistic sky simulations with different levels of foregrounds complexity. The proposed test is able to identify a bias on the tensor-to-scalar ratio of $\gtrsim 10^{-3}$ in $\sim 90\%$ of our simulations, with this bias value being of the same order of the accuracy targeted by LiteBIRD. Additionally, for our particular experimental configuration, the test is passed when the bias is lower than the sensitivity on the $r$ parameter, and no warning is raised. These results provide an important step forward in the development of statistical tools for validating future measurement of cosmological parameters, against foregrounds contamination.

The vanilla scotogenic model (VSM) featuring three right-handed neutrinos and an inert scalar doublet, offers a unified explanation of neutrino masses, dark matter (DM), and the baryon asymmetry of the Universe through leptogenesis. The typical mass scale of such a scenario lies in the vicinity of $\sim$ 10 TeV and above, whereas enhanced second-generation Yukawa couplings lower the leptogenesis scale to $\sim 1$ \TeV, allowing the model to be probed at the future muon colliders. Adhering to DM, neutrino mass, Leptogenesis, and flavour dependent constraints, the charged scalar is likely to be a long-lived particle (LLP). We analyse both the prompt and displaced vertex signatures of the model to find that, prompt mono-photon signals remain challenging, but LLP searches offer a promising avenue to probe such a framework, subject to the timing resolutions, and displaced-vertex reconstruction efficiency.

We obtain two families of neutral planar black branes in a potential-free dilaton-coupled Lovelock–Horndeski theory. Heterotic compactification relates higher-dimensional curvature to scalar dynamics and motivates the interaction structure. At fixed scalar zero mode, the horizon radius and temperature vary while the complete stationary Wald entropy remains constant and positive. The exponential scalar factor at the horizon exactly compensates the area growth, giving this behavior a direct geometric explanation. An exact coefficient analysis determines the two four-dimensional branches and their continuation to every higher dimension through closed coupling relations. The linear family is conformally flat and leaves the AdS scale free at fixed couplings; the fractional family is Weyl curved and fixes that scale. The common kinetic relation also excludes their realization through a real one-scalar flat-torus reduction of a metric–dilaton parent.

Traditionally, the disc is believed to evolve under the influence of turbulent viscosity, although the importance of this mechanism has recently been questioned. Alternatively, magnetic disc wind or gravitational instability could be considered, but which of these three mechanisms contributes the most at a given evolutionary stage remains an open question. We present global numerical hydrodynamic simulations of protoplanetary disc evolution in the thin-disc limit on disc lifetime timescales, including all three mechanisms of mass and angular momentum transport. We calculate the gravitational, viscous, and magnetic torques to assess the contribution of each mechanism. We found that these transport mechanisms occupy distinct zones of influence in the disc depending on the stage of evolution: the dominance of disc self-gravity during the early phase is replaced by the prevalence of magnetic disc wind and viscosity, with the latter being especially relevant at the disc periphery. We show that a noticeable decrease in disc mass occurs only after the termination of the embedded phase. The suppression of disc viscous spreading is achieved only for the most intense wind; otherwise, the disc continues to grow in size till the end of simulations. The spiral structure contributes to the temporary retention of dust in the disc. However, this is insufficient to prevent the depletion of dust on long timescales. The results emphasize the importance of a comprehensive approach to long-term simulations of protoplanetary discs with no single mechanism of mass and angular momentum transport regarded as exclusive.

Spherical p-spin models provide a mean-field framework for glassy dynamics. Coupling such systems opens a controlled way to probe how they evolve jointly, develop cross correlations, and possibly share common aging scales. We study spherical p-spin systems with site-independent inter-system couplings and generally correlated quenched disorders. We derive closed multi-subsystem two-time equations for correlations, responses, and spherical constraints. A marginal one-step replica-symmetry-breaking construction provides static benchmarks for overlap plateaux, aging crossover scales, and effective temperatures. We then specialize to two ferromagnetically coupled p=3 systems and compare dynamical data with marginal 1RSB predictions. Independent quenched disorders reduce the equal-time correlation between the systems below its disorder-free value, while correlated disorders enhance it. For sufficiently strong coupling, finite-time fluctuation-dissipation estimates within and between the systems are compatible with a common effective temperature even when one or both subsystems would equilibrate as a paramagnet in isolation. This common value lies above the effective temperatures that the constituent systems would have separately and increases with disorder correlation and coupling strength. The marginal 1RSB value T/m captures these trends but is slightly below the finite-time dynamical estimate. For weak coupling, the dynamical results instead suggest that two aging regimes develop for each system, with partial equilibration within each. We perform a marginal replica analysis with two-step breaking, whose predictions compare favorably with the numerical measurements. Our numerical accuracy is insufficient to determine whether the observed finite-time crossover will eventually become a sharp transition.

Consider a branching random walk (BRW) of depth $n$ with standard Gaussian increments, conditioned on all endpoints lying in an interval of radius $r$ (which may depend on $n$), i.e. a small ball event. We prove that this conditioning results in exponential decay of correlations between the endpoints, with correlation length $O(r)$. Our proof is based on the renormalization group, which in this context captures the effect of the endpoint conditioning on earlier steps in the walk. This effect can be separated into so-called relevant and irrelevant parts, and in our setting the relevant part makes the conditioned BRW behave like a branching Ornstein-Uhlenbeck walk for the first $n-O(r)$ steps, leading to the correlation decay. The irrelevant part shrinks in a nontrivial manner, and the simplest argument to bound it uniformly only yields correlation length $O(r^2)$. To achieve the optimal $O(r)$ bound, we establish that the irrelevant part shrinks horizontally in space before decaying uniformly. The BRW is a prototypical example of a log-correlated Gaussian field, and it forms the basis of many hierarchical field theories in the mathematical formulation of quantum field theory. As such, we present our results in a general form which is applicable to other hierarchical field theories with confining potentials, of which the small ball conditioned BRW is an example. We apply our general result to two other models: first, the sinh-Gordon model which has a strictly convex potential, so at the level of covariances the model behaves like one with a quadratic potential, i.e. the model has a positive mass. Second, we consider generalizations of the $\phi^4$ model with any power $\alpha \geq 2$; as $\alpha$ increases from $2$ to $\infty$, these power potentials naturally interpolate between the massive (quadratic) potential and the infinite square well potential of the small ball event.

A BV structure is constructed on the space of zero modes of a quadratic elliptic higher abelian gauge theory. The associated BV integral is shown to be independent of the choice of zero-mode Lagrangian under mild hypotheses. The construction yields explicit zero-mode partition functions for several $p$-form abelian gauge theories.

Barycentric Rényi divergences were introduced in [Mosonyi, Bunth, Vrana, Linear Algebra and its Applications, 2024] as an alternative to standard Kubo-Ando constructions to define multivariate quantum Rényi divergences. They are defined via a variational expression and depend on a finite collection of quantum relative entropies $D^{q_x}$. When all the relative entropies are monotone under CPTP maps then so are the corresponding barycentric Rényi divergences, and when all the relative entropies are additive then the corresponding barycentric Rényi divergences are subadditive under tensor product. Additivity has only been established before for the case where all $D^{q_x}$ are chosen to be the Umegaki relative entropy, which is also the only case where the barycentric Rényi divergence (called the minimal one) was known to admit an explicit expression. Here we settle the problem of additivity by showing that for any choice of monotone quantum relative entropies, the regularized barycentric Rényi divergence coincides with the minimal barycentric Rényi divergence on invertible inputs. This in turn implies that if at least two of the $D^{q_x}$ are strictly larger than the Umegaki relative entropy (in a precise sense), then the resulting barycentric Rényi divergence is not even weakly additive.

The area compressibility modulus is a key descriptor of lipid membrane mechanics, but the molecular interactions that determine this elasticity are not evident from the total modulus alone. Here, molecular dynamics simulations of a POPC bilayer described by the coarse-grained Martini 3 force field were combined with virial stress analysis to decompose the area compressibility modulus into contributions from molecular groups and their interactions. Partial lateral tensions were evaluated as functions of membrane area strain, and their derivatives at the equilibrium state were used to obtain the corresponding contributions to the area compressibility modulus. Hydrocarbon chains provided the dominant positive contribution, accounting for approximately 70% of the total modulus, whereas water-lipid interactions contributed approximately 30%, predominantly through water-headgroup interactions. Within the bilayer, the headgroup and headgroup-chain contributions were of similar magnitude but opposite in sign and nearly canceled. Direct intermonolayer interactions contributed only about 3% of the bilayer-only modulus, indicating an almost additive elastic response of the two monolayers. The hierarchy of elastic contributions differed markedly from that of equilibrium partial tensions, showing that interactions responsible for static stress balance are not necessarily those governing membrane stiffness. This decomposition provides a microscopic interpretation of lipid bilayer area elasticity.

We study the numerical geography and tangent geometry of very amply polarized Calabi–Yau threefolds $(X,H)$ through the positivity of the first jet bundle $J^1(H)$. Writing $d=\int_X H^3$, $c=\int_Xc_2(X) H$, and $e=\int_X c_3(X)$, we exploit two different positivity properties of this single bundle. Mixed intersections on $\mathbb{P}(J^1(H)^*)$ give $e\ge-5d-c-c^2/(4d)$, while a volume estimate for a perturbed tautological class gives $e\ge40d\left[(1-\frac{c}{10d})^{3/2}-1\right]$; in particular $e+6c\ge0$, improving Sun's inequality $e+10c\ge0$. As consequences, we obtain the uniform Hodge bounds $-4d-80\le h^{1,1}(X)-h^{2,1}(X)\le173d/66$, the lower bound $\mathrm{deg}X^\vee\ge78$ for the dual hypersurface, and, in the critical case $X\subset\mathbb{P}^6$, the upper bound $d\le34$. We also prove that, for every $m\ge2$, the tangent-incidence morphism associated with $|mH|$ is the normalization of the tangent variety, conjecture tangent birationality for complete embeddings $X\subset\mathbb{P}^N$ with $N\ge7$, and verify it for several families.

We present a complete analytic expression for the $N$-body Hamiltonian of nonspinning point particles at second post-Newtonian (2PN) order in the Arnowitt-Deser-Misner (ADM) gauge. Recent work reduced the general $N$-body Hamiltonian to a form containing a single unresolved integral term, which prevented a fully explicit closed-form representation. Here, we evaluate this integral analytically and thereby obtain a fully explicit closed-form expression for the general 2PN $N$-body Hamiltonian. We outline the main steps of the derivation and validate the analytic expression through direct numerical comparisons with the original integral representation.

Normally strong and tough, steel$\unicode{x2014}$with iron as its base$\unicode{x2014}$falls prey to severe embrittlement when infiltrated by hydrogen; the insights into why are not well understood. This work explores how hydrogen affects bond strength in iron during fracture and why it reduces cohesion between fracture surfaces, laying bare the central role of electrostatic repulsion.