Papers

We construct a linear map from the space of spin polynomials in the critical Ising model on a lattice to the state space of the $M(4,3)$ minimal model of conformal field theory. The kernel of the map consists precisely of null fields, i.e., spin polynomials that vanish in all correlations. For a polynomial $\Op$ which is not a null field, we define its scaling dimension $\Delta_{\Op}\in\Z_{\geq0}\cup(\Z_{\geq0}+\frac{1}{8}),$ to be the lowest $\Loper{0}+\Loperbar{0}$ eigenvalue in the decomposition of its image into homogeneous components. We show that as the mesh size $\delta$ goes to zero, the rescaled field $\delta^{-\Delta_{\Op}}\Op$ has a non-trivial scaling limit, when inserted in correlations with other such fields. Moreover, all these limits can be expressed in terms of correlations of primary fields of $M(4,3)$ and the Virasoro action in the continuum. The highest weight vectors of $M(4,3)$, the joint eigenvectors of $\Loper{0}$ and $\Loperbar{0}$ with the same eigenvalues $0,1/16,1/2$ for both, are the images of the constant $1$, the spin at a single lattice vertex, and the energy at a single lattice edge, respectively. For the proof, we construct a map from a larger lattice field space, accommodating also fermion and disorder insertions, to a direct sum of two fermionic Fock spaces. This direct sum contains contains the state spaces of both the $M(4,3)$ and the free fermion CFT. The main technical ingredient of the proof is a new version of the exact fermionic current action on the space of lattice local fields due to C. Hongler, K.K. and F. Viklund, combined with some new advances in discrete complex analysis. Our results are valid on arbitrary isoradial graphs.

The feasibility and potential performance of optical clocks based on all-optical atom chips using neutral strontium atoms have been investigated. The key benefits of all-optical atom chips are their ability to trap alkali-earth atoms, and how easily these atoms can be manipulated and examined. The planar configuration of the chip enables ring photonic resonators to be incorporated into its structure, making it a promising candidate for active optical atomic clocks. Using the 'magic wavelengths' of the trapping optical fields (813 nm and 390 nm for strontium atoms) minimises frequency shifts in the intercombination clock transition caused by variations in optical field intensity. However, this frequency shift can be compensated for using optical AC Stark shifts, which are generated by the trapping optical fields and have frequencies below the 'magic frequencies'. Furthermore, it has been demonstrated that atom chip clocks can operate using solely repulsive, blue-detuned evanescent light fields when the attraction of the trapped atoms towards the photonic waveguide is realised through van der Waals forces alone. According to estimates, this could result in the short-term fractional frequency stability of the strontium atom-chip optical clocks being limited to ~10^{-16} per second, with an accuracy of about 5 x 10^{-15} for fractional intensity stability in the trapping light fields of 0.001.

We consider whether the translation Noether current of a linearised metric spin-2 theory admits a strictly gauge-invariant local representative. For Fierz-Pauli and dynamically regular pure curvature-squared theories in four dimensions, we show that no such representative exists under the stated locality, polynomiality and covariance assumptions. A direct enumeration first excludes nonzero symmetric rank-two tensors at the dimension and derivative order of the quadratic action: in the curvature-squared case, the parity-even conservation kernel consists of the identically vanishing Lanczos–Lovelock combination, while both parity-odd coefficients vanish. Homogeneity of the actions in total derivative number then allows projection by field degree and derivative number, extending the exclusion to all finite-order local polynomial representatives with constant coefficients and no explicit coordinate dependence. The translation current nevertheless defines a nonzero conserved-current class. Independently, a constant translation is a Killing reducibility parameter of the linearised gauge symmetry and determines a nonzero linear surface-charge class, which is distinct from the quadratic energy current. A separate calculation shows why a direct compensator cancellation available in Maxwell theory fails for the metric spin-2 field, although this calculation is not needed for the current-class result. Maxwell theory, propagating free $p$-forms and Yang–Mills theory linearised about the trivial vacuum provide comparisons in which translations are not reducibility parameters and strictly gauge-invariant stress tensors exist. Gauss–Bonnet and pure flat-space $R^2$ gravity lie outside the regular scope of the result, through variational triviality and dynamical degeneracy, respectively.

Earthquake preparation involves progressive damage accumulation, strain localization, and changes in the organization of seismicity. We investigate preparatory processes preceding seven episodes of major earthquakes in the Kuril - Kamchatka subduction zone during 2014 - 2025, including the 29 July 2025 MW 8.8 Kamchatka megathrust earthquake. We track damage evolution using the seismic regularity coefficient dc and seismic strain dynamics coefficient SSD, defined for seismic series. Before 2022, each episode of strong seismicity was preceded by a pronounced dc minimum, commonly accompanied by an SSD minimum, followed by an increase in dc toward a maximum near the strong event or event group. After 2022, dc minima became shallower and were superimposed on a sustained upward trend. We interpret this transition as evidence that the metrics recorded two superimposed processes. The cycles before 2022 reflect complete strain-localization histories on southern or more distant structures that did not contribute to the segment ruptured in 2025. In contrast, the upward dc trend from 2022, with only shallow minima preceding Episodes 6 and 7, marks coupled behavior within the eventual main rupture segment, also influenced by stress transfer from southern source regions.

Resource constraints and imperfect quantum operations remain major challenges for quantum machine learning (QML) on noisy intermediate-scale quantum (NISQ) devices, particularly for fault-diagnosis tasks involving imbalanced and heterogeneous data. This work proposes QTN-RQNN, a Quantum Tensor Network-Based Recurrent Quantum Neural Network that integrates tensor-network-inspired nearest-neighbor interactions with recurrent quantum processing. The model sequentially encodes input features while propagating quantum memory across recurrent steps and incorporates QSMOTE for class balancing. QTN-RQNN is evaluated on four heterogeneous fault-diagnosis datasets SPID, CWRUBD, EFDD, and SFDD and compared with QNN, QTN-QNN, and RQNN baselines through classification, ablation, multi-seed, convergence, and quantum-resource analyses. Results show dataset-dependent predictive behavior, indicating that increased quantum architectural complexity does not universally improve classification. On SPID, QTN-RQNN improves the RQNN F1-score from 0.3077 to 0.4516 and ROC-AUC from 0.4485 to 0.6970, while the remaining datasets exhibit different performance-resource trade-offs and sensitivity to recurrent timesteps and circuit depth. Across all datasets, QTN-RQNN reduces the two-qubit-gate count from 32 to 24 per sample relative to RQNN, corresponding to a 25% reduction without increasing the four-qubit requirement; the same relative reduction is obtained for QTN-QNN over QNN. These findings establish QTN-RQNN as a resource-conscious recurrent quantum architecture and highlight the need to jointly consider predictive performance and circuit-resource requirements for near-term quantum fault diagnosis.

The PLATO mission, planned to launch in spring 2027, will observe a fixed Southern field, LOPS2, for at least 2 years with the goal of discovering and deriving precise parameters for planets as small as Earth around FGK dwarfs and sub-giants. Afterwards, PLATO could continue to monitor the same field or move to a Northern field, LOPN1, overlapping with the Kepler field. We assess these two observing strategies in terms of sensitivity of detecting small and long period planets, and subsequently we estimate yields for both observing strategies. Within this we account for including the Kepler data in the LOPN1 field, monitoring of up to 8 years of the LOPS2 field, and the sensitivity improvement from combining TESS and PLATO data since both fields have been and will be continued to be observed with TESS. We find that by monitoring both fields, and hence more stars, the total number of newly discovered planets is maximised. However, to optimise the number of discovered small and long periods planets, long-term monitoring of one field produces the best results. The combination of Kepler and PLATO data improves detection sensitivities; however, as this only covers a fraction of the LOPN1 field and stellar sample, it improves the yields of small and long period planets only marginally. Hence, to detect and characterise small and long period planets in this sparsely explored exoplanet parameter space, a longer continuous observation of the LOPS2 field is best.

Simulations of the evolution of matter on static metric backgrounds allow us to estimate backreaction effects like dynamical friction at first order in the matter density. Previous simulations of dynamical friction have used boosted isotropic and quasi-isotropic Kerr coordinates, which simplifies the extraction of the relevant diagnostics but results in a more complicated implementation of the evolution. In particular, the lack of horizon penetrating coordinates means that high resolutions are needed to ensure convergence, and the boosted, spinning black hole metric cannot easily be written in a closed form, making it more costly to evaluate. In this paper we describe how to reformulate the calculation of the diagnostics in the boosted Kerr-Schild frame for the non-spinning case. We verify that our implementation reproduces previous results quantifying dynamical friction in wave-like dark matter in the appropriate regimes. We discuss the subtleties of transforming diagnostic observables between frames in a 3+1 evolution and develop a general framework for this process.

We develop a field-redefinition-invariant description of hadronic amplitudes outside the WZW sector at $\mathcal{O}(1/f_a)$, including general flavour-conserving and flavour-changing quark couplings. Starting from the most general CP-conserving Lagrangian for ALP interactions with the QCD sector, we identify invariant Wilson coefficient combinations and match them onto the $U(3)$ chiral theory. Using LSZ reduction, we choose fields for which ALP–meson mixing vanishes at this order; amplitudes then depend only on direct invariant couplings, while the anomalous gluonic interaction remains encoded in the $U(1)_A$ sector. For the baryon octet, we derive the general vector and axial couplings and identify, to our knowledge for the first time, an independent invariant ALP–baryon interaction from a second topological singlet structure in the $U(3)$ baryon Lagrangian. We constrain flavour-changing couplings with rare hyperon decays and show in an explicit ultraviolet model that running and matching can generate them from flavour-diagonal high-scale couplings. Finally, we estimate baryon–antibaryon widths and find that, in a gluophilic benchmark, their sum can exceed individual exclusive mesonic widths for $2~\text{GeV} \le m_a \le 3~\text{GeV}$.

We establish a Thouless–Anderson–Palmer (TAP) variational formula for the free energy of spherical $2$-spin models whose interaction matrices have a compactly supported limiting spectral distribution. The formula holds at every inverse temperature and, in particular, extends the TAP representation previously obtained for the spherical Sherrington–Kirkpatrick model. Our main contribution is a new microcanonical proof designed to handle marginality. We partition the sphere according to the smallest collection of top eigendirections carrying a prescribed fraction of the norm. On every element of this partition, the remaining degrees of freedom are effectively at high temperature and their contribution can be computed through spherical-integral asymptotics. The resulting auxiliary variational problem separates the macroscopic low-temperature contribution from the high-temperature fluctuation term; its maximization recovers the usual TAP functional and Plefka condition. This decomposition also shows why neighborhoods of the TAP maximizers alone do not capture the Gibbs mass: all eigendirections associated with large eigenvalues contribute on the same exponential scale, a manifestation of the marginality of spherical $2$-spin states.

We introduce a discrete spectral curve from $\mathscr{N}=2$ double-scaled SYK whose topological recursion defines quasi-polynomial volumes in integer boundary lengths. The curve has two edge theories: a local $\mathscr{N}=2$ theory at the lower edge and a bosonic theory at the upper edge. Focusing on the local $\mathscr{N}=2$ theory, we compute its finite-$q$ volumes and independently check the first few using the string equation. In the $q\rightarrow 1$ continuum limit, these recover the super Weil-Petersson volumes of Turiaci and Witten. Finally, we give an all-genus intersection-theoretic interpretation of these local volumes on the moduli space of stable marked curves, in terms of a deformed spin class with a gap-dependent $\kappa$-class dressing.

We develop an analytical approach to the Kondo problem based on an effective partition function that generalizes the sophomore's dream integral. The Kondo crossover is represented as a passage through an approximately equidistant ladder of its Lee-Yang zeros in the complex plane, rather than as a singularity on the real axis. Summation over this ladder yields the Gamma function $\Gamma(\alpha + T_K/(2 \pi T))$ as the universal crossover backbone, where the offset $\alpha =1/2$ is fixed by the Friedel sum rule. The Euler-Maclaurin expansion connects the discrete zero structure to the Nozieres Fermi-liquid theory through Bernoulli numbers. A two-cutoff formula provides a compact, essentially one-parameter description of the full crossover in terms of a temperature-space Fano lineshape which is a thermal average of the energy-space Fano resonance observed in STM. Drift corrections are treated. The approach extends to $\mathrm{SU}(N)$ Coqblin-Schrieffer, underscreened and Anderson impurity models, and Kondo lattices.

Rare-earth-ion based molecular crystals are emerging as a promising platform for quantum information applications, combining long optical coherence times with the chemical tunability of coordination chemistry. Here we present a comprehensive optical characterisation of twelve Eu$^{3+}$-based molecular complexes, with a focus on the coherent $^{5}\text{D}_{0} \longrightarrow \ ^{7}\text{F}_{0}$ transition at $\sim$580 nm. Judd-Ofelt analyses are performed across all complexes, providing insights into ligand-field environments, local point-group symmetries, and the resulting branching ratios of the coherent transition. We find that lower point-group symmetry (C$_1$, C$_2$) yields higher branching ratios of the $^{5}\text{D}_{0} \longrightarrow \ ^{7}\text{F}_{0}$ transition, exceeding 1% in several complexes. Optical inhomogeneous linewidths measured at 4.2 K reveal narrow linewidths for some complexes of below ten GHz, indicative of a highly ordered crystalline environment. Optical coherence measurements of one of the complexes, 5-Eu, yields an optical coherence time of $T_{\text{2}}^{\text{opt}} = 2.3~\mu\mathrm{s}$ at 4.2 K, comparable to the best-performing molecular systems reported to date. Systematic characterisation and quantitative comparison will be key to find structure-property relations guiding rational design of optimised complexes for quantum information applications.

Can quantum data reliably answer questions chosen from earlier results? We prove that $M$ adaptive Pauli predictions on $n$ qubits require $\Omega(\sqrt{\min\{n,M\}})$ copies at fixed accuracy. Published upper bounds make this tight for $M\le n$. Thus $n$ adaptive predictions cost $\Theta(\sqrt n)$ copies, whereas a fixed list costs only $O(\log n)$. The lower bound uses diagonal states and commuting observables, identifying a statistical cost of adaptation. We also quantify how this cost increases with precision.

Machine learning methods are increasingly used to predict chemical properties directly from the molecular structure to bypass the often prohibitive cost of quantum mechanical calculations. Recent work has shown that including the ground-state electron density as input to the machine learning model can improve accuracy in this setting. This work employs the recent surrogate functional framework originally developed for orbital-free density functional theory and extends it to predicting molecular properties. We show that passing the ground-state density as input to the model, while simultaneously enforcing it to be the minimum of the surrogate functional, surpasses state-of-the-art performance for six out of seven extensive properties of the QM9 dataset. Additionally, the approach shows improved generalization to larger molecules taken from the QM40 dataset. On all extensive properties of both datasets, our approach outperforms models that are informed by the ground-state density but do not enforce the surrogate functional constraints.

Resolving the ambiguity surrounding current Venusian volcanism is a primary objective for upcoming missions like EnVision and VERITAS. This study uses the Venus Planetary Climate Model to simulate the dispersal and detectability of volcanic plumes containing water vapour (H2O), hydrogen chloride (HCl), carbon monoxide (CO), and carbonyl sulphide (OCS) within a three-dimensional atmospheric environment. We model localised gas enhancements at altitudes probed by nightside spectral windows (8.62, 20.91, and 35.45 km above surface). Results indicate that plumes persist longest in the deep atmosphere (8.62 km) at equatorial latitudes, where H2O enhancements remain distinguishable from low background variability for up to 100 hours, forming distinct downstream streaks. In contrast, at 35 km, high intrinsic variability in chemically active species (CO and OCS) driven by atmospheric dynamics obscures plume signatures and chemically inert species disperse within 0.5-2 Earth days. Plumes at high latitudes disperse more rapidly than at low latitudes at all altitudes. We perform sensitivity tests with trace gas increases of 50%, 40%, 30%, 20%, 10%, and 3% above baseline and plume injection times of 6, 12, 28, 38, and 126 hours at all three altitudes and two latitudes. We conclude that observing inert gases, in particular H2O, at low altitudes and latitudes offers the best opportunity for successful plume detection.

Complex disordered conductors can display highly structured and parameter-sensitive transport even in the absence of a thermodynamically stable glass phase. Overlap distributions originally developed for replica symmetry breaking (RSB) provide a useful diagnostic of this organization, provided that their interpretation is distinguished from the equilibrium Parisi construction. In this study, we report RSB-like overlap phenomenology and parametric mesoscopic glassiness in a graphene-based electronic Lévy glass, a device that mimics optical phenomena via electronic processes. By tuning the Fermi energy, we can control the number of propagating wave modes and observe reentrant changes from narrowly centered to broad or bimodal overlap distributions. The phenomenology is observed in both graphene-based and conventional two-dimensional electron-gas electronic Lévy glasses, indicating its generality. Sample-resolved overlap distributions show that the effect is intrinsic to each disorder landscape, whereas the normalized conductance variance shows that the growth of the absolute variance is mainly caused by the increasing mean conductance. We therefore interpret the overlap as a measure of correlation among hierarchically organized transport pathways and the reentrant behavior as evidence of pinning, parameter-induced reorganizations, and mesoscopic chaos in coherent transport.

Backgrounds arising from quark- and gluon-initiated jets misidentified as hadronically decaying tau leptons constitute a major experimental challenge for analyses involving tau leptons. The MUltivariate Fake-Factor INference (MUFFIN) approach, a machine-learning-based method for estimating this background directly from observed events, is presented. Boosted decision tree reweighting is used to learn multidimensional, per-object correction factors directly from observed data, thereby modelling the jet to hadronic tau lepton misidentification probability across the kinematic and topological phase space without relying on low-dimensional parametrisations. Performance studies are presented using proton-proton collision data collected by the CMS experiment at the CERN LHC at $\sqrt{s}$ = 13.6 TeV, corresponding to an integrated luminosity of 62.4 fb$^{-1}$. Compared to low-dimensional parametrisation methods, improved modelling of key kinematic observables is achieved, particularly in regions of high $p_\mathrm{T}$. The improved modelling leads to a reduction of up to 70% in the systematic uncertainty associated with jets being misidentified as hadronically decaying tau leptons. The MUFFIN method provides a robust and scalable method for background estimation in precision measurements and searches for beyond-the-standard-model physics involving tau lepton final states.

We present the new release of nuclear parton distribution functions (nPDFs) from the nCTEQ collaboration: nCTEQ26. In this global analysis, we combine our recent, more selective studies of different experimental measurements and extend them to determine a modern set of nPDFs based on the largest selection of data considered to date. This selection includes neutral- and charged-current deep-inelastic scattering (DIS), fixed-target Drell-Yan, and a large variety of collider data from RHIC and LHC Runs I and II. On the theoretical side, we match this considerably extended kinematic range with a new nPDF parametrization that combines a flexible functional form of the x-dependence with a quadratic logarithmic nuclear A-dependence as well as target-mass and deuteron corrections for the reliable inclusion of high-x DIS data. Following our previous successful work, we partially employ a data-driven approach that allows us to not only include open heavy-quark data, but also quarkonium data. In addition, we establish the consistency of this approach by comparing it to an alternative fit based on perturbative predictions of open heavy-quark data alone. We determine the uncertainties of our nCTEQ26 nPDFs with a Hessian error analysis, test their reliability by comparing our nPDFs to other, similar recent analyses, and make predictions for current and future experimental measurements that have not been included in the analysis.

Exceptional points (EPs) are usually introduced as defective degeneracies of non-Hermitian Hamiltonians and, in fully open quantum dynamics, of Liouvillian generators. Here we formulate an operational theory of exceptional points that does not invoke a Hamiltonian or a master equation. The primitive dynamical object is a completely positive trace-preserving (CPTP) quantum channel $\Phi$, applied an integer number $n$ of times, while physical data are probabilities $p_n^{\mathbf A}(x|\rho)$ associated with states $\rho$ and observables $\mathbf A$ having measurements results $x$. We define exceptional channels through nontrivial Jordan chains of $\Phi$ and show that a Jordan block of order $m$ generates discrete polynomial-exponential terms with maximal degree $m-1$. This places the physics of exceptional points in contact with what can be directly measured in experiments.

Qubits are powerful computational resources because each additional qubit doubles the size of the accessible state space. This expressive power comes at a cost: adding qubits also increases circuit size, constraint overhead, and exposure to hardware noise. These limitations are especially critical for near-term quantum computers, making the number of qubits required to formulate a problem a central practical concern. In this work, we present a method for efficiently mapping logistics and routing problems onto qubits through structure-aware encoding reduction. We demonstrate the method on a benchmark problem of latency-resilient routing under dual-link failures. For this benchmark, the reduced formulation substantially lowers both the qubit count and the compiled circuit complexity while preserving the original optimization task. By running the reduced model on the same trapped-ion quantum computer as the benchmark, we obtain a 100X improvement in the success probability. This finding shows how careful problem formulation can make current quantum hardware substantially more effective for practical optimization.

Connectivity estimation needs to be fast and thus usually relies on semi-empirical models. We previously established that optimised magnetohydrodynamics (MHD) models can also be used to derive magnetic connectivity, yielding good results, especially for complex configurations. However, the modelling is not the only factor that can impact the connectivity estimation. Models' results, both semi-empirical and MHD, depend heavily on the input data used to drive the simulation. In order to quantify this impact on our connectivity estimation, we used 20 different maps by four providers. We selected the period of July 2019, which corresponds to Carrington rotation (CR) number 2219, because it had already been studied in a previous paper. It corresponds to a period of minimum activity, meaning minimal interference from transient structures, but with a high-speed stream and several polarity switches. We have compared our results with in situ data from ACE and developed several visualisation techniques to validate connectivity not only for a specific date but also for a full CR. The choice of the input magnetic map drastically affects the connectivity estimates, with global scores going from 28% global agreement to 63% in the most extreme case. The HMI and GONG maps consistently gave the best connectivity estimations, with more than 50% correct results of the full CR. For this specific period, the GONG-ADAPT maps yielded the least reliable results, with a score below 35%. This is not surprising, as we have shown before that COCONUT required parameter adjustments for these maps. However, WSO maps which showed poor coronal agreement actually provided good connectivity estimates, showing that the Heliospheric Current Sheet (HCS) location is in the end the most crucial parameter for connectivity. Consistent data over a full Carrington rotation are to be favored compared to daily.

We analyze ferroelectric domain wall motion, shape, and internal structure arising from coupling between polarization and screening charge. Universal cases are organized by electrical boundary conditions, charge conservation and dynamics, and polarization free energy. We consider exposed surfaces, interfaces beneath a dielectric layer and top electrode, and interfaces with a blocking mixed ionic-electronic conductor. Screening occurs through local exchange, exchange with lateral transport, or strictly conserved redistribution. Analytical derivations and finite-depth calculations establish screening drag, velocity branches, and conditions for spatial instability. For an isolated wall joining differently compensated domains, strict surface conservation and zero far-field current exclude steady translation of the screening profile, while allowing transient displacement, finite-sample arrest, and charge-balanced structural changes. Conservation also constrains long-distance transport around a moving junction in an adjoining conductor. Large-field simulations in the top-electrode geometry reveal nonlinear corrugation, transfer toward longer wavelengths, and coupled polarization rotation. First-order polarization energetics allow two interphase fronts enclosing a paraelectric core; multiaxial polarization permits wall rotation and competing intermediate ferroelectric domains. A driven structural-screening reduction supports stable periodic behavior. Reduced-variable diagrams summarize motion and structural regimes, while BaTiO3 and BiFeO3 examples connect them to material thermodynamics. Small-signal analysis distinguishes displacement, polarization, and electrostatic response functions. These results provide a framework for wall dynamics and structural transitions under different driving and screening conditions.

The Kelvin-Helmholtz (KH) instability is a fundamental signature of the natural world, manifesting in phenomena ranging from atmospheric clouds to the iconic turbulence of Jupiter's Great Red Spot. While the linear dynamics of this instability is well-understood, the ultimate fate of the fluid — the final stationary state to which it relaxes — remains a formidable challenge. In this paper, we present a general non-equilibrium statistical mechanics framework that allows us to predict the asymptotic vorticity distribution of a sheared 2D Euler fluid. By constructing a self-consistent ansatz for the solution of the Vlasov equation, we determine the stationary stream function without explicitly solving the time-dependent Euler equations. We demonstrate that the relaxation leads to a population-inverted core, where high-energy states are fully occupied, surrounded by a tenuous halo of vortices in the lower-energy regions of configuration space. This result establishes the core-halo structure as a robust statistical consequence of the system's evolution, offering a universal framework for understanding the saturation of shear-induced turbulence in inviscid 2D fluids.

We discuss three simple connections between generative diffusion and optimal transport. First, the joint law of the data and of their Ornstein-Uhlenbeck noising is, at every time, the solution of an entropic optimal-transport problem, at a temperature set by the noise level. Backward diffusion can consequently be read as an annealing which gradually decreases the entropic regularization. Second, we study the speciation transition–how the modes of the data distribution emerge during generation–and compare how it happens in diffusion and flow matching with respect to optimal transport. Using Gaussian mixtures as high-dimensional example, we show that the dynamical instability through which diffusion and flow matching separate the modes becomes, for optimal transport, an exponentially thin boundary layer at the beginning of generation, which is rounded by entropic regularization. Third, considering a generic forward dynamics with a general confining potential, we show that the backward process driven by the score also satisfies a drift-based variational principle whose minimal cost is the entropy difference between initial and final distributions.

We complement and extend our recent study of the non-linear evolution of the Gregory-Laflamme instability of black strings in Einstein-Gauss-Bonnet gravity in five spacetime dimensions. First, we study time-dependent perturbations of uniform black strings in Einstein-Gauss-Bonnet theory and determine the growth rates as a function of the coupling. We find that for positive Gauss-Bonnet couplings, the black strings are more unstable than in general relativity in the sense that the growth rates are larger and shorter wavelengths are unstable. In the second part of the paper we show that the hyperbolicity of the equation of motion of Einstein-Gauss-Bonnet theory is determined by an effective metric when the dynamics is restricted to spherical symmetry in the asymptotically flat directions. When the effective field theory becomes strongly coupled, as it happens near the endpoint of the Gregory-Laflamme instability of the black string, this effective metric becomes degenerate and the Cauchy evolution breaks down. Applying this criterion to uniform black strings, we find that for any positive Gauss-Bonnet coupling there is an open set of regular solutions (including the one of minimal thickness) on which the effective metric degenerates in a neighbourhood of the horizon. Therefore, we argue that these solutions cannot be attained from weakly coupled initial data by Cauchy evolution and the solutions of the linearized equations around them cannot be interpreted as approximations to nearby non-linear evolutions. We provide further evidence for this picture with non-linear simulations of the Gregory-Laflamme instability. The non-linear simulations terminate through a loss of hyperbolicity of the Tricomi or Keldysh type, depending on the sign of the Gauss-Bonnet coupling.

Experimental detection of multipartite Bell nonlocality faces many challenges. The increase in the size of the system demands a higher fidelity of state preparation, a higher detection efficiency, and a larger number of correlators that need to be estimated. These issues are even more pronounced if one wishes to detect a more restrictive variant of Bell nonlocality called genuine multipartite nonlocality (GMNL). In this work, we introduce two classes of multipartite Bell inequalities that are capable of detecting GMNL correlations and address different experimental hurdles in GMNL detection. The first class consists of the number of correlators that scales linearly with the number of parties. The second class increases the number of correlators and, in return, provides higher noise robustness of GMNL detection. Both classes of inequalities are constructed to detect GMNL in graph states, and in fact both can be used for self-testing of graph states and the performed measurements.

Quantum entanglement is a fundamental resource in quantum information science, commonly consumed to perform tasks like quantum teleportation and quantum key distribution. Entanglement concentration converts partially entangled pure states into nearly perfect Bell pairs. While its efficiency is well understood in the asymptotic limit, practical protocols must operate with finite systems. In this finite regime, and at the low error levels relevant in practice, performance is penalized by corrections that reduce the achievable yield. We investigate whether this fundamental finite-size penalty can be mitigated by an entanglement catalyst: an auxiliary state that aids the transformation but is returned exactly and uncorrupted. Although such a catalyst cannot increase the leading-order asymptotic yield, we show that it fundamentally alters the finite-size scaling. For every bipartite pure state with nonuniform Schmidt coefficients, we exactly determine the optimal second-order correction to the yield and show that catalysis completely overcomes this finite-size penalty.

In an earlier study of the Laplacian eigenvalues with strongly attractive Robin boundary conditions in polygons it was found that if each corner is either concave or non-resonant, then the asymptotic behavior of the individual eigenvalues is determined by an effective one-dimensional operator on the boundary with Dirichlet boundary conditions at the corners. The non-resonance condition was formulated in terms of an eigenvalue bound on truncated sectors, and it was only shown to be satisfied by the right and obtuse opening angles. In the present work, we determine the full range of non-resonant angles: it turns out that the non-resonance condition fails only for the opening angles $\frac{\pi}{2n+1}$ with $n=1,2,3,\dots$, and these critical values are equivalently characterized in terms of the jumps of the eigenvalue counting function and the existence of bounded generalized eigenfunctions. This resolves the numerically supported conjecture stated by Dauge and Lafranche.

The collective-risk dilemma has become a paradigm for studying cooperation in a wide variety of social experiments, initiatives that generate increasingly rich datasets describing individual actions over successive decision-making processes. Beyond the purely descriptive analysis of such empirical datasets, a methodological framework is required to interpret and reproduce the observed dynamics, a scheme that may be skewed by exogenous biases. Here, we introduce a data-driven, non-parametric method for simulating individual decisions together with a validation protocol for assessing the fidelity level of the outcomes they generate. Our methodological contribution is based on an empirical heuristic ensemble: agents are represented by a finite set of behavioural heuristics, probabilities conditioned on different observable features of the game state, endowed with a hard-voting arbitration that determines their per-round final decisions. This reproducible generative framework allows for behavioural inference in different collective-risk dilemma setups: Behavioural heuristics are seeded directly from empirical data assessing conditional probabilities, without a priori assumptions; a plurality vote with uniform random tie-breaking resolves between competing heuristics each round, adding no free parameters; validation follows a pattern-oriented approach, comparing synthetic and empirical macro-indicators against single-heuristic and uniform-random baselines; synthetic data generated allow exploration of scenarios or experimental setups that have not been empirically realised; as a worked example, we instantiate our methodological approach on the xAire citizen science collective-risk dilemma experiment run in Barcelona.

Practical fault-tolerant quantum computing requires qubit-efficient quantum error correction (QEC). Clifford deformations (CDs) modify the stabilizers of a QEC code to lower its logical error rate at no additional resource cost. However, the number of possible CDs grows exponentially with the number of qubits, making exhaustive search infeasible beyond small codes. In this work, we further show that under circuit level noise the optimal CD depends strongly on both the noise model and decoder. To make systematic CD optimization possible, we introduce Evolution-Based Best-arm Identification (EBBI), a shot-efficient search algorithm that treats the circuit, noise model and decoder as a black box. We benchmark EBBI's performance on the rotated surface code, under two strongly $Z$-biased circuit-level noise models with the PyMatching decoder. At distance 3, EBBI finds the optimal CD using up to $\sim 1100\times$ fewer shots than random search. At distance 5, when run at the target error rate, the median EBBI run converges to the CDs we believe to be optimal, while random search never converges. Under a $Z$-biased SI1000-like noise model, EBBI discovers a new CD, the B-XZZX code, which we generalized to larger distances. It differs from XZZX on only a fraction $\mathcal{O}(d^{-1})$ of the qubits at code distance $d$, yet its relative advantage grows from $\approx 5\%$ at $d = 3$ to $\approx 12\%$ at $d = 11$. We thus show that the B-XZZX pattern found by EBBI can be systematically scaled to larger code distances. Our work represents a first step towards scalable CD optimization for general QEC codes.