In contrast to the usual bulk-boundary correspondence, topological states localized within the bulk of the system have been numerically identified in quasicrystalline structures, termed bulk localized transport (BLT) states. These states exhibit properties different from edge states, one example being that the number of BLT states scales with system size, while the number of edge states scales with system perimeter. Here, we define a procedure to identify BLT states, which is based on the physically motivated crosshair marker and robustness analyses. Applying the procedure to the Hofstadter model on the Ammann-Beenker tiling, we find that the BLT states appear mainly for magnetic fluxes within a specific interval. While edge states appear at low densities of states, we find that BLT states can appear at many different densities of states. Many of the BLT states are found to have real-space localization that follows geometric patterns characteristic of the given quasicrystal. Furthermore, BLT states can appear both isolated and in groups within the energy spectrum which could imply greater robustness for the states within such groups. The spatial localization of the states within a certain group can change depending on the Fermi energy.

This study addresses the computational challenges of forecasting volatility in high-dimensional commodity markets. Building on the Network log-ARCH framework, we introduce a novel class of network topologies from GARCH-informed correlation weights, obtained from conditional covariance estimates of multivariate GARCH models, rather than relying on the heuristic distance measures commonly used in clustering methods. We evaluate the proposed models forecasting performance through a rolling-window exercise using a panel of OPEC members crude oil prices. The results identify network volatility models incorporating these new GARCH-informed weights as the statistically superior specifications. Remarkably, the proposed framework matches standard DCC-GARCH predictive accuracy while delivering up to 62,000-fold computational gains. By explicitly modeling contemporaneous spillovers through interpretable spatial ARCH-like lags estimated via GMM, the proposed approach offers an optimal trade-off between parsimony, interpretability, and performance. The findings establish GARCH-informed network models as robust, scalable alternatives for systemic risk measurement and volatility forecasting in interconnected financial markets.

Understanding how well future cosmological experiments can reconstruct the mechanism that generated primordial inhomogeneities is key to assessing the extent to which cosmology can inform fundamental physics. In this work, we apply a quantum metrology tool - the quantum Fisher information - to the squeezed quantum state describing cosmological perturbations at the end of inflation. This quantifies the ultimate precision achievable in parameter estimation, assuming ideal access to early-universe information. By comparing the quantum Fisher information to its classical counterpart - derived from measurements of the curvature perturbation power spectrum alone (homodyne measurement) - we evaluate how close current observations come to this quantum limit. Focusing on the tensor-to-scalar ratio as a case study, we find that the gap between classical and quantum Fisher information grows exponentially with the number of e-folds a mode spends outside the horizon. This suggests the existence of a highly efficient (but presently inaccessible) optimal measurement. Conversely, we show that accessing the decaying mode of inflationary perturbations is a necessary (but not sufficient) condition for exponentially improving the inference of the tensor-to-scalar ratio.

A comprehensive assessment of theoretical uncertainties defines an important frontier in nuclear structure research. Ideally, theory predictions include uncertainty estimates that take into account truncation effects from both the interactions and the many-body expansion. While the uncertainties from the expansion of the interactions within effective field theories have been studied systematically using Bayesian methods, many-body truncations are usually addressed by expert assessment. In this work we use a Bayesian framework to study many-body uncertainties within many-body perturbation theory applied to finite nuclei. Our framework is applied to a broad range of nuclei across the nuclear chart calculated from two- and three-nucleon interactions based on chiral effective field theory. These developments represent a step towards a more complete and systematic quantification of uncertainties in \emph{ab initio} calculations of nuclei.

The rapid advances in artificial intelligence (AI) have largely been driven by scaling deep neural networks (DNNs) - increasing model size, data, and computational resources. Yet performance is ultimately governed by network dynamics. The lack of a principled understanding of DNN dynamics beyond heuristic design has contributed to challenges in robustness, suboptimal performance, high energy consumption, and pathologies in continual and AI-generated content learning. In contrast, the human brain appears largely resilient to these problems, and converging evidence suggests this advantage arises from dynamics poised at a critical phase transition. Inspired by this principle, we propose that criticality provides a unifying framework linking structure, dynamics, and function in DNNs. First, analyzing more than 80 state-of-the-art models, we show that a decade of AI progress has implicitly driven successful networks toward criticality - explaining why some architectures succeeded while others failed. Second, we demonstrate that explicitly incorporating criticality into training improves robustness and accuracy while mitigating key limitations of current models. Third, we show that major AI pathologies - including performance degradation in continual learning and model collapse during training on AI-generated data - reflect a loss of critical dynamics. By maintaining networks near criticality, we provide a principled solution to these failures, demonstrating that criticality-based optimization prevents degradation and collapse. Our results establish criticality as a substrate-independent principle of intelligence, connecting AI progress with fundamental principles of brain function, and offering both theoretical insight and practical strategies to ensure long-term DNN performance and resilience as models scale.

Independently from the formation mechanism of primordial black holes in the early Universe, their generation is accompanied by a ringdown phase during which they relax to a stationary configuration and gravitational waves under the form of quasinormal modes are emitted. Such gravitational waves generate an irreducible and unavoidable stochastic background which is testable by current and future experiments. In particular, for primordial black holes with masses exceeding $10^{14}\,M_{\odot}$, the associated stochastic background lies within the frequency range accessible to current and upcoming cosmic microwave background experiments, thereby providing a direct observational way to probe the existence of such extremely massive objects.

We consider the perturbative renormalisation of the $Φ^4_d$ model from Euclidean Quantum Field Theory for any, possibly non-integer dimension $d<4$. The so-called BPHZ renormalisation, named after Bogoliubov, Parasiuk, Hepp and Zimmermann, is usually encoded into extraction-contraction operations on Feynman diagrams, which have a complicated combinatorics. We show that the same procedure can be encoded in the much simpler algebra of polynomials in two unknowns $X$ and $Y$, which represent the fourth and second Wick power of the field. In this setting, renormalisation takes the form of a \lq\lq Wick map\rq\rq\ which maps monomials into Bell polynomials. The construction makes use of recent results by Bruned and Hou on multiindices, which are algebraic objects of intermediate complexity between Feynman diagrams and polynomials.

It is known that, for an oriented hypergraph with (vertex) coloring number $χ$ and smallest and largest normalized Laplacian eigenvalues $λ_1$ and $λ_N$, respectively, the inequality $χ\geq (λ_N-λ_1)/\min\{λ_N-1,1-λ_1\}$ holds. We provide necessary conditions for oriented hypergraphs for which this bound is tight. Focusing on $c$-uniform unoriented hypergraphs, we then generalize the bound to the setting of \emph{$d$-proper colorings}: colorings in which no edge contains more than $d$ vertices of the same color. We also adapt our proof techniques to derive analogous spectral bounds for \emph{$d$-improper colorings} of graphs and for edge colorings of hypergraphs. Moreover, for all coloring notions considered, we provide necessary conditions under which the bound is an equality.

The dimer model is a classical statistical mechanics model which is exactly solvable in two dimensions, but about which little is known in higher dimensions. In analogy with large $N$ limits in lattice gauge theory, we study a large $N$ limit of the dimer model in any dimension $d$. The dependence on $N$ comes from the multinomial tiling model introduced by Kenyon and Pohoata, which gives a general framework for adding a dependence on $N$ to a tiling model. We study the behavior of this model on periodic bipartite graphs in ${\mathbb R}^d$, in the scaling limit as the multiplicity $N$ and then the size of the graph go to infinity. In this iterated limit, in any dimension $d$, we prove a variational principle and show that random configurations concentrate on a limit shape which is the unique solution to an associated system of Euler-Lagrange equations. The rate function of the variational principle is the integral of a surface tension function, which we can compute explicitly for lattices in any dimension $d$ as the Legendre dual of the free energy for the model on the torus. We give a unified methodology for computing the surface tension and Euler-Lagrange equations in any dimension $d$. A new structure called the critical gauge also emerges in the large $N$ limit. We show that the critical gauge functions converges in the scaling limit to a limiting gauge function which is the unique solution to a dual Euler-Lagrange equation. This limiting gauge function determines the limit shape and vice versa. We further use our techniques to compute explicit limit shapes in some two and three dimensional examples, such as the Aztec diamond and "Aztec cuboid". This is one of the first stat mech models in dimensions $d\ge3$ where limit shapes can be computed explicitly.

Recently, novel exact identities known as Fluctuation-Response Relations (FRRs) have been derived for nonequilibrium steady states of Markov jump processes. These identities link the fluctuations of state or current observables to a combination of responses of these observables to perturbations of transition rates. Here, we complement these results by deriving analogous FRRs applicable to mixed covariances of one state and one current observable. We further derive novel Inverse FRRs expressing individual state or current response in terms of a combination of covariances rather than vice versa. Using these relations, we demonstrate that the breaking of the Onsager symmetry requires the presence of state-current correlations. On the practical side, we demonstrate the applicability of FRRs for explaining the behavior of fluctuations in quantum dot devices or enzymatic reaction networks.

We show theoretically that an initially homogeneous planar Couette flow of a concentrated polymeric fluid is linearly unstable to the growth of two-dimensional (2D) perturbations, within two widely used constitutive models: the Johnson-Segalman model and the Rolie-Poly model. We perform direct nonlinear simulations of both models in 2D to show that this instability leads to a state of elastic turbulence comprising several narrow shear bands that dynamically coalesce, split and interact. Importantly, we show that this 2D instability arises not only in fluids that have a non-monotonic constitutive curve, and therefore show shear banding in 1D calculations, but also in shear thinning fluids with a monotonic constitutive curve, for which an initially homogeneous base state is stable in 1D. For the former category, the high shear branch of the constitutive curve is unstable to 2D instability in both models, so that the high shear band may be turbulent. In the Rolie-Poly model, the low shear branch is also likewise unstable. Our work provides the first simulation evidence for elastic turbulence in highly entangled polymeric fluids. It also potentially explains rheo-chaotic states seen experimentally in shear banding wormlike micelles. We additionally demonstrate elastic turbulence within both models in the planar Poiseuille geometry.

As the complexity of software systems rises, methods for explaining their behaviour are becoming ever-more important. When a system fails, it is critical to determine which of its components are responsible for this failure. Within the verification community, one approach uses graph games and Shapley values to ascribe a responsibility value to every state of a transition system. As this is done with respect to a specific failure, it is called backward responsibility. This paper provides tight complexity bounds for the computation of backward responsibility values for reachability, Büchi and parity objectives. For Büchi objectives, a polynomial algorithm is given to determine the set of responsible states, i.e. states with positive responsibility value. To analyse systems that are too large for standard methods, the paper presents a novel refinement algorithm that iteratively finds the set of responsible states. Several heuristics are proposed to guide the refinement algorithm. Its utility is demonstrated with a tool that implements refinement in addition to several other responsibility computation techniques.

This paper presents the first observation of top-quark pair production in association with two photons ($t\bar{t}γγ$). The measurement is performed in the single-lepton decay channel using proton-proton collision data collected by the ATLAS detector at the Large Hadron Collider. The data correspond to an integrated luminosity of 140 fb$^{-1}$ recorded during Run 2 at a centre-of-mass energy of 13 TeV. The $t\bar{t}γγ$ production cross section, measured in a fiducial phase space based on particle-level kinematic criteria for the lepton, photons, and jets, is found to be $2.42^{+0.58}_{-0.53}\, \text{fb}$, corresponding to an observed significance of 5.2 standard deviations. Additionally, the ratio of the production cross section of $t\bar{t}γγ$ to top-quark pair production in association with one photon is determined, yielding $(3.30^{+0.70}_{-0.65})\times 10^{-3}$.

The present paper deals with the stability analysis for the geodesic flow of a step-two nilpotent Lie group equipped with a left-invariant pseudo-Riemannian metric. The Lie-Poisson equation can be described in terms of the so-called $j$-mapping, a linear operator associated to the step-two nilpotent Lie algebras equipped with the induced scalar product. The stability of equilibrium points for the Hamilton equation is determined in terms of their Williamson types.

We discuss the behavior of general Floquet time crystals (FTCs), including prethermal ones, in closed systems acting as AC sensors. We provide an analytical treatment of their quantum Fisher information (QFI) dynamics, which characterizes the ultimate sensor accuracy. By tuning the direction and frequency of the AC field, we show how to induce transitions resonantly between macroscopic paired cat states in the FTC sensor. This allows for robust Heisenberg scaling precision (QFI $\sim N^2 t^2$) for exponentially long times in the system size. The QFI dynamics exhibit, moreover, a characteristic step-like structure in time due to the eventual dephasing along the cat subspaces. The behavior is discussed for various initial sensor preparations, including ground states and low- and high-correlated states. Furthermore, we examine the performance of the sensor along the FTC phase transition, with the QFI capturing its critical exponents. Our findings are presented for both linear and nonlinear response regimes and illustrated for a specific FTC based on the long-range interacting LMG model.

Transversal logical gates offer the opportunity for fast and low-noise logic, particularly when interspersed by a single round of parity check measurements of the underlying code. Using such circuits for the surface code requires decoding across logical gates, complicating the decoding task. We show how one can decode across an arbitrary sequence of transversal gates for the unrotated surface code, using a fast "logical observable" minimum-weight-perfect-matching (MWPM) based decoder, and benchmark its performance in Clifford circuits under circuit-level noise. We propose windowed logical observable matching decoders to address the problem of fully efficient decoding: our basic windowed decoder is computationally efficient under the restriction of quiescent (slow) resets. Our 'advanced' two-step windowed decoder can be computationally inefficient but allows fast resets. For both windowed decoders we identify errors which scale sublinearly in $d$ - depending on the structure of the circuit - which can lead to logical failure, and we propose methods to adapt the decoding to remove such failures. Our work highlights the complexity and interest in efficient decoding of fast logic for the surface code.

Electron pairing at low temperatures leads to superconductivity. A fundamental question is whether more complex states - characterized by order in four-electron composite objects, termed electron quadrupling or composite order - can exist in materials, and if so, under what conditions they emerge and what properties they exhibit. These states lie beyond the scope of Bardeen-Cooper-Schrieffer theory, and a microscopic description of them remained elusive. In the first part of the paper, we provide a general microscopic framework to describe these and the other four-fermion composite states. In the second part of the paper, we derive and solve a specific fermionic model in two and three dimensions that hosts time-reversal symmetry-breaking electron quadrupling order. The fermionic microscopic theory is used to estimate the specific heat and electron density of states.

We experimentally study the interaction between a cold atom cloud and many longitudinal modes of a high quality Fabry-Perot cavity, by measuring signatures of collective light shifts in the cavity transmission spectrum of an optical frequency comb probe. Using a resonator coupled to more than $10^5$ intracavity atoms, we detect significant shifts of $\sim 100$ cavity modes simultaneously, which is a direct manifestation of physics beyond the hitherto explored regime of cavity-cold atom interaction with only single or few longitudinal modes at a time. For the cavity mode closest to the atomic resonance, we demonstrate a bistability in the transmission spectrum, arising due to a combined coupling of the cloud to an external pump laser and a cavity mode probed by the optical frequency comb. These results provide a first step toward deeper exploration of multifrequency cavity quantum electrodynamics, where ultrashort pulsed sources could be used for optical manipulation, cooling and entanglement of cold atoms in a resonator.

We propose a novel nonlocal spin-1/2 theory in which the form factor depends on the Dirac operator rather than on the d'Alembert operator. In this scenario, we explore some classical and quantum aspects of this new theory. At the classical level, we investigate the dispersion relation of free spin-1/2 particles and find that it increasingly deviates from the standard case as the nonlocal effects become relevant. At the quantum level, we compute the fermionic one-loop effective action for the nonlocal spin-1/2 theory with Yukawa coupling and show that the contributions of nonlocal effects are significant in the UV limit, while in the IR they are suppressed by a UV cutoff scale, which has been chosen to coincide with the nonlocality scale $Λ$. We minimally couple a $U(1)$ gauge field to the nonlocal spin-1/2 field theory and explicitly demonstrate that this theory is gauge invariant. Finally, we obtain a nonlocal version of the Pauli equation and the impact of the nonlocality in the $g$-factor of massive particles.

Decentralized storage systems face a fundamental trade-off between replication overhead, recovery efficiency, and security guarantees. Current approaches either rely on full replication, incurring substantial storage costs, or employ trivial erasure coding schemes that struggle with efficient recovery especially under high storage-node churn. We present Walrus, a novel decentralized blob storage system that addresses these limitations through multiple technical innovations. At the core of Walrus is RedStuff, a two-dimensional erasure coding protocol that achieves high security with only 4.5x replication factor, while enabling self-healing recovery that requires bandwidth proportional to only the lost data $(O(|blob|/n)$ versus $O(|blob|)$ in traditional systems). Crucially, RedStuff is the first protocol to support storage challenges in asynchronous networks, preventing adversaries from exploiting network delays to pass verification without actually storing data. Walrus also introduces a novel multi-stage epoch change protocol that efficiently handles storage node churn while maintaining uninterrupted availability during committee transitions. Our system incorporates authenticated data structures to defend against malicious clients and ensures data consistency throughout storage and retrieval processes. Experimental evaluation demonstrates that Walrus achieves practical performance at scale, making it suitable for a wide range of decentralized applications requiring high-integrity, available blob storage with reasonable overhead.

We investigate the generation of non-stabilizerness, or magic, in a multi-particle quantum walk by analyzing the time evolution of the stabilizer Rényi entropy $M_2$. Our study considers both single- and two-particle quantum walks in the framework of the XXZ Heisenberg model with varying interaction strengths. We demonstrate that the spread of magic follows the light-cone structure dictated by the system's dynamics, with distinct behaviors emerging in the easy-plane ($Δ< 1$) and easy-axis ($Δ> 1$) regimes. For $Δ< 1$, magic generation is primarily governed by single-particle dynamics, while for $Δ> 1$, doublon propagation dominates, resulting in a significantly slower growth of $M_2$. Furthermore, the magic exhibits logarithmic growth in time for both one and two-particle dynamics. Additionally, by examining the Pauli spectrum, we show that the statistical distribution of level spacings exhibits Poissonian behavior, independent of interaction strength or particle number. Our results shed light on the role of interactions on magic generation in a many-body system.

We have discovered specific conditions for generic scattering systems to act as wave splitters that are robust to any change in relative amplitude or phase of an arbitrary injected waveform. Specifically for complex systems with tunable parameters, these conditions for robust splitting (RS) are abundant, and by using multiple tunable parameters the relative amplitude and phase of the output signals can also be tuned. The splitting property of the systems works for all possible input phase differences and amplitude ratios and does not require a particular coherent input signal. We show experimentally that the fixed splitting ratios and output phases at RS conditions are robust to 100 dB of relative power and 2$π$ phase changes of the input waves to a complex non-Hermitian two-port system. We also demonstrate that the splitting power ratio can be tuned by multiple orders of magnitude and the RS conditions can be tuned to any desired frequency with suitable tunable perturbations embedded in the system. Although this phenomenon is realized in two-port systems and involves some degree of attenuation, tunable robust splitting can be achieved between any two ports of multiport systems. These results are general to all wave scattering phenomena (electromagnetic, acoustic, etc.) and hold in generic complex scattering systems.

This paper presents a geometrical analysis of finite length XY quantum chains. We begin by examining the ground state and the first excited state of the model, emphasizing the impact of finite size effects under two distinct choices of the Jordan Wigner transformation: the Neveu Schwartz (NS) and Ramond (R) sectors. We explore the geometric features of the system by analyzing the quantum (Berry) curvature derived from the Fubini Study metric, which is intimately connected to the quantum Fisher information. This approach uncovers a rich interplay between boundary conditions and quantum geometry. In the gamma h parameter space, we identify distinct sign changing arcs of the curvature, confined to some region. These arcs mark transitions between the NS and R sectors, indicating fundamental changes in the structure of the fermionic ground state. Remarkably, the number of such transition lines increases with system size, hinting at an emergent continuum of topological boundary effects in the thermodynamic limit. Our findings highlight a novel mechanism where boundary conditions shape quantum geometric properties, offering new insights into finite size topology and the structure of low dimensional quantum systems.

Energy transfer (ET) is a dipole-dipole interaction, mediated by the virtual photon. Traditionally, ET happens from the higher (donor) to lower bandgap (acceptor) material. However, in some rare instances, ET can happen from the lower-to-higher bandgap material, depending on the strong overlap between the acceptor photoluminescence (PL) and the donor absorption spectra. In this work, we report an ET process from the lower bandgap MoS2 to the higher bandgap WS2, due to a near 'resonant' overlap between the MoS2 B and WS2 A excitonic levels. Changing the MoS2 bandgap from direct-to-indirect by increasing the layer number results in a reduced ET rate, evidenced by the quenching of the WS2 PL emission. Our work shows at 300 K, the ET timescale of ~33 fs is faster than the reported thermalization of the MoS2 excitonic intervalley scattering (K to K') time and competing with the ultrafast charge transfer timescale. Thus, allowing us to open a new direction in understanding the competing inter/intralayer processes.

Nanoscale conductors are interesting for thermoelectrics because of their particular spectral features connecting separated heat and particle currents. Multiterminal devices in the quantum regime benefit from phase-coherent phenomena, which turns the thermoelectric effect nonlocal, and from tunable single-particle interactions. This way one can define quantum thermocouples which convert an injected heat current into useful power in an isothermal conductor, or work as refrigerators. Additionally, efficient heat management devices can be defined. We review recent theoretical and experimental progress in the research of multiterminal thermal and thermoelectric quantum transport leading to proposals of autonomous quantum heat engines and thermal devices.

We experimentally investigate the dynamics of exciton polariton Josephson junctions when the coupling between condensates is periodically modulated through self-induced mechanical oscillations. The condensates energy detuning, the analog of the bias voltage in superconducting junctions, displays a plateau behavior akin to the Shapiro steps. At each step massive tunneling of particles occurs featuring Shapiro-like spikes. These characteristic changes are observed when the condensates Josephson frequency $ω_\textrm{J}$ is an integer multiple of the modulation frequency $ω_\mathrm{M}$.

In the value-added literature, it is often claimed that regressing on empirical Bayes shrinkage estimates corrects for the measurement error problem in linear regression. We clarify the conditions needed; we argue that these conditions are stronger than the those needed for classical measurement error correction, which we advocate for instead. Moreover, we show that the classical estimator cannot be improved without stronger assumptions. We extend these results to regressions on nonlinear transformations of the latent attribute and find generically slow minimax estimation rates.

Decentralization is understood both by professionals in the blockchain industry and general users as a core design goal of permissionless ledgers. However, its meaning is far from universally agreed, and often it is easier to get opinions on what it is not, rather than what it is. In this paper, we solicit definitions of 'decentralization' and 'decentralization theatre' from blockchain node operators. Key to a definition is asking about effective decentralization strategies, as well as those that are ineffective. Malicious, deceptive, or incompetent strategies are commonly referred to by the term 'decentralization theatre.' Finally, we ask what is being decentralized. Via thematic analysis of interview transcripts, we find that most operators conceive of decentralization as existing broadly on a technical and a governance axis. This informs a two-axis model: network topology and governance topology, or the structure of decision-making power. Our key finding is that `decentralization' alone does not affect ledger immutability or systemic robustness.

To analyze the $\pm J$ XY spin-glass in three dimensions, we verified a method aimed at obtaining a high-precision dynamical exponent $z$ from the correlation length in the nonequilibrium relaxation process. The obtained $z$ yielded consistent and highly accurate results in previous studies for relatively well-studied models -- specifically, the three-dimensional (3D) ferromagnetic Ising model and the 3D $\pm J$ Ising model. Building on these previous studies, we used this method and the dynamical scaling method to analyze the 3D $\pm J$ XY model and obtained highly precise critical temperatures and exponents. These findings support the spin chirality decoupling picture, explaining the experimental spin-glass phase transition.

Confirming a conjecture of Erdős on the chromatic number of Kneser hypergraphs, Alon, Frankl and Lovász proved that in any $q$-colouring of the edges of the complete $r$-uniform hypergraph, there exists a monochromatic matching of size $\lfloor \frac{n+q-1}{r+q-1}\rfloor$. In this paper, we prove a transference version of this theorem. More precisely, for fixed $q$ and $r$, we show that with high probability, a monochromatic matching of approximately the same size exists in any $q$-colouring of a random hypergraph, already when the average degree is a sufficiently large constant. In fact, our main new result is a defect version of the Alon--Frankl--Lovász theorem for almost complete hypergraphs. From this, the transference version is obtained via a variant of the weak hypergraph regularity lemma. The proof of the defect version uses tools from extremal set theory developed in the study of the Erdős matching conjecture.