Papers

We develop multilevel adaptive-rank iterative methods for the solution of linear and nonlinear systems arising from high-dimensional partial differential equations. Our contributions are threefold. First, we extend the projection method of Ballani and Grasedyck [6] to enable flexible preconditioning of high-dimensional linear systems in low-rank tensor formats. Second, we construct multilevel preconditioning strategies by adapting geometric multigrid methods to the low-rank setting. In contrast to prior work, which primarily employs multigrid as a standalone solver, we emphasize its role as an efficient and robust preconditioner. Third, we integrate these techniques within an inexact Newton framework for the solution of nonlinear systems. The proposed methods are evaluated on a range of model problems, including both linear and nonlinear equations, to assess their convergence behavior and computational efficiency. The results demonstrate that multilevel adaptive-rank strategies yield robust and scalable preconditioners, providing effective solvers for high-dimensional problems in low-rank formats.

Motivated by the need to extrapolate the results from ground-based experiments to the conditions of high-speed flight, we present the Lie equivalence symmetry analysis of the hypersonic stagnation-point boundary layers. We demonstrate the application of the equivalence symmetry on the set of coupled ODEs which are physically relevant in hypersonics. By allowing the property laws to transform along with the independent and dependent variables, the invariants derived within the similarity-reduced stagnation-point ODE formulation identify families of non-linear maps that can be used to extrapolate the laboratory-scale predictions to flight. In practice, implementing these maps requires the laboratory-scale ODE solution together with the lab- and flight-side thermochemical property data, which are generally available from existing databases. The maps are derived for the similarity-reduced non-dimensional temperature across the boundary layer and are shown to {collapse with independently computed flight solutions} for a range of relevant cases.

We present a rigorous electronic-structure theory of strictly localized orbitals associated with a spatial partition of the one-electron Hilbert space that remains well defined in the complete basis-set limit. Each strictly localized orbital is supported on a spatial domain and may be discontinuous at domain interfaces. Using the interior-penalty discontinuous Galerkin method, these strictly localized orbitals can be employed in variational electronic-structure calculations despite their discontinuities at domain interfaces. As a proof of concept, we present numerical illustrations on one-dimensional diatomic model systems. They show that variational calculations can be carried out in a basis of strictly localized orbitals while maintaining good agreement with conventional calculations. Moreover, these strictly localized orbitals naturally lead to chemically intuitive representations of many-electron wave functions in the spirit of valence-bond theory.

A variation of the measured neutron flux using ${}^3$He detectors at a TRIGA Mk II nuclear research reactor during steady-state operation is reported in this article. The observed effect shows a statistically significant anti-correlation ($> 7\,\sigma$) between the temperature in the reactor pool and recorded neutron count rates. Following reactor start-up under nominal operating conditions, the effect occurs for a specific time period until both thermal equilibrium and a constant neutron count rate are reached. Simultaneous neutron and temperature measurements are performed in different configurations around the reactor in order to gain qualitative insights about the temperature dependent count rate behavior.

The multipoint kinetics (MPK) equations extend point kinetics models by tracking neutron populations in lumped reactor regions, offering improved spatial resolution at modest computational cost. However, determining the coupling coefficient matrix $K$ from transient data remains an open problem without established experimental procedures. This work provides some commentary on the task of recovering $K$ from observable forward flux measurements during reactor transients. Analytical solutions to the Kobayashi MPK formulation in the case of no precursors and with a single precursor family are derived in spectral form, enabling a mathematically rigorous investigation of eigenmode behavior and parameter observability. Coupling coefficient recoverability is investigated using modal sensitivity analysis and the Hessian condition number of the spectral recovery problem. The inclusion of delayed neutron precursors delays this eigenmode divergence but may be insufficient for enabling practical recovery of $K$ in many scenarios. In conclusion, capturing the behavior of nondominant eigenmodes without oversampling the dominant eigenmode is critical to the recoverability of $K$ through transient data.

Alloyed aluminium nitride compounds constitute a promising class of ferroelectric materials due to their high remanent electric polarizations, large band gaps and structural compatibility with a growth on Si substrates. Such materials nonetheless possess large coercive fields and polarization-switching mechanisms are still debated. We performed first-principles calculations to investigate the stability of isolated point defects in the vicinity of a vertical inversion domain wall (DW). We found that all studied defects are energetically more stable at or near the DW. Depending on their nature, they can have the opposite effect on the displacement of the DW, which occurs during polarization switching. Finally, we discuss how likely the different defects may be responsible for leaking currents and degraded ferroelectric properties.

This review examines the theory of superconductivity in systems with singular dynamical electron-electron interaction and contrasts it with a conventional BCS superconductivity. Examples include metals near a Quantum Critical Point, quantum dots and system near a localization (Mott) transition. We show, that the singular interaction destroys the traditional separation of energy scales, invalidating the significance of Cooper logarithm, and, as the consequence, the whole BCS framework. We explore the universal model with dynamical interaction $\Gamma (\Omega) \propto 1/|\Omega|^\gamma$ (the $\gamma$-model) and analyze the competition/interplay between the tendency towards pairing and towards non-Fermi liquid behavior. We show that superconductivity still develops once the pairing interaction exceeds a certain threshold, but the origin of the pairing is qualitatively different from that in BCS theory. We show that the gap equation at $T=0$ has an infinite set of topologically distinct solutions. These solution disappear one by one once the pairing interaction becomes non-singular (massive). We review the physics underlying these phenomena and outline future directions.

We report an ab initio and master-equation investigation of the gas-phase reactions of thioformaldehyde (H2CS) with CN and CCH radicals, motivated by the recent detection of the S-containing species HCSCN and HCSCCH in cold interstellar environments. Structures and frequencies were obtained at the DSD-PBEP86/aug-cc-pVTZ level, with energetics refined by CCSD(T)-F12a calculations and kinetics treated using an energy-grained master equation. The CN + H2CS reaction proceeds through orientation-dependent entrance channels. Two barrierless addition pathways lead to a connected multi-well network that preferentially forms cyano thioformaldehyde, HCSCN + H, whereas abstraction-type channels leading to HNC + HCS or HCN + HCS contribute only marginally. The calculated kinetics indicate capture-controlled low-temperature reactivity and a strong preference for HCSCN formation, suggesting that this reaction should be considered in astrochemical models of cold clouds. For CCH + H2CS, barrierless capture gives access to two connected entrance adducts. Although the cyclic product is the most exothermic channel, its formation is kinetically hindered by a high-lying late transition state. The flux is shared between propynethial formation, HCSCCH + H, and the HCCH + HCS channel, with the latter being favored. These results show that subtle differences in radical structure, bonding preferences, and entrance-channel topology strongly affect product branching in S-containing radical-molecule reactions. The computed mechanisms and rate coefficients provide useful input for astrochemical models of sulfur chemistry in cold molecular clouds and for interpreting recent molecular detections in sources such as TMC-1.

The James Webb Space Telescope (JWST) has recently revealed evidence of supermassive black holes (SMBHs) forming in the cores of high redshift galaxies that grew in mass extremely rapidly during the first billion years of the universe. In this study we present a new solution where the growth mass factor of BHs, $\gamma(t) \propto \dot M_{BH}/M_{BH}$, varies with time, following the changes of radiative efficiency, $\epsilon$, and Eddington ratio, $\lambda_{Edd}$, caused by the variation in accretion flow. By optimizing the accretion rate, $\dot M_{BH}$, we obtained a solution that is universal, that is, which applies to any BH at any redshift. This suggests that the mass of the BH is a thermodynamics state function, in good agreement with the no hair theorem and the four laws of mechanics of BHs.

We numerically calculate the shear viscosity of quark-gluon matter via the Green-Kubo relation with an improved ZPC model. We include all $2\leftrightarrow 2$ parton cross sections at finite temperature, which are based on perturbative QCD and screened with thermal masses, and consider massless quark-gluon systems with Boltzmann statistics in chemical equilibrium. We then compare the Green-Kubo results with the analytical results from the leading-order Chapman-Enskog method for the same parton cross sections over the temperature range $150-600$ MeV. We also examine the simpler case of isotropic and constant parton cross sections. Overall, we find that the two methods agree rather well. Specifically, the Green-Kubo results are greater than the Chapman-Enskog results by an average of $\sim 9\%$ for isotropic and constant cross sections and by an average of $\sim 3\%$ for finite-temperature pQCD cross sections, where the difference between the two methods is presumably due to higher-order corrections to the leading-order Chapman-Enskog results.

In this work, we study the fluctuations of a Mixture of Experts (MoE) generated by a quantum neural network trained via gradient flow on supervised learning problems. Our main results establish the Central Limit Theorem (CLT), and Sanov's principle for an MoE as the number of experts diverges. We demonstrate that the fluctuations of the empirical measure of its parameters close to its corresponding limit probability measure solve a linear transport equation. As a byproduct, we show that the MoE converges to a limit function which solves an evolution equation governed by the neural tangent kernel associated with the quantum neural network.

The scientific utility of large single-dish radio telescopes depends critically on the stability and fidelity of their beam patterns, which govern angular resolution, sensitivity, and polarimetric accuracy. For the 32-m Ghana Radio Astronomy Observatory (GRAO) antenna, electromagnetic simulations reveal residual sidelobes, structural diffraction, and cross-polar leakage that limit performance in high-dynamic-range and polarisation-sensitive observations. To address these limitations, we develop a finite-impulse-response (FIR) spatial filtering framework that reformulates beam optimisation as a digital signal processing problem. By exploiting the equivalence between angular displacement and spatial frequency, classical FIR design methods, window-based and Parks-McClellan algorithms are adapted to operate directly on simulated Jones fields. This approach enables controlled suppression of high spatial frequency artefacts responsible for sidelobes and polarisation mixing, while preserving the telescope's diffraction-limited resolution. Applied to the GRAO 5 GHz beam model, the method achieves substantial reductions in near-in sidelobe ripple, improves beam smoothness, and lowers cross-polar leakage below -30 dB at boresight. These improvements translate into enhanced calibration stability and polarimetric precision, strengthening the telescope's capacity for Very Long Baseline Interferometry, spectral-line surveys, and pulsar timing. Beyond GRAO, the method provides a generalisable, non-invasive, and computationally efficient pathway for beam control applicable to other single-dish and phased-array instruments. The results establish digital spatial filtering as a practical complement to conventional optical or mechanical optimisation, advancing the integration of electromagnetic modelling and signal processing in next-generation radio astronomical instrumentation.

Accurate initialization of polymer architectures remains a critical yet underappreciated determinant of reliability in molecular dynamics simulations of soft matter systems. Errors in coordinate generation and connectivity assignment frequently introduce artificial stresses, topological inconsistencies, and numerical instabilities that propagate throughout simulation trajectories. Here, we present a topology-preserving Python framework for generating star and cyclic polymer architectures with deterministic bond connectivity, exact ring closure, excluded volume enforcement, and spatial-hashing-based overlap detection. The algorithm produces LAMMPS-compatible data files under atom style full without reliance on third-party libraries. We demonstrate that the generated structures exhibit mechanical stability at initialization, suppressed artificial energy spikes, and consistent thermodynamic behavior during equilibration. Benchmark comparisons against naive random placement schemes reveal significant reductions in overlap-induced instabilities and improved reproducibility of structural and dynamical observables. The presented framework establishes initialization as a controlled physical boundary condition rather than a stochastic preprocessing step, thereby enhancing the reliability and reproducibility of polymer molecular dynamics simulations.

This paper investigates the effectiveness and structural limits of Variational Quantum Classifiers (VQC) for detecting network anomalies in the era of Noisy Intermediate-Scale Quantum (NISQ) systems. Using the official 20% research subset of the NSL-KDD dataset, a 4-qubit classifier featuring a 24-parameter trainable ansatz was developed, utilizing amplitude encoding to embed 16 principal components. On a held-out partition of this subset, the model achieved a consistent binary-classification accuracy of 88%. A comparative evaluation with two fundamentally different optimizers, COBYLA and SPSA, found that the observed performance plateau is not attributable to convergence to local minima, a result we interpret as consistent with an encoding-related expressibility limit rather than an optimization artifact. An architectural parity comparison with a classical neural network (a Tiny MLP with four nodes, achieving 97% accuracy) highlighted the expressiveness gap associated with data overcompression into restricted quantum states. The model was trained on a class-balanced set spanning the 22 raw NSL-KDD attack categories and evaluated in-sample as a probe of representational capacity: under this configuration the VQC reached only 9% accuracy and exhibited a degenerate mode collapse onto a small subset of classes. We interpret this behavior as consistent with the loss of linear separability induced by excessive compression in the quantum probability space, while explicitly noting that our experiments do not isolate the encoding from the ansatz depth, optimizer budget, and measurement-decoding scheme (see Limitations). Motivated by these observations and by Cover's theorem, we outline an alternative paradigm: a 16-qubit VQC with angle encoding that expands the Hilbert-space representation rather than relying on aggressive classical dimensionality reduction.

In X-ray scanning probe tomography, reconstruction quality generally improves with larger numbers of projections. However, additional projections increase experiment costs, acquisition time, and the radiation dose imparted to the sample. One mitigation to these trade-offs is to adopt a sequential design of experiments, in which each subsequent measurement is determined as a function of previously acquired data in order to maximize information gain. In scanning probe tomography, a widely used heuristic to maximize information is to align beams with the edges of the sample. A key challenge, however, is that the true sample is unknown, so identifying edge-aligned beams typically requires reconstructing the sample based on available measurements. This work proposes a novel sequential design method that identifies edge-aligned measurements directly from the sinogram, bypassing any reconstruction, thereby improving computational efficiency and reducing the experimental design's susceptibility to reconstruction errors. Our method dynamically selects the next set of measurement beams by maximizing an acquisition function that balances exploration and exploitation over the domain of all possible measurements, improving reconstruction quality while reducing measurement redundancy.

The pair-density wave (PDW) state, characterized by Cooper pairing at finite momentum, is a long-sought superconducting phase whose possible realization in Kagome metals is particularly intriguing in the strongly correlated regime. We investigate superconductivity in the extended $t$-$J$ model on the Kagome lattice and show that the symmetry-enforced sublattice structure of the Bloch wavefunctions gives rise to a rich landscape of unconventional pairing states. When the chemical potential is tuned to a sublattice-pure ($p$-type) van Hove singularity (vHS), a PDW state inevitably emerges. Near the $m'$-type vHS, which features opposite mirror eigenvalues to the conventional $m$-type vHS, intraband chiral, uniform, and nematic pairing states compete. When further-neighbor hoppings drive the $p$- and $m'$-type vHSs towards near degeneracy, phase frustration in the interband pairing channel stabilizes a chiral interband state. Our results reveal the previously overlooked $m'$-type vHS as a distinct route to unconventional superconductivity rooted in electronic correlations and mirror-symmetry-constrained Bloch wavefunctions.

We investigate the gravitational form factors (GFFs) and the generalized parton distributions (GPDs) of the deuteron within the framework of the hard-wall AdS/QCD model. The momentum dependence of the GFFs obtained here is in good agreement with the results of the soft-wall AdS/QCD model. The value of the gravitational mean square radius in this model agrees with the experimental data. GFFs provide a holographic description of the. Deuteron GPDs are obtained from GFFs via sum rules and have shapes of plots similar to those for GPDs extracted from the electromagnetic form factors (EFFs) calculated in the framework of the soft-wall AdS/QCD model.

We present analytic results for the next-to-next-to-leading-order QCD corrections to heavy-quark production in charged-current deep-inelastic scattering, retaining the exact dependence on the charm quark mass. We compute the complete partonic coefficient functions for the structure functions $F_2$, $F_L$, and $F_3$ in the quark and gluon channels, including contributions with up to three heavy quarks in the final state. Working within the reverse-unitarity framework, we use integration-by-parts and canonical differential-equations techniques to express all contributions with at most two final-state heavy quarks in terms of manifestly real Goncharov polylogarithms which allow for a robust and efficient numerical evaluation. The three-heavy-quark contribution involves elliptic structures for which we give a general representation in terms of Chen iterated integrals, as well as expressions in terms of rapidly convergent expansions that are valid in the perturbative $Q\gtrsim 5~{\rm GeV}$ region and also allow for a flexible and fast numerical evaluation. We validate our results against known exact results at lower orders, massless NNLO coefficient functions, and existing leading-power expansions in the asymptotic limit where the virtuality $Q$ is much larger than the charm mass.

Long-term records of the Martian atmosphere based on general circulation models and reanalysis of atmospheric state variables are important to understand the diurnal, seasonal, and climatological changes of the planet. Atmospheric dynamics of the Martian atmosphere are strongly influenced by the characterization of dust lifting, solar insolation, and spatial variations in topography. We present ARCO-Mars, a unified Analysis-Ready Cloud-Optimized dataset providing integrated access to three independent Mars atmospheric reanalysis products: EMARS, MACDA, and OpenMARS spanning over Mars Years 24-35. These reanalyses assimilate thermal infrared retrievals from the MGS/TES, ODY/THEMIS, and MRO/MCS instruments, providing both two and three-dimensional surface and atmospheric state variables, including temperature, winds, surface pressure, and dust optical depth. The dataset is stored in Zarr v3 format and hosted on HuggingFace, enabling efficient cloud-based access without requiring local storage of the full archive. We compare the state variables between the three reanalysis products to identify systematic differences, attributed to differences in data assimilation and general circulation models. ARCO-Mars provides a community resource for Mars atmospheric science, numerical weather prediction validation, and machine learning applications, including weather forecasting and data assimilation.

Temporal networks underlie a wide range of social, technological, and biological phenomena, highlighting how temporal inhomogeneities drive interactions in complex systems. Despite vast research on the area, the way temporal network connectivity evolves across time scales remains poorly understood. By analyzing temporal network data of informational and societal origin, involving tens of systems, millions of nodes, and observation periods from days to years, we find systematic evidence of an optimal time scale for coarse-graining interaction events. At this level of aggregation, networks are maximally dynamic in their local structure, while retaining system-wide connectivity. To understand the origins of such a seemingly generic interplay of time and topology, we explore a minimal temporal network model based on uncorrelated renewal processes, and show that intermittent yet globally connected activity may arise solely due to heterogeneities in inter-event times and degrees, and no other system-specific details. All coarse-grained empirical networks studied show persistent patterns of cyclic node degree change yet stationary system-level degree distributions, a striking coexistence of microscopic self-regulation and macroscopic stability. Our results give support to the notion of a universal pattern in temporal networks that involves both time and topology, via the nontrivial interplay of aggregation and temporal inhomogeneity, with consequences for the study of spreading dynamics on networks and the balance between robustness and adaptability in complex systems.

Kagome lattice crystal systems present interesting symmetry-protected band structure features such as flat bands, van Hove singularities, and linearly dispersing Dirac/Weyl points that provide a rich playground for strongly correlated electron physics. Motivated by the rich properties and charge density wave evolution through the 1-6-6 series of compounds, we present our results in single crystal growth and characterization of the of Lu$_{1-y}$Y$_y$(Nb$_{1-x}$Ta$_x$)$_6$Sn$_6$ double-alloy system, including evolution of the charge density wave transition, electrical transport behavior and resultant phase diagrams. Using a novel growth technique, the synthesis of high quality crystals with extended length along the crystallographic $c$-axis allows us to follow the gradual suppression of charge density wave (CDW) order with Y substitution, and observe quantum oscillations in both magnetoresistance and magnetization throughout the series. We review the evolution of Fermi surfaces, effective masses and quasiparticle dispersion through the alloy series, revealing a decrease in size of Fermi surfaces that trends with both substitutions, and a scaling between effective mass and Fermi wavevector that suggests a regime with Dirac-like dispersion. The ability to fine-tune crystallographic, ground state and electronic dispersion properties of the \lit\ system with minimal impact of disorder opens a path torward further understanding the nature of the kagome lattice and its novel states and interactions.

We investigate the domain structures of the \(G_2\) vacuum and the associated static potentials within the domain model, considering both zero and non-zero aggregate flux vacuum domains. Potentials associated with domains of zero aggregate flux exhibit favorable Casimir scaling and convexity properties at intermediate distances, and their long-range behavior matches the expected ordering of constant potential values according to representation. In contrast, potentials derived from domains with nonzero aggregate flux deviate from the key features of the confining force, as the absence of a minimal center-flux magnitude renders such configurations physically improbable. Furthermore, the potential ratios for \(SU(3)\) and \(SU(2)\) subgroups are found to be consistent with Casimir ratios of \(G_2\) at intermediate regimes, suggesting a possible role for these subgroups in the confinement mechanism of the \(G_2\) gauge group.

We develop a macroscopic continuous-variable model of stimulated four-wave mixing (4WM) yielding closed-form expressions for the mean intensity, variance, and covariance of bright probe and conjugate beams, valid for arbitrary transverse profiles of the pump and seed to all orders in the nonlinear interaction strength. The model uses a Dirac-comb expansion of the pump field, making the photon statistics computable pixel-by-pixel from one set of expressions. In the plane-wave limit, we recover the phase-insensitive amplifier results. Beyond this limit, the formalism explicitly demonstrates the spatial routing of information observed in earlier experiments: the seed angular spectrum is transferred to the twin-beam intensities, whereas the angular spectrum of the squared pump field is transferred to the spatial cross-correlation between the probe and conjugate. We characterize the parameter window of high-fidelity image transfer in the covariance, which is controlled by the seed-to-pump waist ratio and the interaction strength. Our model provides, in one analytical framework, a theoretical account of experiments encoding information in the bright intensities or non-locally in the spatial cross-correlations.

It is commonly assumed that the spin-orbit angles of binary black holes (BBHs) originating from dense stellar environments rapidly converge to an isotropic distribution following a number of strong gravitational encounters. We challenge this assumption by modeling the evolution of the BBH orbital angular momentum orientation through successive binary–single encounters as a random walk on the unit sphere, yielding an exact solution for the orientation distribution after $n$ encounters and a closed-form expression for the number of encounters required to reach isotropy. To characterize the step distribution, we conduct a large suite of Newtonian point-particle scattering experiments with an equal-mass binary, varying the mass of the single, and obtain semi-analytic expressions for both the mean step size and the full distribution of steps. Applying these results to BBHs with initially aligned spins, as may arise from the evolution of primordial massive binaries, we find that spin-orbit alignment can survive several strong encounters before being erased. This has direct implications for the slight trend toward spin-orbit alignment reported in GWTC-5.0 as well as for the retention of hierarchical merger products, such as the components of GW231123.

Quantum error mitigation on noisy devices is limited not only by residual bias but also by the shot noise and calibration errors introduced by the mitigation procedure itself. We derive finite-shot mean-square-error boundaries for probabilistic error cancellation (PEC), Clifford data regression (CDR), and no mitigation for noisy Pauli-observable estimates. Exact PEC removes the target bias under an exact noise inverse at the price of a quasi-probability variance overhead, whereas population linear CDR can have smaller target-shot variance but retains a calibration floor when the training and target noise responses do not match. This competition yields a finite CDR-dominant operating window whose upper endpoint scales as $B_{\mathrm{PEC}=\mathrm{CDR}}(p)\propto 1/(\delta_1^2p)$, where $\delta_1$ is the first-order CDR calibration mismatch. We further prove a target-response projection theorem showing that response-blind affine CDR removes the first-order bias only when the target noise response is affine in the ideal target value; otherwise a nonzero projection error gives an irreducible local calibration floor. The same mean-square-error formulation extends to second-order calibration, commuting Pauli Hamiltonians, finite CDR training shots, and residual PEC model bias. A closed-form two-qubit calculation and QAOA simulations support the predicted no-mitigation, CDR-dominant, and PEC-dominant regimes.

We propose and analytically demonstrate that the eigenphases of the scattering matrix provide direct, phase-sensitive signatures of EPs in open PT-symmetric systems. Using a 1D PT-symmetric quantum dimer with balanced gain and loss, coupled to continuum leads, we track the evolution of the scattering eigenphases across the PT-exact to broken transition. The imaginary parts of the eigenphases develop localized structures of opposite sign as the EP is approached, reflecting the emergence of gain/loss asymmetry in the scattering eigenmodes. The EP is located by the algebraic degeneracy condition of the S-matrix eigenvalues, and corroborated by two further, formally distinct analyses–the merging of the transmission resonances and the dynamics of the complex poles and zeros of S(E)–which place the transition within the same narrow parameter window, providing strong evidence for its location and physical reality. We then introduce the integrated imaginary scattering eigenphase G(gamma), which condenses the eigenphase information into a single experimentally accessible scalar and constitutes a fourth, resonance-free route to the same transition. G(gamma) is negligibly small in the PT-exact phase and undergoes a sharp transition–a pronounced inflection followed by saturation into a plateau–near the EP. The inflection point of G(gamma) precedes gamma_EP and coincides with the maximum amplitude of the transmission resonances, revealing that peak gain/loss asymmetry and eigenstate coalescence are governed by independent conditions in open systems–a direct fingerprint of their finite coupling to the continuum. Because the analysis is formulated entirely at the level of the S-matrix–without reference to any specific physical realization–the results are universally applicable across wave systems, like photonic, acoustic and microwave platforms where phase-resolved measurements are available.

Subdiffusive fractional Brownian motions produce localized aggregation when particles are stopped at exponentially distributed times. In applications where clumping and long-distance dispersal events are observed simultaneously, such as in some instances of seed dispersal, this model fails to describe the tails of the data. The resulting redistribution kernel has only an exponentially decaying tail, whereas a heavier tail is needed for modeling the long-distance dispersal observed. Here we propose a model in which subdiffusive particles stop at exponentially distributed times, but with a rate parameter that is Gamma distributed. This heterogeneity in stopping rates causes the density of final radial positions to have a heavy-tailed distribution. Our model retains the strong localized clumping characteristic of subdiffusive fractional Brownian motion while simultaneously generating the heavy tails required for realistic long-distance dispersal.

Stationary wave functions at the integer quantum Hall transition are known to be multifractal, but the exact form of the multifractality spectrum has remained a subject of debate. While conformal field theory arguments predict a parabolic law, numerical simulations show deviations from parabolicity. We resolve this discrepancy by pointing out that powers of the local wave intensity fail to obey the Gaussian Free Field and Abelian Fusion Hypothesis assumed in earlier analysis. Rather, due to the non-Abelian nature of the underlying effective field theory, wave intensity correlators are dressed by insertions of background charge distributed uniformly in space. An exact expression for the $q$-moments of point-contact generated eigenstates is presented. Numerical tests are performed for the critical Chalker-Coddington network model on a rectangular torus. Our results are in precise agreement with the predictions of conformal symmetry realized as a level-4 current algebra.

We investigate the intensity stability of the superradiant laser. Our study focuses on the architecture where a continuous beam of atoms in an electronically excited state crosses the mode of a high-finesse Fabry-Perot cavity, which has been proposed as a new architecture of an active optical clock. We show that such superradiant laser can become unstable and develop chaotic behavior. We derive an analytical criterion for this instability and find that it may only occur when the lifetime of photons in the cavity is significantly shorter than the lifetime of atoms. This criterion allows for refining the necessary parameters to run a superradiant laser as a frequency reference in the optical domain. In particular, we point-out the consequences of the instability on intensity fluctuations and laser linewidth. On the other hand, we also point out that the superradiant laser, when in the unstable regime, can become an interesting playground for studying chaos. At the mean-field level, there is a direct mapping to the Bénard instability associated with fluid turbulence; however quantum fluctuations associated with photon out-coupling and atom re-filling substantially modify the expected behaviors. Finally, we point-out the existence of a regular self-pulsing regime at large atom numbers.

The aim of this work is to study two-prover quantum games (i.e., games with quantum inputs and outputs) from an operator-algebraic and operator-space point of view. We characterize several notions of the value of such games by formulating them in terms of tensor norms in the category of operator spaces. The main results of the paper concern the description of the so-called no-signalling value of these games, for which we not only provide a precise operator-space formulation, but also establish close connections between this study and some problems in operator algebras. In particular, we show how the recent counterexample to Grothendieck's theorem for operator spaces given in \cite{Ara} can be understood as a direct consequence of results in quantum information theory. We also obtain new upper bounds on the gap between the no-signalling value and the quantum value of two-prover quantum games, improving the best previously known estimates.