We construct for a Schur concave function $f$ on the set of quantum states a tight upper bound on the difference $f(ρ)-f(σ)$ for a quantum state $ρ$ with finite $f(ρ)$ and any quantum state $σ$ $m$-partially majorized by the state $ρ$ in the sense described in [1]. We also obtain a tight upper bound on this difference under the additional condition $\frac{1}{2}\|ρ-σ\|_1\leq\varepsilon$ and find simple sufficient conditions for vanishing this bound with $\,\min\{\varepsilon,1/m\}\to0\,$. The obtained results are applied to the von Neumann entropy. The concept of $\varepsilon$-sufficient majorization rank of a quantum state with finite entropy is introduced and a tight upper bound on this quantity is derived and applied to the Gibbs states of a quantum oscillator. We also show how the obtained results can be reformulated for Schur concave functions on the set of probability distributions with a finite or countable set of outcomes.

In this work we explore the potential of implementing an optical quantum optimizer using non-linear optics, specifically using sum-frequency generation and/or two photon absorption. This proposal uses Zeno effects to enforce independence constraints and then a linear protocol to find a maximum independent set in a way where the elements of the set can be weighted. Our proposal can either be viewed as an implementation of the entropy computing paradigm presented in [Nguyen et.~al.~Communications Physics 1, 411, 8] which uses real rather than imaginary time evolution, or as quantum annealing within a Zeno constrained subspace. We discuss how such a device could be built, and considerations such as error mitigation, particularly for photon-loss errors. We numerically study aspects of the protocol, including the effect of coherent versus incoherent incarnations of the Zeno effect, finding superior performance from the former.

Reddened Type-1 quasars offer a unique window into the structure and evolution of active galactic nuclei (AGN), yet their physical origin and the source of their reddening remain uncertain. Optical surveys often miss these dust-obscured objects, resulting in an incomplete view of the quasar population. In this work, we construct a sample of 6,600 Type-1 quasars at redshifts $0.5 \leq z \leq 1.2$ by combining deep optical imaging from HSC with mid-infrared photometry from WISE, enabling a more complete selection that is not biased against reddened objects. We perform detailed SED modeling using the CIGALE code, enhanced by synthetic photometry derived from SDSS spectra to better constrain the optical continuum. We classify quasars into blue and reddened Type-1 populations based on their continuum slopes and compare their SEDs and emission line properties. As expected from this definition, reddened Type-1 AGN show higher dust extinction, with a median $A_V = 0.60^{+0.32}_{-0.19}$ mag, compared to $A_V = 0.06^{+0.10}_{-0.03}$ mag for blue objects. But they also exhibit smaller torus half-opening angles, with a median of $25.7^{+10.1}_{-8.7}$ deg, compared to $33.3^{+11.1}_{-5.9}$ deg for blue objects. While such extinction could arise on either galaxy or nuclear scales, the systematically stronger narrow-line equivalent widths and weaker Balmer broad lines in reddened Type-1s indicate that the obscuration acts on nuclear scales, likely from dust concentrated near the polar axis. We discuss the possibility that these structural differences may be linked to a sub-pc outflow, that carries dusty gas into the polar region and evacuates the torus region.

Many-body cages have very recently emerged as a general route for nonergodic behaviour in quantum matter. Here, we show that new types of many-body cages can be engineered in Floquet circuits with the potential to realize novel nonequilibrium quantum states. For that purpose, we first identify an explicit, general construction of Floquet circuits capable of hosting many-body cages. We then present a generic strategy to engineer and structure Floquet many-body cages. We demonstrate the developed scheme for the quantum hard disk model as a generic constrained model system, realizable for instance in Rydberg atom arrays. We construct Floquet circuits yielding Floquet many-body cages with topological properties and $π$-quasienergy modes, implying `time crystalline' spatiotemporal order. Our results can be directly extended to general quantum circuits, thus providing a new tool to engineer nonequilibrium behaviour in driven systems.

We study the computational complexity of 2-local Hamiltonian problems generated by a positive-weight symmetric interaction term, encompassing many canonical problems in statistical mechanics and optimization. We show these problems belong to one of three complexity phases: QMA-complete, StoqMA-complete, and reducible to a new problem we call EPR*. The phases are physically interpretable, corresponding to the energy level ordering of the local term. The EPR* problem is a simple generalization of the EPR problem of King. Inspired by empirically efficient algorithms for EPR, we conjecture that EPR* is in BPP. If true, this would complete the complexity classification of these problems, and imply EPR* is the transition point between easy and hard local Hamiltonians. Our proofs rely on perturbative gadgets. One simple gadget, when recursed, induces a renormalization-group-like flow on the space of local interaction terms. This gives the correct complexity picture, but does not run in polynomial time. To overcome this, we design a gadget based on a large spin chain, which we analyze via the Jordan-Wigner transformation.

The Energy Conserving Descent (ECD) algorithm was recently proposed (De Luca & Silverstein, 2022) as a global non-convex optimization method. Unlike gradient descent, appropriately configured ECD dynamics escape strict local minima and converge to a global minimum, making it appealing for machine learning optimization. We present the first analytical study of ECD, focusing on the one-dimensional setting for this first installment. We formalize a stochastic ECD dynamics (sECD) with energy-preserving noise, as well as a quantum analog of the ECD Hamiltonian (qECD), providing the foundation for a quantum algorithm through Hamiltonian simulation. For positive double-well objectives, we compute the expected hitting time from a local to the global minimum. We prove that both sECD and qECD yield exponential speedup over respective gradient descent baselines--stochastic gradient descent and its quantization. For objectives with tall barriers, qECD achieves a further speedup over sECD.

Scalar-induced gravitational waves (SIGWs) have recently attracted considerable interest, both as a possible explanation for the nanohertz signal reported by the Pulsar Timing Array (PTA) collaboration and for their connection with primordial black hole (PBH) physics. In addition to SIGWs, scalar-tensor-induced gravitational waves (STGWs) have emerged as a promising cosmological source of the stochastic gravitational wave background (SGWB). In this paper, we compute the STGWs generated during a generic matter-dominated (MD) era, as well as during an early matter-dominated (eMD) epoch followed by a sudden transition to the standard radiation-dominated (RD) stage, working in the Poisson gauge. We find that, in a purely MD age, the corresponding energy density rapidly dilutes, whereas in the presence of an eMD phase it remains non-vanishing due to the short duration of the eMD period. We then investigate whether the STGW signal could provide a dominant contribution to the $\texttt{NANOGrav 15-year}$ dataset and we forecast the prospects for its detection with future observations by the Square Kilometre Array (SKA). In particular, we consider STGWs generated during both eMD and RD eras, including their linear-order contributions. Our results show that the GWs induced by scalar-tensor mixing constitute a viable target for future, more sensitive detections of the SGWB.

We introduce a new equation-of-motion coupled-cluster method based on a pair coupled-cluster doubles (pCCD) reference, termed frozen-pair EOM-CCSD (EOM-fpCCSD). This approach combines the computational efficiency of the pCCD ansatz with a dynamical correlation correction, enabling a reliable description of electronically excited states within the EOM framework. The method has been implemented in the open-source PyBEST software package. Its performance is systematically benchmarked against standard EOM-CCSD and its pair-tailored variant (EOM-ptCCSD), using both canonical Hartree-Fock and pCCD natural orbitals. For charge-transfer (CT) excitations taken from the QUEST database, EOM-fpCCSD yields excitation energies very close to those of EOM-CCSD, outperforming EOM-ptCCSD, as well as to the theoretical best estimates (TBEs). Working within the localized pCCD natural orbital basis allows us to determine the directed CT character, which quantifies the directed charge flow from one molecular domain to another. Numerical results show that EOM-fpCCSD, EOM-CCSD, and EOM-ptCCSD provide nearly identical descriptions of the directed CT character, despite changes in excitation energies. The true advantage of EOM-fpCCSD becomes evident for the challenging QUEST subset of doubly excited states. While EOM-ptCCSD performs similarly to standard EOM-CCSD, EOM-fpCCSD significantly outperforms both methods for these problematic states compared to TBEs. In addition to improving the accuracy of excitation energies, EOM-fpCCSD also converges for several states that standard EOM-CCSD and EOM-ptCCSD fail to converge. These results demonstrate that EOM-fpCCSD offers a promising and computationally efficient route toward a more accurate description of complex electronic excitations.

We investigate the cosmological implications of non-polynomial quasi-topological gravity (NPQTG), a novel class of modified gravitational theories in which the background dynamics is encoded in a single function of the Hubble parameter. This framework provides a minimal and theoretically consistent extension of general relativity, incorporating higher-curvature effects while preserving second-order field equations and avoiding higher-derivative instabilities. We first establish the general conditions for cosmological viability and construct explicit realizations, including polynomial, quartic, power-law and non-polynomial models, demonstrating how different functional forms lead to distinct expansion histories. Focusing on the quartic and power-law cases, we show that the resulting cosmological evolution reproduces the standard thermal history of the Universe and gives rise to an effective dark-energy sector of geometric origin, with dynamical equation-of-state behavior that can lie in the quintessence or phantom regime. We then confront the models with observational data from Type Ia Supernovae, Cosmic Chronometers, and Baryon Acoustic Oscillations, using a Bayesian MCMC analysis. We find that both models provide an excellent fit to the data, remaining fully compatible with current constraints and statistically competitive with $Λ$CDM. Our results demonstrate that NPQTG offers a simple and efficient framework for describing late-time cosmic acceleration with dynamical dark energy, while maintaining theoretical consistency and observational viability.

Little Red Dots (LRDs) are a population of compact, red sources that have emerged as one of the most puzzling findings of JWST. Variability provides a direct probe of their central engines. Here we present the first joint spectroscopic and photometric time-domain study of LRDs undertaken with the JWST TWINKLE slitless spectroscopy program. Surveying the FRESCO GOODS-North legacy field, TWINKLE monitors a complete, H$α$-flux-limited sample of 18 LRDs at z = 3.9-6.8, achieving a rest-frame baseline of $\sim$140-220 days. We detect no variability in photometry, H$α$ line flux, or line shape across the sample. If LRDs resembled AGN in reverberation mapping samples -- the foundation for black hole mass calibrations and luminosity scaling relations -- we would expect >10 sources to show measurable fluctuations. Observing none implies a 5.9$σ$ deficit. The non-detections hold across all broad H$α$ emitters within TWINKLE's field of view -- the 18 V-shaped LRDs as well as 9 non-LRDs. Comparison with simulated light curves disfavors sub-Eddington accretion and is instead consistent with super-Eddington accretion, other mechanisms that suppress variability, or perhaps no AGN whatsoever. If LRDs do harbor black holes, calibrations derived from sub-Eddington systems may not apply, thereby explaining JWST's apparently "overmassive" black holes. These observations provide unique constraints on the physics of one of the most enigmatic populations discovered by JWST.

Supersonic winds from massive stars carry great amounts of kinetic power and modify the surrounding interstellar medium. Through this interaction a stellar bubble is formed. Theoretical studies and recent observations suggest that the winds of massive stars could be sources of Galactic cosmic rays. The first detection of synchrotron emission from the bubble of a single star was reported, indicating the presence of relativistic electrons. Studying the non-thermal emission from a single massive star can help to better understand the acceleration of particles taking place in massive star clusters. WR 102 is the perfect case of study. In this work, we present the first high-energy model for the bubble of WR 102: G2.4+1.4. We aim at fitting the radio data and predicting gamma-ray emission. We assume that both electrons and protons are accelerated at the wind shock. We applied a classical model for the stellar bubble and adopted a one-zone model for estimating the radiation produced by the relativistic particles near the acceleration region. Additionally, we computed the expected emission from the protons that diffuse to the outer regions of the bubble. Also, we estimated the leptonic and hadronic contributions expected from cosmic rays. We fitted the observations considering that 3% of the wind kinetic power goes into relativistic electrons, and a magnetic field of 250 $μ$G. The dominant component at high energies is produced by locally accelerated protons reaching the shell. Protons might reach PeV energies in the wind bubble, but the predicted gamma-ray flux is too low to be detectable.

We investigate how strongly late-time inferences about DE dynamics depend on the functional prior used to represent the expansion history. Using identical late-time combinations of CC, DESI BAO measurements, the Pantheon+ SN1a sample, and the H0DN prior, we compare a node-based reconstruction of the reduced Hubble function $E(z)$ with a representative family of smooth low-dimensional DE EoS parametrizations, including CPL. Over the redshift range constrained by the data, both approaches yield consistent $H(z)$, and, in the absence of H0DN, compatible values of $H_0$. However, a clear method dependence emerges at intermediate redshift ($z\sim1.7$): the reconstruction favors stronger deceleration, $q_{\rm Rec}(1.7)\simeq0.56-0.61$, whereas the smooth parametrizations cluster at $q(1.7)\simeq0.32-0.40$, implying a persistent $\sim2-3σ$ discrepancy across dataset combinations and parametrizations. For the EoS-based parametrizations, whose effective DE densities remain positive by construction, the preferred $w_{\rm DE}(1.7)<-1$ values correspond to NECB-violating (phantom-like) behaviour, but this is a less robust discriminator as $w_{\rm DE}$ becomes ill-conditioned as $ρ_{\rm DE}\to0$. In the effective-fluid mapping, the reconstruction accommodates the same late-time kinematical preference through a rapid descent of $ρ_{\rm DE}(z)$ toward very small values and a sign change, whereas the EoS-based parametrizations absorb it through smoother, and in several cases NECB-violating, evolution over $z\sim1-2$. Although the reconstruction improves the best-fit likelihood, especially with H0DN, Bayesian evidence continues to favor the simpler parametric descriptions. Our results isolate $z\sim1.5-2$ as the key window in which EoS-based DE parametrizations can compress localized kinematic structure and associated features of DE that are still permitted by current late-time data.

The emergence of Cryptographically Relevant Quantum Computers (CRQCs) presents a critical threat to classical cryptographic systems, particularly widely adopted protocols such as RSA, Diffie-Hellman (DH), and Elliptic Curve Cryptography (ECC). Given their extensive use in the financial sector, the advent of quantum adversaries compels banking institutions to proactively develop and adopt quantum-safe communication mechanisms. This paper introduces a hybrid quantum-safe architecture, orchestrated via Software-Defined Networking (SDN) key distribution. The proposed framework enables the early integration of Classical Cryptography (CC), Quantum Key Distribution (QKD), and Post-Quantum Cryptography (PQC) within a Dynamic Multipoint Virtual Private Network (DMVPN) environment, providing highly scalable, full-mesh, site-to-site encrypted communications for enterprise networks. This is particularly relevant at a time when PQC algorithms have not yet been incorporated into finalized IPsec standards. The architecture has been validated across a five-node testbed comprising three physical nodes within a campus network in Madrid and two private-cloud nodes located in the north of Spain and Mexico. The deployment leverages a heterogeneous mix of physical and virtual devices, diverse technology providers, Discrete Variable QKD (DV-QKD) and Continuous Variable QKD (CV-QKD) implementations, and mutually incompatible key-delivery interfaces (ETSI004, ETSI014 and Cisco SKIP), demonstrating flexibility, scalability, and interoperability across environments. Through this framework, we demonstrate that quantum-safe communication in financial networks is not only technically feasible but also scalable, interoperable, and resilient. The proposed architecture establishes a robust, flexible, and future-proof foundation for secure financial communications in the era of quantum computing.

We develop a variationally consistent mesoscopic extension of Cosserat elasticity motivated by the breakdown of compatibility in classical formulations. By admitting compatibility-breaking perturbations, the classical theory ceases to remain closed under admissible variations, necessitating an enlargement of the constitutive framework. This leads naturally to a formulation in which torsion and curvature are treated as independent distributed measures of defects. The theory is constructed using a Palatini-type variational approach, with the coframe and connection as independent fields. The resulting Euler--Lagrange equations yield both the standard balance laws and defect-related excitation fields. Material invariance gives rise to configurational forces and moments, which emerge as Noether currents and are directly linked to defect transport governed by the Bianchi identities. The framework provides a unified description of defect kinematics, configurational mechanics, and microstructural evolution. Illustrative examples and numerical evaluations demonstrate how defect transport generates configurational forces and highlight the underlying Maxwell-type structure of the theory. The proposed formulation offers a consistent geometric foundation for the analysis of structured solids with evolving internal geometry and provides a basis for future developments in defect dynamics and dissipative processes.

It is known that the semiclassical approximation to the gravity path integral can be leveraged to explain certain inherently quantum aspects of gravity. One such aspect is the state-counting interpretation of the Bekenstein-Hawking entropy of black holes. A second aspect is the Page curve for the entanglement entropy of Hawking radiation, which agrees with expectations from unitarity. We show that these two questions are equivalent from the gravity path integral point of view. In particular, the Hawking's information loss puzzle gets resolved automatically by considering any (over)complete basis of black hole microstates which is compatible with black hole entropy. The tool which relates the two questions is a convex optimization problem for the von Neumann entropy of Hawking radiation.

Comparison of the measured spectral emission properties of single-crystal Cu(001) and W(111) photocathodes to established photoemission theories reveal evidence for an additional one photon emission process predominantly affecting electron emission near and below the photoemission threshold. This additional photoemission process is postulated to be due to a momentum-resonant Franck-Condon mechanism mediated by inelastic Umklapp electron scattering. An initial first-principles simulation of this emission process (involving the electron thermal effective mass, the inelastic electron mean free path at the vacuum level, and the number of Fermi surfaces in the metal), when combined with a direct one-step band emission model, is consistent with the measured spectral dependencies of both the quantum efficiency and mean transverse energy of electron photoemission from the two single-crystal metal photocathodes.

Through semiclassical methods the subject of quantum chaos motivates and depends on Hamiltonian chaos research. Presented here is a selection of Hamiltonian chaos topics that in this way get directly related to any of a variety of quantum chaos research problems. The chapter begins with a description of various useful theoretical and computational tools of chaos research, e.g.~surfaces of section, paradigms of chaos, stability analysis, and symbolic dynamics... This is followed by discussions regarding the geometry of chaos, how chaotic systems respond to perturbations, and the complexification of Hamiltonian dynamics. The emphasis is on intuitive explanations and illustrations of various ideas with the references containing more mathematically rigorous expositions.

We study the dynamical spin and nematic correlations in the bilinear-biquadratic spin-1 chain in the critical phase hosting deconfined spinons. We demonstrate how spinon interactions can be directly probed in the presence of a magnetic field or a single-ion anisotropy. Our analytical predictions are supported by numerical matrix-product-state (MPS) simulations of the underlying microscopic model.

Inspired by the structure of $srs$ Laves networks in $\mathbb{R}^3$ that underpin the celebrated gyroid surface, we construct a Laves network of identical three-coordinated vertices on $S^3$ with double-twist. This network is a subset of the vertices and edges of the 600-cell, and can be viewed as a bipartite graph of disjoint 24-cell vertices inscribed in the 600-cell. We describe mutually entangled realizations of this network on $S^3$, and describe their relation to the well-known $srs$ Laves network structure in $\mathbb{R}^3$.

A screening of oxygen profiles in mid-T treated SRF cavities is crucial, in order to infer physical correlations between the microscopic cavity lattice and cavity performance - a problem concerning acceleration physicists for years. This thesis provides an analysis of oxygen diffusion profiles for three differently treated samples: Two mid-T baked and the third with the standard EuXFEL recipe. The measurement method utilizes EXAFS spectroscopy and was carried out at the DELTA facility in Dortmund. The result suffers heavily under noise, making the quantity of the result barely useable. Qualitatively, no deviations of current models regarding the profiles, could be proven, and no results of previous studies were contradicted. The experimental analysis is described in precision, interpretations of the possible are undertaken and theoretical considerations regarding error estimation and possible EXAFS simulations for future attempts are provided. A repetition at the PETRA III facility is indicated.

This paper examines the polarization-dependent output of various types of 3-mode photonic lanterns fabricated using double-clad fibers. We explore the sensitivity of the modal response across several types of photonic lanterns, from the fully symmetric and strongly coupled structure of regular photonic lanterns to the fully asymmetric structure of mode-selective photonic lanterns. We demonstrate the high sensitivity of the output of photonic lanterns with strong coupling between their ports to the polarization of the input state. In contrast, ports with high isolation or low coupling, such as in mode-selective photonic lanterns, exhibit responses that are almost polarization independent.

The tunable interaction between stationary quantum bits and propagating modes of light allows for the encoding of quantum information in the state of itinerant photons. This ability fulfills a central requirement for quantum networking, enabling quantum state transfer between distant quantum devices. Conventionally, a symmetric envelope of the photon wavepacket is used for such purposes. Yet, the use of alternative \textit{temporal modes} enables multiple applications in waveguide quantum electrodynamics that remain unexplored experimentally. Here, we use superconducting quantum circuits to generate individual itinerant microwave photons shaped in three mutually orthogonal temporal modes. We transfer the created photons across a 30-m cryogenic link, showing that the orthogonality allows us to decide at the receiver which mode to absorb, reflecting the other two with a selectivity ratio of 40. This experimental capability extends the microwave-frequency quantum communication toolbox, enabling a new photonic degree of freedom.

The Wiedemann--Franz law, which determines the universality of the ratio of thermal conductivity to electrical conductivity, is studied in the hydrodynamic electron transport regime, where electron--electron scattering predominates over scattering by disorder. In this case, the different relaxation of electric and thermal currents can lead to a violation of the Wiedemann--Franz law, which is expected to be even more pronounced in mesoscopic electron systems. This paper reports the propagation of hot electrons in a GaAs hydrodynamic narrow channel, studied using micrometer-resolution photoluminescence thermometry. A temperature dependence of the Lorenz number was obtained, indicating a violation of the Wiedemann--Franz law. The important role of narrow constrictions in this violation was also demonstrated, and theoretical arguments are presented.

In Hermitian impurity scattering, each isolated late-time exponential is the fingerprint of a bound state. We show that this correspondence breaks down in non-Hermitian bands. For a single impurity in a non-Hermitian lattice, the late-time signal is controlled by isolated complex frequencies selected by the analytic continuation of the Green's function relevant to real-time dynamics, which we term dynamical poles (DPs). DPs need not coincide with static bound states: one may appear without any bound-state counterpart, while a static bound state may be dynamically invisible. The remainder of the signal is an incoherent background set by complex continuum edges. Our results establish that the real-time analytic structure of the Green's function, not the static eigenvalue problem alone, organizes non-Hermitian impurity scattering.

Slender magnetic elements provide a versatile platform for programmable shape-morphing under remote magnetic actuation. However, a general and physically interpretable framework for the inverse design of a `magneto-elastica' under prescribed boundary conditions remains lacking. In this work, we develop an explicit analytical formulation for the inverse design of a magneto-elastica based on the integral form of the moment equilibrium equations. This approach yields direct constraints on the admissible curvature and rotation fields, enabling a systematic characterization of the feasible design space. We identify the key dimensionless parameters that govern the competition between magnetic torques and elastic restoring moments and show that the applied boundary conditions are an essential ingredient. We obtain closed-form solutions for the beam tapering profiles required to generate desired actuated shapes in the cases of clamped--free and clamped--clamped configurations; in the latter case, this includes analytical expressions for the boundary reactions. The formulation recovers the classical inverse elastica in the absence of magnetic fields and reveals a linear scaling between curvature deviation and magnetic mismatch. A tessellation strategy based on stiffness tailoring is further proposed for the design of discretized morphing surfaces. The theoretical predictions are validated against discrete elastic rod simulations and experiments across representative geometries. This work establishes a consistent analytical framework for the inverse design of a magneto-elastica and provides new insight into magnetically-induced shape programming in slender structures.

VLBI measurements of the sizes of compact extragalactic radio sources, jetted active galactic nuclei, provide data for probing the angular size--redshift relation, offering a complementary test to other distance--redshift methods. We analyse a significantly expanded dataset to reassess the angular size--redshift relation and its potential for constraining cosmological model parameters, focusing on the matter density parameter $Ω_{\mathrm{m}}$ in a flat $Λ$ Cold Dark Matter Universe. This is the first major update of the compact-source angular size test in the past quarter of a century, using a dataset an order of magnitude larger than in previous studies. MCMC analysis on real data and on multiple mock catalogues to evaluate parameter constraints in the presence of observational scatter. In addition, we conducted a test with 100 randomized catalogues created by shuffling redshifts while preserving other observables. We also explored how astrophysical parameters depend on fixed cosmological models with different $Ω_{\mathrm{m}}$ values. The randomization test showed that the posterior distributions from randomized data do not overlap with those from real observations, confirming that the measured angular size--redshift relation is physically meaningful. The astrophysical model parameter that describes the redshift dependence of the source angular size exhibits degeneracy with $Ω_{\mathrm{m}}$. Simulated mock catalogues indicate that the method is able to constrain $Ω_{\mathrm{m}}$ if the data scatter is below $\sim20\%$. Scaling estimates suggest that high-quality data of samples of several thousands to $\sim 100\,000$ sources, a standardisation calibration approach, and/or refining sample selection criteria are needed to fully exploit the potential of the angular size--redshift test with this type of objects (abridged).

Recent advances in data-driven modeling have shown that diffusion models can successfully generate synthetic Lagrangian trajectories in turbulent flows. Building on this progress, we extend the method to the joint generation of pairs of Lagrangian velocity trajectories, enabling a fully data-driven representation of turbulent pair dispersion, a long-standing fundamental problem with broad relevance in fluid dynamics. We demonstrate that diffusion models accurately reproduce the evolution of particle-pair separation, including deviations from Richardson's classical scaling law, while simultaneously preserving all key single-particle statistical properties reported in previous studies. These findings underscore the potential of diffusion-based generative models to emulate high-dimensional, multi-scale turbulent dynamics, further establishing them as a powerful tool for scientific modeling and for future geophysical and astrophysical applications.

We propose a variant of the model-independent method for determining meson charge radii from spatial moments of correlation functions on the lattice. Traditional determinations based on fits to the momentum transfer squared dependence of form factors are subject to systematic uncertainties arising from the choice of fit ansatz. By contrast, model-independent methods based on spatial moments provide a useful framework for determining the slope of the form factor without assuming its functional form. Recently, Feng et al. proposed a model-independent method, which drastically suppresses the finite-volume effect in the charge radius coming from higher-order contributions of the expansion of the form factor with respect to the momentum transfer squared. In this work, we introduce an auxiliary function of the momentum transfer squared and reformulate the method in terms of its product with the form factor, rather than the form factor itself, thereby further suppressing higher-order contributions, notably in cases of small volume and large radius. In particular, we investigate quadratic and logarithmic forms as practical choices for this auxiliary function. Applying this method to mock data based on a monopole form factor, as well as to actual lattice QCD data using $N_f=2+1$ gauge ensembles at $m_π\simeq 0.5$ and $0.3$ GeV, we find that it reduces residual finite-volume effects and provides an effective framework for meson charge radius determinations.

We present an efficient implementation of the low-cost linear-response coupled-cluster singles and doubles (LR-CCSD) method for computing static and frequency-dependent polarizabilities in systems with significant relativistic and electron-correlation effects. The approach employs X2C-based Hamiltonians (X2CAMF and X2CMP) and incorporates Cholesky decomposition to reduce memory requirements. In the current implementation, costly three- and four-external index integrals are generated on the fly, eliminating the need for their storage. Benchmark results indicate that the X2CMP Hamiltonian provides more consistent performance than X2CAMF, particularly for large and highly augmented basis sets. The proposed FNS++CD-X2CMP-LR-CCSD method shows excellent agreement with four-component reference values across a wide range of systems. Additionally, different strategies for constructing the FNS++ basis were assessed, and an averaged density approach was found to offer a favorable balance between accuracy and computational cost. On average, about 73% of the virtual spinor space is removed, demonstrating the efficiency and consistency of the FNS++ density-based truncation approach. The present implementation enables accurate and scalable relativistic response calculations for large molecular systems, as demonstrated by the calculation of the static polarizability of the Uranium Hexafluoride complex with a triple-zeta basis set more than 1400 basis functions.

Hilbert space fragmentation refers to exponential growth in the number of dynamically disconnected Krylov sectors with system size. It is taken as evidence of ergodicity breaking, since conventional symmetries generate at most a polynomial number of sectors. However, we demonstrate that generalized symmetries can fragment the Hilbert space. Models with higher-form, subsystem, and gauge symmetries can have exponentially many symmetry sectors. We further prove that non-invertible symmetries can induce additional fragmentation within individual symmetry sectors. Fragmentation in several known models arises from generalized symmetries, and the presence of exponentially many Krylov sectors therefore does not by itself imply ergodicity breaking. Finally, we show that disorder free localization arises naturally from Krylov-restricted thermalization when sectors lack translation invariance, requiring neither ergodicity breaking nor gauge symmetry.