Papers

Based on eigendecomposition and matrix perturbation theory, we propose an alternative method for analyzing perturbations in massive gravity that is applicable to both the base theory and its various modifications. We demonstrate the validity of this approach even in seemingly singular regimes. Applying this framework to mass-varying massive gravity, we compute perturbations for all constant-scalar Schwarzschild-(A)dS black hole solutions. We show that, under the condition $\beta = \alpha^2$, the tensor sector of these black holes reduces to that of general relativity, while the scalar sector remains free from tachyonic instabilities given appropriate parameter choices. A deeper relationship is also revealed between the solutions with generic parameters and those with $\beta = \alpha^2$: their solution manifolds intersect at a specific locus where the perturbation vanishes.

The Palomar~5 (Pal~5) globular cluster and its tidal tails provide a sensitive probe of globular-cluster evolution in the time-dependent Milky Way potential. We study the past 3~Gyr evolution of Pal~5 using collisional direct \(N\)-body simulations with PeTar, adopting Galactic potential models that include spiral arms, the Galactic bar, halo flattening, the Large Magellanic Cloud (LMC), and bar deceleration. We find that halo shape strongly influences the projected stream track, reflecting Pal~5's sensitivity to Galactic force-field flattening. The LMC causes only modest direct changes to the present-day projected stream morphology, but can alter the pericentric distance and hence the progenitor's mass evolution. The Galactic bar strongly affects stream length and debris redistribution along the tails, producing model-dependent density structures and leading–trailing asymmetries. Comparison with observations from Erkal et al. (2017) and Xiao et al. (2025) shows that no single model simultaneously reproduces all observed properties of Pal~5, including cluster evolution, stream length, track, width, and line-density profile. Although our simulations capture several global properties, the remaining discrepancies indicate that a more precise match likely requires better constraints on the initial properties of the Pal~5 progenitor and a more complex Galactic potential, including perturbations from small-scale perturbers such as dark matter subhalos and giant molecular clouds. Future work may combine self-consistent direct \(N\)-body simulations with particle-spray methods to investigate these discrepancies more efficiently.

We investigate the two-body decay of fermionic dark matter, $\chi(\bar{\chi})\to X+\nu(\bar{\nu})$, where the light mediator $X$ subsequently decays into photons. We consider two benchmark models: an axion-like particle with $a\to\gamma\gamma$, and a kinetically mixed dark vector with $A'\to3\gamma$. This decay topology produces a monochromatic neutrino line from the primary decay together with a broad secondary photon continuum. A key feature of the scenario is that the photon signal depends on the mediator decay length, whereas the neutrino line is produced promptly and is insensitive to the subsequent propagation of $X$. We derive dark matter lifetime limits from current and projected MeV gamma-ray and neutrino searches, including both Galactic and delayed extragalactic photon contributions. We find that photon constraints generally dominate for short-lived mediators, while neutrino-line searches can become competitive or provide the leading sensitivity in regions where mediator propagation substantially suppresses the photon signal. This conclusion remains stable under conservative extragalactic-only limits and a simplified treatment of Galactic spatial smearing.

We investigate the structure of neutron stars (NSs) admixed with fermionic dark matter (DM) using three density-dependent relativistic mean-field (DDRMF) functionals (DDME, DDB, and GDFM) for $\beta$-equilibrated nucleonic matter. Modeling DM as the lightest neutralino interacting via Higgs exchange, we treat the DM Fermi momentum $k_F^{\rm DM}$ as a control parameter in the range $0.02$-$0.06$ GeV. We solve the coupled mean-field and Tolman-Oppenheimer-Volkoff equations to obtain the mass-radius relation, maximum mass $M_{\rm max}$, radial sound speed profile $c_s^2$, and tidal deformability $\Lambda$. In all models, DM softens the equation of state, systematically reducing $M_{\rm max}$, the radius $R_{1.4}$ (at $1.4M_{\odot}$), and the tidal deformability $\Lambda_{1.4}$ (at $1.4M_{\odot}$) as $k_F^{\rm DM}$ increases. Consequently, the $2 M_\odot$ pulsar limit and NICER data place a model-dependent upper limit on the DM content, while the GW170817 tidal bound requires a minimal DM content for the stiffest functional. Using a recent Bayesian inference of the DDRMF equation of state as the nucleonic reference band, we evaluate if this DM imprint can be distinguished from nucleonic uncertainties using only measureable quantities. Analyzing the tidal deformability $\Lambda$ and mass-radius slope $dR/dM$ at fixed mass, we find that $\Lambda$ is a sharp discriminator: at $1.4 M_\odot$ and $k_F^{\rm DM}=0.06$ GeV, the DM-induced reduction of $\Lambda$ reaches $\simeq 8$ times the nucleonic $1\sigma$ width (model-independently $7.5$-$7.8\sigma$). The DM track leaves the nucleonic $1\sigma$ band for $k_F^{\rm DM}\gtrsim0.03$-$0.04$ GeV, whereas $dR/dM$ becomes diagnostic only for the heavier ($1.8$-$2.0 M_\odot$) branch.

Forecasting the outcomes of transition-metal-catalyzed reactions is notoriously complex due to the interplay of diverse physical and chemical variables. A persistent computational bottleneck has been effectively merging broad electronic descriptors with the localized, three-dimensional geometry of the reactive site. To bridge this representation gap, we present ChemFusion, a hybrid neural network that fuses conventional electronic features with explicit 3D atomic coordinates. Using a cross-attention mechanism, the model enables global electronic states to dynamically attend to specific spatial constraints within un-pooled molecular point clouds. When benchmarked against a diverse library of cross-couplings, this approach delivers exceptional predictive performance, decisively surpassing traditional single-modality frameworks. Importantly, extracting the attention matrices reveals that the architecture autonomously learns to identify and penalize restrictive steric hindrances. This provides a physically grounded interpretability, demonstrating that spatially aware networks can navigate complex reaction sterics that standard statistical models typically miss.

Recent experiments have reported evidence for Wigner crystals (WCs) in rhombohedral graphene. Here, we investigate Wigner crystallization in rhombohedral tetralayer graphene using projected Hartree-Fock (HF) calculations and time-dependent Hartree-Fock (TDHF) calculations. We first perform HF calculations with one electron per Wigner unit cell, and find nematic WCs (nWCs) that spontaneously break the threefold rotational symmetry $C_3$ and $C_3$-invariant WCs. In particular, there are two nWC regions in the phase diagram: one larger region at large displacement fields and low electron densities, and another smaller region at intermediate fields and high densities. Both the nWCs and the $C_3$-invariant WCs are valley-polarized states with zero Chern number, and have positive indirect gaps in the HF band structure. We then perform TDHF calculations to further test the local stability of the WC states. We find that all $C_3$-invariant WCs and half of the nWCs are locally stable, while the remaining nWCs are unstable towards WCs with two electrons per unit cell or metallic states. The predicted stable nWC phase can be identified experimentally by scanning tunneling microscopy through its anisotropic charge distribution or by angle-resolved transport measurements via a direction-dependent depinning voltage.

Characterizing non-Gaussian quantum states is of paramount importance for continuous-variable quantum information processing, yet conventional homodyne-measurement-based state tomography remains limited by optical loss, detector efficiency, and measurement bandwidth. Here, we introduce an integrated framework for loss-tolerant characterization and certification using high-gain phase-sensitive optical parametric amplification and power measurements. Our computationally efficient semidefinite programming approach enables faithful reconstruction of parity-symmetric quantum states from amplified quadrature measurements while substantially relaxing detector-efficiency requirements and increasing the measurement bandwidth. We further develop a certification framework that directly quantifies non-Gaussianity via stellar-rank witnesses and Wigner negativity, using the same quadrature-power measurements. We demonstrate the efficacy of the proposed framework through both simulated and experimental data for representative quantum states, including single-photon, Schrodinger cat, and Gottesman-Kitaev-Preskill (GKP) states. By unifying loss-tolerant measurements, state tomography, and nonclassical-state certification within a single experimentally accessible framework, our approach provides a practical pathway toward verifying increasingly complex states and can be readily implemented with current quantum photonic technologies.

We consider economic theory from the perspective of a total automation economy, one with no human involvement in production either in manufacturing or in management. One can naturally ask whether a total automation economy is fundamentally a centrally planned economy or, alternatively, whether efficiency demands decentralization into local decisions by competing agents – agentic production. A soviet economist, Leonid Kantorovich, developed linear programming as a method companies or governments can use to optimize production. Ironically, he is also generally credited with showing that the most efficient production is achieved through decentralization – a free market economy with competing agents. Here we review Kantorovich's dualization in detail. We take the objective of the economy to be maximizing production weighted by (human) market price. A fundamental issue is whether an automated pursuit of this objective might have alignment vulnerabilities as the economy evolves. Another question is whether dualization provides insight into the utility of agentic AI systems (multi-agent AI systems) generally.

We report the progress achieved on the development of a two-dimensional Optical Parallel-Plate Avalanche Counter (OPPAC) prototype for heavy-ion tracking. The device consists of two uniform thin parallel plates of 10 x 10 cm2 effective area, separated by a gap of 3 mm. The gap is filled with Tetrafluoromethane (CF4) at low pressure (up to 50 Torr). By applying a voltage difference between parallel plates, a uniform electric field is established within the gap. Electroluminescence emission is produced during the electron avalanche triggered by a charged particle that crosses the gas gap. The light is detected by an optical readout comprising four arrays of collimated Silicon Photomultipliers (SiPMs) deployed around the gas gap. The position of the particles is reconstructed by processing the light signals collected by all the SiPMs by computing the center of gravity of the light distribution within the SiPM arrays. The SiPM signals are read out and processed by a data acquisition (DAQ) system based on the General Electronics for TPC (GET). Preliminary results from a test with an alpha-particle source and a 100 MeV/u 40Ca beam demonstrate a sub-millimetre intrinsic position resolution sigma_det = 0.7 mm) while preserving good linearity over the entire detector active area.

Large language models (LLMs) can plan tool-mediated scientific work, but scientific instruments remain difficult to connect to such agents: vendor APIs may load only inside acquisition host processes, facilities may prohibit cloud-hosted agents, and natural-language interfaces can emit physically unreasonable arguments. We present a method for connecting local LLMs to scientific instruments through the Model Context Protocol (MCP). It combines: (1) a schema-bound tool surface that validates requests against physical bounds before adapter dispatch; (2) a vendor-neutral, host-process adapter pattern separating language-side reasoning from instrument-side execution; (3) a persistent lifecycle for long-running live-processing jobs; and (4) MCP-prompt-registered skills that compose typed tools into reusable multi-step protocols. Our open-source reference server exposes 30 typed tools, 5 live-job types, and 6 skills through a physics-plausible simulator implementing the same protocol surface. Validation is software-only: all 120 hardware-independent tests pass deterministically, while 15 local-LLM integration tests pass 12-15 of 15 across runs because of model nondeterminism. A preliminary single-run probe across five open tool-calling LLMs indicates that the schema-bound interface can be driven locally by small open-weight models without cloud dependency; it is not a benchmark and has no confidence intervals. The method provides a bounded, testable, and reproducible foundation for closed-loop agentic instrumentation research.

In electronic materials, flat bands are associated with compact electron localization, with implications for superconductivity, ferromagnetism and strongly correlated systems. The physical significance of their counterparts in elastic media is far less charted. Here we report a strategy to achieve elastic flat bands through an inertial retrofitting of classical lattice architectures. The idea is to alter the cell geometry to realize a network of inertial anchors, effectively partitioning the lattice into an array of weakly coupled emergent resonators, whose resonances appear as flat bands in the phonon spectrum. We demonstrate flat-band conditions that combine localized and extended state attributes and induce a giant response that is spatially and temporally persistent. Laser vibrometry experiments reveal three signatures of this mechanism: amplification up to two orders of magnitude compared to pass band and band gap conditions, multi-cell activation that is agnostic to the source location, and a persistent transient response even after several excitation cycles.

For the nearest-neighbour Edwards–Anderson Ising model on the discrete torus, we prove existence of the quenched thermodynamic limit and almost-sure self-averaging of the free-energy density. The only moment assumption in the main argument is $\E|J|<\infty$, and no symmetry or centering of the coupling law is needed. The proof avoids periodic subadditivity: the wrap-around bonds form a surface-order perturbation, while a tiling argument and the strong law of large numbers give the free-boundary limit. We also obtain the quantitative bounds $(O(L^{-1})$ for the disorder-averaged finite-volume correction. A precise common probability space is specified, since an almost-sure statement across volumes is otherwise not well defined.

The electric charges that make up charge distributions and currents in classical electromagnetism (EM) are point charge electrons with a fixed finite charge. This means that a truly continuous charge distribution or current cannot be formed because that would require infinitesimal charges. If the number of electrons in any distribution is very large, the distributions can be approximately continuous, and can be used in many applications, but the discrete character of the distributions has a major effect on other physical effects. We consider two of those effects in this paper. Does a point charge have infinite self-energy, and does a moving current loop have an electric dipole moment?

Artificial intelligence (AI) increasingly treats scientific literature as a data source for building databases, training predictive models, and guiding discovery. Yet literature-derived datasets often assume that reported experimental values are internally consistent and directly reusable. Here, we analyze this assumption using solid electrolyte (SE) conductivity data as a representative materials-science case. By tracing values from source articles to curated datasets, we identify recurrent text-figure mismatches, ambiguous axis annotations, unit inconsistencies, and missing measurement context. These discrepancies are often numerically plausible and therefore difficult to detect through routine preprocessing, but they can propagate as structured label noise during database construction and machine-learning reuse. A cross-database example shows how ambiguous reporting can create a 100-fold conductivity error. Our analysis reframes data accuracy as an infrastructure requirement for artificial-intelligence-driven discovery and motivates traceable reporting, curation, and validation practices for reusable scientific data. Keywords: AI for science; Data reliability; Scientific databases; Structured label noise; Literature-derived data; Materials informatics; Solid electrolytes

Motivated by the interactions of the GCR protons with the Martian atmosphere and regolith in the absence and presence of hydrogen, a series of GEANT4 simulations are employed in this study to reveal the influence of hydrogen on the energy spectra of secondary and albedo neutrons together with the associated gamma rays at the Martian surface. Following irradiation of the Martian atmosphere with a planar vertical PAMELA proton beam, the attenuation of the primary proton spectrum through the atmosphere and the range and energy deposition of protons within the regolith are first obtained. The depth profile of the generated neutrons and gamma rays, along with the kinetic energy spectra of the atmospherically produced neutrons and gammas reaching the surface, is then acquired in the absence and presence of 0.11 wt.% hydrogen by voxelizing the regolith into 100 cells of 2-cm thickness. Finally, a surface detector is placed atop the regolith, and the atmospherically produced neutron and gamma spectra are compared with the total neutron and gamma spectra recorded at the surface detector to assess the relative contribution of the atmosphere and the regolith to the overall radiation field reaching the Martian surface. The energy spectra of the albedo neutrons are also obtained in terms of thermal, epithermal, and fast neutrons. The GEANT4 simulations show that the Martian regolith, rather than the atmosphere alone, constitutes the dominant source of the neutron and gamma population arriving at the surface, and that the presence of 0.11 wt.% hydrogen is observable in each energy regime of the albedo neutrons at the Martian surface, while proton transport and the overall neutron and gamma production depth profile remain comparatively insensitive to hydrogen, thereby indicating the elemental variation of the Martian regolith.

The boundary correction to the free energy of a disordered Ising model depends on the boundary condition, the normalization, and the finite-volume sequence. We give a one-dimensional i.i.d. counterexample showing that the surface free-energy density need not be independent of the van Hove sequence and that the corresponding random correction need not converge in probability. For bounded couplings in the Dobrushin uniqueness regime on cubic boxes in dimensions $d\geq2$, we prove convergence of the normalized free-to-fixed boundary free-energy difference in expectation, almost surely, and in every $L^p$, $1\leq p<\infty$. For Gaussian boundary couplings, we derive an exact finite-volume interpolation identity and explain why it does not by itself imply a low-temperature surface limit. For a seam-flip free-energy difference $D_L$ across a set $S_L$ of independent symmetric bonds of variance $v$, we prove $\Var(D_L)\leq4v\abs{S_L}$; one-dimensional examples show that symmetry and finite moments alone do not determine a stiffness exponent, and the low-temperature Gaussian Edwards–Anderson problem remains open.

Hot-wall fuel-droplet impingement affects liquid redistribution, secondary droplet formation, and droplet evaporation in diesel-relevant spray-wall systems. This study investigates the spreading and breakup of single n-hexadecane droplets, used as a single-component diesel surrogate, on a heated stainless-steel wall at 300-500 {\deg}C over a Weber number (We) range of 5.77-208.61. High-speed backlit images were recorded during experiments and used to classify deposition, rebound, ejection, fragmentation, and splashing regimes, and to measure spreading-factor histories. The measured spreading histories were compared with a lamella-rim model to evaluate its predictive capability before droplet breakup and to infer the lamella state at experimentally observed breakup instants. The 300 {\deg}C cases did not enter the Leidenfrost regime under the present impact conditions and therefore serve as a non-Leidenfrost reference, deviating from the model predictions. For Leidenfrost cases at 350-500 {\deg}C, the model captures the pre-breakup spreading trajectory, including higher-We cases that later undergo breakup. Wall temperature has a limited influence on the early spreading stage but more strongly affects later breakup timing after lamella thinning, especially in the intermediate-We regime. At high We, breakup becomes increasingly inertia-dominated. Model-inferred lamella thicknesses evaluated at experimentally observed breakup instants are mainly concentrated between 0.010 and 0.017 of the initial droplet diameter. These results suggest that model-inferred lamella thickness can complement conventional Weber-number and temperature-based regime maps by providing local-state information for breakup timing in hot-wall fuel-droplet impingement models.

This chapter is intended as an introduction to dense matter and the equation of state of neutron stars and their mergers. It begins with a brief description of neutron star interiors, followed by a historical overview of the theoretical frameworks used to describe them focusing on relativistic formalisms, including different degrees of freedom, models, symmetries, and phases. It also provides an overview of our current understanding of dense matter (including theory, experiments, and observations) and discusses the advances we expect to see in the field over the next decade.

Master–slave synchronization reconstructs the evolving state of a reference (or master) system by continuously correcting a second system, the slave, using observations of the master. In applications, the observations are often contaminated by noise, so the corrections injected into the slave are themselves uncertain. In this paper we aim at quantifying the effect of noisy observations on master–slave synchronization for a family of evolution equations that combine a quadratic transport term with a polynomial linear differential operator. The family includes the Burgers, Kuramoto–Sivashinsky, Kawahara, Benney–Lin and Nikolaevskiy equations, among others. Under periodic boundary conditions, a Fourier–Galerkin approximation of order $K$ yields a finite-dimensional master–slave system in which white observation noise of intensity $\sigma$ is modeled through an Itô stochastic differential equation. In this framework, we first establish local exponential stability of noiseless synchronization for sufficiently strong scalar coupling. Then we compare the stochastic synchronization error with its noiseless counterpart resulting from the same initial slave state, isolating in this way the effect of noise. Assuming bounded reference paths, the mean-square deviation between the noiseless and noisy synchronization errors is $\mathcal O(\sigma^2)$ on finite time intervals. Under additional regularity assumptions, we also bound the error between the finite-resolution stochastic slave model and the infinite-dimensional deterministic master field, explicitly separating spectral approximation error, deterministic synchronization error and observation noise. Numerical experiments for the Kawahara and Nikolaevskiy equations confirm the predicted noise scaling.

Quantum Hamiltonian descent (QHD) formulates continuous optimization as time-dependent quantum dynamics, where a kinetic term drives exploration and a potential term encodes the objective function. Digital implementations of QHD require encoding the search space into qubits, and this choice can shift the dominant cost among logical qubits, circuit depth, non-Clifford rotations, and potential synthesis. In this work, we present an encoding-aware resource analysis comparing one-hot and binary amplitude encodings for QHD. We derive gate-count scalings, construct and validate circuits against classical \Sch-equation solvers, and estimate Clifford+$R_z$ and fault-tolerant Clifford+$T$ resources on benchmark optimization problems. Binary encoding reduces the data register from $O(dN)$ to $O(d\log N)$ qubits and gives comparable asymptotic scaling for both kinetic and potential evolutions. Across all benchmark problems studied, binary encoding also uses fewer $R_z$ rotations than one-hot encoding, making it the preferred option for fault-tolerant implementations where arbitrary rotations dominate the cost. Kinetic approximations based on low-momentum spectra and approximate QFTs can further reduce the binary kinetic cost to polylogarithmic scaling. However, for targets such as Ackley, potential synthesis can dominate the total cost and reduce the benefit of kinetic approximations. These results suggest that exploiting the analytic structure of the target function to compile the potential evolution in QHD more efficiently is needed for further resource reductions.

We consider incompressible FENE dumbbells coupled to a reversible Markov operator on a compact continuum of internal states. At zero centre-of-mass diffusion we prove that state averaging is an exact factor map and that a Lagrangian state lift is its unique inverse on the natural energy-solution classes. Thus existence, multiplicity, and uniqueness of the state-resolved system are precisely those of its scalar FENE projection; the internal-state dynamics creates no additional large-data nonuniqueness. The lift is driven by a trace-free matrix fibre evolution and permits nonlinear local activities, including rates with linear dependence on the singular Kramers stress.We also prove a sequential form of this structure. For state-resolved regularizations with relative-entropy-prepared initial fibres and no viscous dissipation defect, the complete densities converge strongly without reconstructing them after the scalar limit. Consequently the full drag,state-dependent activity, singular stress, and non-atomic Jeffreys production all pass to the limit. The argument combines stability of regular Lagrangian flows with a relative-entropy estimate for simultaneously varying matrix drifts and jump rates. A stationary oscillation shows that the preparation cannot follow from the natural entropy bounds alone. With positive centre-of-mass diffusion we independently construct global large-data weak solutions and identify the same nonlinear terms. An explicit infinite-rank kernel proves that these results are not finite-species reductions.

In Newtonian spacetime, the canonical description of a classical $N$-particle system requires $3N$ degrees of freedom. Not all of these are physical, however, since the conservation of the net momentum implies that only $3(N-1)$ accelerations are independent. Hence, three constraints can be used to eliminate the unphysical centre-of-mass variables, at the level of the Lagrangian, leaving only the subset of observable displacements and momenta, which are relational. Imposing the constraints does not change the dynamics of these variables, at the classical level, and is analogous to a gauge-fixing procedure, which removes redundancy in the description of the system. In classical physics, therefore, the number of physical degrees of freedom equals the number of independent relational degrees of freedom. Here, we show that this is not the case in quantum mechanics. While an operator-analogue of the classical net momentum exists, it cannot be used to impose constraints that restrict the degrees of freedom in the theory, without a loss of physical information. This means that all $3N$ canonical degrees of freedom are physical, even though only $3(N-1)$ of them are relational. We explore the physical consequences of the non-relational variables and show that they give rise to generalised uncertainty relations (GURs), for the relational quantities that define the quantum reference frame (QRF). Hence, it is shown that the non-relational degrees of freedom refer to the frame itself and that the non-Heisenberg terms in the GURs define its Galilean-invariant spreads, in both real space and momentum space. The implications of this result for recent work on relational models, including the “perspective neutral” framework for QRFs, are discussed. Its implications for the wider relational program, and, in particular, the relevance of the latter to quantum gravity research, are also critically assessed

Magnetoresistance hysteresis is often used to estimate the coercive field of a magnetic material. We reanalyse our published magnetotransport and magnetometry data on compacted powders of the half-metallic ferromagnet CrO2 and show that this identification can fail in a granular conductor. The field Hp at the resistance maximum may be close to, above, or below the bulk coercive field Hc, depending on temperature and measuring current. For three samples with different particle shapes and insulating-shell thicknesses, the digitized ratio Hp/Hc follows the same qualitative sequence and suggests a common crossover near 15 K. We interpret this behaviour as a change in which interparticle junctions control the electrical response. Bulk magnetometry averages over the entire magnetic volume, whereas tunnelling resistance gives the largest weight to the small set of links that carries the current. Cohn's exact network-sensitivity theorem provides a rigorous linear-response definition of these transport weights. In simple terms, Cohn showed that the influence of a given contact on the total resistance is proportional to the square of the current flowing through that contact. Combined with known magnetic pair-correlation effects, this leads to the concept of transport-weighted coercivity. In granular sensors and spin-dependent composites, the resistance peak cannot automatically be treated as the bulk coercive field. Conversely, the difference Hp - Hc may serve as a diagnostic of current-path localization, barrier evolution, and device-to-device variability.

The Baldereschi point of a crystal is a wavevector in the Brillouin zone at which every smooth periodic function of wavevector lies close to its mean value. Although originally introduced in the context of one-electron methods, mean-value points are ideal for explicitly correlated many-electron methods such as quantum Monte Carlo simulations, which can only use a single Bloch wavevector in the Brillouin zone of a simulation supercell. We have therefore evaluated and tabulated the Baldereschi mean-value points of all fourteen three-dimensional Bravais lattices.

A vertex-reinforced random walk steps to a neighbour with probability proportional to $1+\beta n^{a}$, where $n$ counts previous visits to that neighbour and $a\in(0,1)$ sets the memory strength. On the rooted $b$-ary tree the exponential growth of the vertex set drives the walk outward while the reinforcement pulls it back. We report a sharp condensation transition of the occupation measure at a finite $\beta_c(a,b)$: below it the occupation spreads and the range grows linearly; above it a single vertex holds an $O(1)$ fraction of the time, stable in the observation time, while the range keeps growing very slowly, at a rate better described by $\log t$ than by any power. We do not find the range to be bounded, and keep this condensation distinct from finite-range localization. Four estimators locate the same threshold, which shows no systematic drift out to $t=3\times10^{7}$. In a frozen environment the walk is reversible, with edge conductances $c_{uv}=w_{u}w_{v}$, $w_{v}=1+\beta n_{v}^{a}$, and measure $\mu_{v}\propto w_{v}\sum_{u\sim v}w_{u}$ describing the condensed core, whose neighbour coupling we test directly. Reversibility places the escape at the frontier within the branching-number criterion for biased walks on trees, predicting $\beta_c\propto b-1$; the measured lines for $b=2,3,4$ collapse under division by $b-1$ to a few percent (bootstrap). The value $a=1/2$ that governs the walk on $\mathbb{Z}$ enters only as the marginal exponent of the condensed profile. Near $\beta_c$ the occupancy is non-self-averaging and bimodal, a coexistence-type phenomenology.

A single missing atom can drive a topological phase transition in a lattice that is otherwise trivial for all values of its parameters. We demonstrate this in a two-dimensional honeycomb lattice with anisotropic nearest-neighbor hopping ratio $t'/t$. The pristine lattice is topologically trivial for all $t'/t$ by the Nielsen-Ninomiya fermion-doubling theorem: Dirac valleys appear in pairs whose topological charges cancel identically in any bulk invariant. A single vacancy breaks this cancelation, acting as an internal boundary with defect winding number $\nu_3=\mp 1$ for $t'/t<2$. At $t'/t=2$, the two Dirac valleys merge and annihilate; the number of active pseudospinor degrees of freedom drops from $m=2$ to $m=1$, violating the condition $d+D+1=2m$ required for a non-trivial winding number. The winding number collapses to $\nu_3=0$: a topological phase transition within a fixed symmetry class (BDI), driven entirely by a bulk Lifshitz transition and observable only through the vacancy. The defect zero mode crosses over from algebraic (${\sim}1/r$) to stronger spatial confinement, with its inverse participation ratio reaching a sharp minimum at criticality. Wavefront dislocations in the local density of states provide a direct, spatially resolved image of $\nu_3$, accessible in graphene and in photonic and cold-atom analogs.

We introduce a hierarchy of entanglement measures Ek based on k-symmetric PPT extensions. Each Ek, defined via a minimal eigenvalue shift and computed by semidefinite programming, is faithful, convex, and monotone under free operations. The hierarchy strictly refines PPT-robustness at k = 1, detects bound entanglement at k = 2, and converges exactly to the separability measure as k -> infinity. Numerical experiments on Horodecki, Werner, UPB, and random states demonstrate practical scalability. Our framework unifies computational efficiency with operational fidelity in a single tunable family – a combination previously believed to be fundamentally incompatible in entanglement quantification. It supplies, for the first time, a systematically improvable resource-theoretic yardstick that accounts for all entangled states, including the bound entangled ones that have long resisted quantitative treatment.

The Lee-Yang theory is based on the theorem concerning a property of the ferromagnetic Ising model partition function proved by T. D. Lee and C. N. Yang in 1952. It provides powerful tools for understanding the very nature of phase transitions and critical phenomena in various spin and similar models. Sometimes, this theory is applied to models for which the theorem's validity has not been proved. By the main result of E. H. Lieb and A. D. Sokal, Commun. Math. Phys. 80, 153 (1981), for a given ferromagnetic model, this validity is guaranteed by the same property of the single-spin partition function. Due to the anisotropy term $\sum_i \Delta S_i^2$, the single-spin partition function of the Blume-Capel model fails to have the Lee-Yang property for $\beta \Delta> \ln 2$. In this article, we show that the ferromagnetic interaction in such a model can induce the Lee-Yang property, even for these values of $\beta \Delta$. To the best of our knowledge, it is the first result of this kind.

Recent works of Galligo, Najnudel, and Vu (2025) and Najnudel and Vu (2026) study repeated differentiation for polynomials of the form $P(z)=p(z^m)$, where $p$ is a deterministic polynomial of degree $n$ with real, non-negative roots, in the regime where $m$ and $n$ are large. If $m\gg \log(n)$ and the root distribution of $P$ converges to a compactly supported, radial probability measure $\mu_0$, these works show that for $0\le t<1$, the root distribution of the $\lfloor nmt\rfloor$-th derivative of $P$ converges to a compactly supported probability measure $\mu_t$ given by an explicit formula for its radial quantile function. We give a substantially simplified proof of this result and also extend the result from repeated differentiation to repeated applications of the differential operator $z^a(d/dz)^b$. We also compute the limiting root distribution in the case when $m$ is fixed and $n$ tends to infinity.

We establish a direct operational connection between the one-time measurement (OTM) and two-time measurement (TTM) protocols for quantum work statistics, showing that OTM work values, including coherence signatures, can be reconstructed from standard TTM data through classical post-processing without any modification of the experimental setup. This reveals that coherence information commonly attributed to OTM schemes is already latent within TTM data and becomes explicit upon a natural post-processing step. For a driven two-level system subject to finite-resolution energy measurements, this reconstruction unveils a resolution-driven statistical transition in the work distribution: whereas projective and weak measurements yield smooth distributions, intermediate resolutions produce non-analytic structures whose character is determined by the dynamics and a critical meter resolution. We show that the non-analyticity of the OTM work distribution takes the form of square-root divergent peaks at specific work values, and that the separation between these singular points is an experimentally accessible quantity that vanishes at the critical resolution with a universal exponent. The same dynamical quantities that govern the transition also encode the relative entropy of coherence of the driven state, enabling coherence quantification from energy measurements alone. We demonstrate experimental accessibility in a nitrogen-vacancy center platform with parameters drawn from current experiments, where both sides of the transition and the coherence signatures are within reach of existing technology.