Papers

Unconventional magnets combining vanishing net magnetization with spin-split electronic structures and anomalous transport have attracted considerable attention. Using spin-group symmetry analysis, we derive general conditions for odd-parity spin splitting in two- and three-dimensional coplanar noncollinear antiferromagnets. We identify a key spin-group symmetry whose relativistic counterpart forbids time-reversal-odd transport and show that breaking it allows such transport in the presence of spin-orbit coupling. Tight-binding calculations validate these symmetry arguments and demonstrate an anomalous Hall effect in a fully compensated odd-parity magnetic state without an external field. By screening a three-dimensional magnetic materials database and constructing two-dimensional heterostructures, we further identify realistic platforms exhibiting pronounced spin-orientation-dependent anomalous Hall and magneto-optical effects. Our results establish a general symmetry framework for time-reversal-odd responses in odd-parity magnets and highlight fully compensated odd-parity magnets as a promising platform for controlling anomalous transport.

We investigate, for the first time, the non-radial $f$-mode oscillations of neutron stars (NSs) with a dark energy (DE) core utilising a fully general relativistic treatment. We construct the stellar profile by considering a relativistic mean field model for nuclear matter and a modified Chaplygin fluid like prescription for DE. We compute the stellar structure, $f$-mode oscillations, tidal deformability, and gravitational wave (GW) energy and strain of the NS with DE core by varying the DE equation of state (EoS) parameters. Our study reveals that the inclusion of DE softens EoS and reduces the maximum mass compared to the pure neutron star. The obtained mass-radius values are consistent with observational constraints from massive pulsars such as PSR J0030+0451 and PSR J0740+6620. We find that the extent of the DE core, determined by the transition density, plays a crucial role in modifying the stellar structure and oscillation properties, with lower transition densities producing appreciable changes over a wider mass range. The $f$-mode frequencies and damping times exhibit systematic modifications, for higher mass configurations, while the correlation between the $f$-mode frequency and tidal deformability remains consistent with observational constraints from GW170817 and GW190814. Further, the normalised oscillation energy distribution remains nearly universal, with only minimal deviations for the higher mass configurations. Finally, we estimate the characteristic GW strain associated with the $f$-mode oscillations and find that the predicted signals lie within the sensitivity band of future third generation GW detectors.

Coronal mass ejections (CMEs) exhibit poorly understood internal velocity distributions. In this work, we introduce an optical flow-based method, DOFCAT (Dense Optical Flow CME Analysis Tool), applied to high-resolution data from ASPIICS/Proba-3 and METIS/Solar Orbiter to examine the internal velocity dispersion of different substructures within CMEs in the Middle Corona. We also introduce a Gaussian-tapered Fourier (GTF) filter that suppresses brightness artifacts in running-difference images from the ASPIICS wideband channel. We then apply DOFCAT to four CME events observed across ASPIICS and METIS, extracting their internal velocity information. Our results show that the velocity profiles of both the CME front and core change with position angle and are non-uniform. For impulsive CMEs, the height offset between the front and core begins to increase following the impulsive acceleration phase, while CMEs without a clear impulsive phase show a more gradual evolution of the height offset. We find that this increase in height difference occurs rapidly between 2.3–3.0\,R$_\odot$. Furthermore, the front shows a higher velocity spread than the core, with impulsiveness evident in the CME leading half. We further compute the radial self-similarity coefficient separately for the front and the core, finding that the front expands non-self-similarly initially and tends toward self-similarity at larger heights, while the core remains relatively self-similar. These findings confirm that CMEs contain complex internal flows and layered substructures within the traditional three-part morphology. Our results demonstrate the utility of DOFCAT on high-resolution coronagraphs for probing CME dynamics and provide new insights into CME initiation and evolution.

In this paper, it is shown that in spacetimes of maximal proper acceleration, there is a reduction of the mean lifetime of the muon. We consider several candidates for the maximal proper acceleration. For all of them, the induced corrections are small, but for the case when the maximal proper acceleration is identified with the Schwinger's acceleration, the effect is detectable in future muon collider facilities.

Fano resonances based on coherent interference between localized Lorentz modes and Fabry-Perot radiation continua have been widely explored for microwave metamaterial sensors, filters, and photonic devices. However, conventional Fano metasurfaces suffer from angular dispersion and polarization-dependent spectral variations, limiting robustness under dynamic illumination. Here, we propose a band-folding-enabled flatband engineering strategy to realize robust Fano resonances in a planar microwave metasurface with a 2x2 enlarged cell of orthogonally arranged H-shaped metallic resonators. The enlarged cell induces Brillouin-zone folding, generating a nearly dispersionless flatband near 15.3 GHz with suppressed momentum dependence and enhanced photonic confinement. This flatband state provides a high-Q localized resonance strongly coupled to the FP radiation continuum, producing a stable asymmetric Fano response. Furthermore, the orthogonal resonator configuration supports two polarization-decoupled dipole modes with comparable excitation efficiency, reducing polarization-induced spectral distortion. Near-field measurements and simulations verify localized flatband features, while far-field experiments demonstrate stable Fano responses under oblique incidence from 0{\deg} to 30{\deg} with minor resonance variation. A temporal coupled-mode theory model is developed to quantitatively describe Fano spectral evolution under different illumination conditions. This work establishes a flatband-mediated route toward robust microwave Fano metasurfaces and offers a general strategy for stable resonant photonic device design.

Pressure can drive Weyl semimetals toward superconductivity through qualitatively distinct reconstructions of their lattices and normal-state electronic structures. Here, we report the first observation of superconductivity in compressed TaRhTe4. This finding enables a direct comparison of the distinct reconstruction pathways leading to superconductivity in TaRhTe4 and the previously studied TaIrTe4, both of which belong to the TaXTe4 (X = Rh, Ir) family of type-II Weyl semimetals. For TaRhTe4, high-pressure electrical-resistance, Hall effect, and magnetoresistance measurements, together with synchrotron X-ray diffraction and first-principles calculations, reveal a superconducting transition that emerges near 20 GPa, with onset Tc increasing to approximately 2.6 K at 65.2 GPa and zero resistance achieved above 63 GPa. The onset of superconductivity coincides with a progressive lattice distortion, a strong suppression of the positive magnetoresistance, and a continuous decrease of the Hall coefficient toward zero. Calculations further show that additional electron-like bands cross the Fermi level (EF) and that N(EF) increases upon compression. This evolution contrasts with TaIrTe4, where the Hall coefficient initially increases before reversing its pressure dependence near the superconducting threshold, while the structural anomaly is confined to a narrower pressure interval. This comparison indicates that superconductivity in the TaXTe4 family is not tied to a unique critical pressure or a single Fermi-surface reconstruction, but can emerge through distinct material-specific pathways once pressure sufficiently reconstructs the low-carrier Weyl-semimetal-derived state into a multiband metallic regime.

Potential energy surfaces and collective inertial functions are essential microscopic inputs for describing nuclear large-amplitude collective motions such as rotation, vibration, and fission. We develop the Nuclear Collective Generator (NCG), a machine-learning framework that predicts the collective potential and six collective inertial functions on the quadrupole deformation $(\beta,\gamma)$ plane from proton and neutron numbers and shell-effect descriptors, providing the microscopic inputs for the five-dimensional collective Hamiltonian (5DCH) used to describe low-lying spectra in even-even nuclei. The NCG combines weighted supervised learning, adversarial refinement, and ensemble averaging to improve reconstruction fidelity and prediction stability. Across 568 even-even nuclei, the reconstructed collective potentials reproduce the covariant density functional theory (CDFT) results with a mean root-mean-square deviation of 0.58~MeV. When propagated through the 5DCH solver, the NCG inputs reproduce the global systematics of equilibrium deformations, low-lying excitation spectra, and electric-quadrupole transition strengths. Near the $Z=82$ shell closure, the NCG softens the collective potential along the $\gamma$ direction, reducing the overestimated collectivity of the original CDFT+5DCH calculations and bringing the $B(E2)$ values closer to experimental data. These results demonstrate that the NCG provides an accurate surrogate for global microscopic collective calculations while retaining their essential physical content.

We present a systematic study of the rest-frame ultraviolet (UV) and optical morphologies of Ly$\alpha$ emitters (LAEs) at $z \simeq 2$-$7$ from the SILVERRUSH multi-narrowband catalog, using JWST/NIRCam imaging from COSMOS-Web. We fit Sérsic profiles in four NIRCam filters (F115W, F150W, F277W, F444W) for LAEs spanning $\sim 2.2$ Gyr of cosmic time. LAE sizes show a mild increase from rest-frame UV to optical wavelengths, with a median optical-to-UV size ratio of $R_{e,\rm opt}/R_{e,\rm UV} = 1.14^{+0.01}_{-0.02}$, indicating a small morphological $K$-correction; this offset is significant at $z \leq 5.7$ but not at $z = 6.6$. The rest-frame optical sizes follow a power-law evolution, given by $R_e \propto (1+z)^{-0.94 \pm 0.09}$, decreasing from $0.91^{+0.07}_{-0.07}$ kpc at $z = 2.2$ to $\sim 0.5$ kpc at $z \gtrsim 5$, in close agreement with a recent JWST study of spectroscopically confirmed LAEs. The rest-frame optical size-mass relation slopes are broadly consistent with those of the general star-forming galaxy (SFG) population, while LAEs lie below it in normalization over $z \sim 3$-$6$. More compact LAEs tend to exhibit higher Ly$\alpha$ equivalent widths, a trend driven mainly by the most compact, marginally resolved sources. These compact systems also occupy elevated SFR surface-density regimes, consistent with a scenario in which concentrated star formation may facilitate Ly$\alpha$ escape. No significant correlation of LAE rest-frame optical size with projected large-scale environment is found over $z \simeq 2$-$7$, suggesting that LAE morphology may be governed primarily by internal galaxy properties, except possibly in the most extreme overdensities.

We investigate Anderson localization in a one-dimensional lattice with non-Hermitian off-diagonal quasiperiodic disorder, extending a recently studied Hermitian mosaic model to the non-Hermitian regime. Using Avila's global theory, we derive the exact Lyapunov exponent and the complete phase diagram in the complex energy plane. This work contains two central findings. First, we discover mobility arcs—open curved segments in the complex plane—as a new class of mobility edges and the generic form of open mobility edges, which coexist with closed mobility rings in a complementary parameter regime. These arcs share the same localization physics as the previously reported mobility lines: eigenstates are delocalized if and only if their energies lie exactly on these sets; any deviation yields localized states. This constitutes a striking measure-zero delocalization phenomenon: delocalized states occupy only zero-measure sets (arcs or lines) in the complex plane, in sharp contrast to the mobility rings, which enclose a finite-area region of delocalized states. Second, we reveal that mobility rings, arcs, and lines all share a common mathematical origin in the generalized Joukowski transformation $P(E) = \frac{1}{2}(u - w^2/u)$, rooted in the algebraic structure of the underlying polynomial: the preimage of the boundary of an elliptical region under the polynomial map $P(E)$ gives the rings, while the branch cut inside this ellipse gives rise to the mobility arcs and lines in the complementary parameter regime.

The static Love numbers of four-dimensional Schwarzschild black holes vanish classically. We show that this is not true in the quantum theory. Working in the worldline effective field theory, we compute the leading quantum correction to the Compton amplitude for massless scalars and photons scattering off a Schwarzschild black hole at first post-Minkowskian order, and find logarithmic divergences associated with the renormalization of the static Love numbers. We conclude that renormalization-group running necessarily generates Love numbers suppressed by the square of the Planck length in units of the horizon radius, $\ell_{\rm pl}^{2}/r_{\rm h}^{2}$. This is consistent with the classical vanishing being a consequence of an accidental symmetry of static general relativity, broken by quantum loops. Extrapolated to gravitational perturbations, our results suggest that the quadrupolar static Love numbers of Schwarzschild are of size $\lambda \sim M r_{\rm h}^{2} \ell_{\rm pl}^{2}$.

The occurrence of chaos in multipendular FP resonators (without light propagation delay) is illustrated. The probability of evolving a chaotic solution in a given time, starting from initial conditions contained in a neighbourhood of a stable equilibrium point, is estimated, and its dependence on the most relevant system parameters is investigated. The possible relevance of these results for interferometric gravitational wave antennas is discussed.

The proposed high-luminosity Super Tau-Charm Facility (STCF) offers a clean experimental environment for threshold studies of exotic hadrons. In this Letter, we evaluate the expected significance for the fully-charmed vector tetraquark candidate $T_{4c}$ in the $e^+e^- \to \eta_c J/\psi$ channel at the STCF. Using Monte Carlo simulations of an energy scan from $\sqrt{s}=6.71$ to $6.79~\mathrm{GeV}$ with $100~\mathrm{fb}^{-1}$ per point, we adopt a high-efficiency single-tag (ST) reconstruction of $J/\psi$ leptonic decays as the primary strategy, with a double-tag (DT) reconstruction of $\eta_c \to K^+K^-\pi^0$ retained as an independent cross-check. Because the signal cross section is governed by the still-uncertain dielectron width $\Gamma_{ee}$, we consider three benchmark hypotheses, $\Gamma_{ee}=0.25, 0.5, 1~\mathrm{eV}$. The corresponding expected ST significances are $5.1\,\sigma$, $10.6\,\sigma$, and $20.5\,\sigma$, respectively. These results indicate that the STCF can provide meaningful sensitivity to fully-charmed tetraquark states near threshold.

We investigate how the chiral anomaly influences the decomposition of nucleon spin between quark spin and orbital motion. We extend the chiral quark soliton model by including a flavor-singlet pseudoscalar field whose mass is generated by the chiral anomaly. Within this framework, we calculate the quark and antiquark helicity and orbital angular momentum distributions, accounting for the singlet field induced by the rotation of the soliton. We vary the anomaly-induced mass while keeping the remaining model parameters fixed to examine how the anomaly affects the spin decomposition. The induced field enhances the quark helicity contribution relative to the conventional pion-only model. Increasing the mass suppresses this enhancement and increases the orbital contribution, while the two contributions continue to account for the nucleon spin. This redistribution remains modest over the parameter values considered and does not qualitatively alter the spin decomposition of the conventional model.

State production and its subsequent decay can each require a different angular-momentum coupling treatment. Although long recognized, this distinction is often overlooked in the two-step model, where $LS$ coupling is traditionally applied to both production and decay ($LS/LS$), even when the decay requires $LSJ$ coupling. We introduce a hybrid $LS/LSJ$ formulation that uses established angular-momentum recoupling theory to project the initial $LS$ alignment onto the fine-structure $J$ states, evaluates their decay in $LSJ$ coupling, and, for well-separated $J$ levels, sums their contributions incoherently. The $1s2s2p\,{}^{4}\!P_J$ manifold produced by single-electron capture in $\mathrm{C}^{4+}(1s2s\,{}^{3}\!S)+\mathrm{He}$ collisions provides a good test case, with $M_L$-resolved theoretical production cross sections and absolute measurements of the Auger single-differential cross section available. Using the same $LS$ production cross sections in both treatments, we find that the hybrid $LS/LSJ$ treatment strongly suppresses and can even invert the Auger anisotropy relative to the traditional $LS/LS$ treatment, substantially improving agreement with the measurements. Such an incoherent hybrid formulation provides the appropriate framework when $LS$ coupling governs the initial interaction dynamics while well-separated fine-structure levels require an $LSJ$ description of the decay.

Imperfect photon sources degrade the performance of interference-based linear-optical entangling gates. We derive a universal fidelity law for these gates in terms of two standard source metrics: Hong-Ou-Mandel visibility and second-order coherence. We model the multiphoton component as an arbitrary overlap between noise and signal photons. While different values of the signal-noise overlap produce different error structures, associated with different physical platforms, all result in the same fidelity law. We test the model on our actively synchronized CNOT-gate experiment and against published results across different platforms, with no free parameters. This framework turns source characterization into a unified benchmark for photonic quantum computing.

We numerically construct the Sasaki–Einstein metric on the link of the cone over the second del Pezzo surface $\mathrm{dP}_2$ and two primitive harmonic basic $(1,1)$-forms at its irregular volume-minimizing Reeb vector. Being toric, the metric in symplectic coordinates is encoded in a single convex function on a polygon. We approximate the correction to the canonical Guillemin potential in two ways: polynomial expansion and neural networks. The polynomial fit achieves a held-out mean-squared Monge–Ampère residual below $10^{-13}$, in contrast to the $10^{-2}$ plateau for the non-volume-minimizing regular Reeb vector. We validate our method against closed-form metrics of $Y^{p,q}$ using curvature invariants, and also against the numerical result of Doran et al. (2007) for the Kähler–Einstein metric of $\mathrm{dP}_3$ using the Laplacian spectrum of low torus-invariant modes. The integrated Riemann-squared curvature of the $\mathrm{dP}_2$ link agrees to two parts in $10^{9}$ with the closed form conjectured from the dual field theory. Our data for the metric and harmonic forms can be used to study warped non-conformal holographic IIB backgrounds, the analogues of the Klebanov–Tseytlin solution on the conifold.

Cryogenic electronics forms a rapidly emerging research domain for high-performance and power-efficient computing applications. Incorporating nanomagnetic components in cryogenic circuitry adds highly valuable functionality, facilitating downscaling, reducing energy consumption and introducing time-reversal symmetry breaking. Furthermore, low-temperature environments enhance magnetic stability and switching efficiency at nanoscale dimensions, reinforcing the potential of cryogenic nanomagnets. To fully leverage these opportunities, magnetic control schemes require alternative options to current-based writing, which is the main bottleneck regarding power consumption and downscaling. In this regard, voltage-based gating of the magnetic state could drastically enhance operational efficiency and integration density. In this work, we investigate cryogenic Voltage Control of Magnetism (VCM) in epitaxial SrTiO$_3$/Fe thin film heterostructures on a CMOS compatible Si substrate. We demonstrate and quantify voltage-controlled modifications of the magnetic domain structure, consistent with electric field-controlled magnetic anisotropy at the Fe/SrTiO$_3$ interface. These findings provide a viable material system for the development of next-generation magnetic domain-based devices for classical and quantum computing.

We present a geometry-refinement workflow that adapts to the cost of an energy–gradient evaluation and the reliability of molecular topology. An initial Cartesian calculation and continuous bonding diagnostics determine whether to begin in projected Cartesian coordinates or in chemically adapted internal coordinates. Chemical perception generates local redundant measurements; sparse rank and conditioning tests combine them into nonredundant, symmetry-adapted coordinates; and a common optimizer uses the selected representation with resident or external calculators. For inexpensive gradients, the projected Cartesian route limits coordinate overhead; a single monitored internal-coordinate step can then provide chemical interpretability. When gradients are costly and topology is certified, symmetry-adapted internal coordinates reduce expensive energy–gradient calls. A quadraticized map improves localized anharmonic cases, while mixed Cartesian/internal charts cover uncertain or complex topologies. Local sparse operators and resident force-field and tight-binding calculators extend both routes to large systems. The same Cartesian calculator contract supports multilevel energy and gradient composition. The measured coordinate pipeline and recurrent resident tight-binding update show near-linear scaling over the tested size ranges; this statement applies to those qualified components, not to arbitrary electronic-structure calculations or cold starts. For certified, directly separable internal charts, the optimizer can use chemically designed Morse or Gaussian maps to quadraticize the local step problem. The quadraticized branch uses a short geometry-local history, while delocalized charts remain unchanged. This reduces iterations in difficult minima without changing the electronic potential or coordinate chart.

We study correlation functions of giant and dual giant gravitons in $\mathcal N=4$ super Yang–Mills theory. Although the two objects correspond to rather different D3 brane configurations in $AdS_5\times S^5$, their gauge theory operators are Schur polynomials associated with transposed Young diagrams. We show that this transposition is accompanied by a formal rank reflection $N\to -N$ at the level of correlation functions. For both $U(N)$ and $SU(N)$, the relation is exact for free correlators at finite $N$, and, using Lagrangian insertion, extends to separated point weak coupling integrands at every loop order. More generally, it applies to any number of Schur polynomial external operators, provided all Young diagrams are transposed. We illustrate the relation in several examples and also discuss evidence for its extension beyond perturbative integrands.

Measurement and classical randomness usually degrade coherence; controlling where and when a subsystem is monitored can instead make them a tunable resource. We introduce a photonic time-multiplexed quantum walk whose fast reconfigurability enables precise position measurements, allowing us to study this interplay in a hybrid quantum-classical pursuit problem: A quantum walker (lamb) evolves on a line while a classical pursuer (lion) performs a lazy random walk. Each lion trajectory drives a distinct coherent, norm-reducing evolution of the lamb, with capture implemented by measurements at the lion's positions; averaging over the recorded trajectories then synthesizes a decoherent process. Counterintuitively, increasing the lion's mobility does not monotonically suppress survival: over a broad range of hopping probabilities, the lamb survives better than against an immobile predator. Directly observing this local enhancement, we demonstrate a manifestly quantum feature aided rather than hindered by classical stochastic control.

We consider whether the kink instability can explain particle acceleration in hard state 'compact' X-ray binary jets. We apply a 1D model to assess the expected growth rate of the instability for a variety of jet models, then scale results from simulations to estimate a dissipation rate for the magnetic energy in the jet. We then consider the effects of radiative cooling on the system. We find that hard state 'compact' X-ray binary jets are likely to be unstable to the kink instability within their acceleration zones across a plausible parameter space. We further find that depending on the parameters of the model, the jets may radiate over a variety of length scales ranging from length scales attributable to a 'failed' jet scenario, to those in keeping with resolved radio observations of 'compact' jets. We discuss the expected evolution of this model through the outburst cycle.

We obtain nonperturbative asymptotic expansions of the electromagnetic form factors of the pi and rho mesons at large spacelike momentum transfer, Q^2->\infty. The calculation is based on a double integral representation in the invariant masses of the composite system. The model parameters are kept at the values fixed in the authors' earlier description of meson electroweak properties. We show that, in the limit of vanishing constituent-quark mass, with the constituent quarks taken to be pointlike, the asymptotic ratio of the longitudinally polarized rho-meson to pion form factors in the helicity basis is consistent with the prediction of perturbative QCD (pQCD) within the adopted parameter ranges.

We introduce a nullspace-guided adaptive (NGA) bootstrap method that improves the energy lower bounds of quantum many-body ground states by refining the bootstrap basis in a dynamic and incremental way. At each iteration, the optimized moment matrix reveals a nullspace of saturated positivity directions, which is intuitively interpreted as annihilators of the approximate ground-state subspace. The NGA bootstrap then prunes operators with small nullspace leverage and grows the basis along descendants of these null directions. By applying the NGA bootstrap to the transverse-field Ising chain, we obtain nearly exact energy lower bounds because the algorithm automatically discovers the eigenoperator structure in terms of Jordan-Wigner fermions from a minimal local bootstrap basis. For the Hubbard chain, it improves upon state-of-the-art energy lower bounds by up to two orders of magnitude, reaching errors ranging from $10^{-3}$ down to $10^{-5}$ in the strongly correlated regimes. We further show that the NGA framework can be used to improve the certified two-sided bounds on general observables. In addition, the bootstrap error decreases approximately as a power law with increasing computational resources. These results suggest that our method provides a practical and scalable route toward accurate bootstrap of general quantum many-body systems.

Cavity-induced electron mass renormalization is an important ingredient of many proposals to control material properties through vacuum field modification. What is its ultimate limit? Here this question is answered by (i) noting that this mass renormalization is essentially due to the field-mediated interaction between the electron and the polarizable degrees of freedom in the cavity mirrors, and (ii) directly evaluating the corresponding Feynman path integral for a 2D electron by numerically exact quantum Monte Carlo. The sought upper limit is provided by the Landau-Pekar polaron in the planar geometry. The presented calculation bridges the gap between cavity control and dielectric engineering of material properties.

We analyse Schrödinger operators with accretive potentials in weighted spaces. We find conditions on potentials and weights for which the Dirichlet realisation, introduced by generalised form methods, has non-empty resolvent set. We establish a domain and graph norm separation property, as well as sufficient conditions for the compactness and Schatten class of the resolvent. Moreover, we investigate the relation between discrete spectra and eigenfunctions of operators in standard and weighted spaces. As applications we extend results on the completeness of eigensystems of operators with accretive potentials from standard to weighted spaces and analyse operator matrices exhibiting a Schur dominance property, in particular, related to a wave equation with strong accretive damping.

We review Bayesian models for estimating the uncertainty induced by missing higher orders in perturbative predictions. These models return probability distributions, which have peculiar shapes typically very different from the Gaussian distribution often assumed in physics analysis. In this work, we are able to obtain smooth probability distributions with quasi-Gaussians shapes by suitably modifying the likelihood and the priors of the models.

Trapdoor claw-free functions (TCFs) underpin much of classical-quantum cryptographic interaction, yet every TCF-based protocol states its guarantees relative to an honestly generated key. We give a family-agnostic abstraction of key certification for (noisy) TCF constructions, built on two notions: a certifiable key relation, an NP relation capturing a family's honest keys with witnesses recoverable from the trapdoor; and certified key generation, which emits with each key a certificate of membership satisfying completeness, certificate soundness with extractability, and key privacy. We instantiate certifiable key relations for different constructions, each met generically by a zero-knowledge argument of knowledge for the relation. As our main application, a generic compiler turns any TCF-based proof of quantumness into a zero-knowledge one, with each security property following from its counterpart in the certification scheme. Finally, we delimit the primitive's reach: for protocols resting on injective invariance, an accepting certificate is itself a family distinguisher, leaking exactly the bit such protocols must hide.

Pion production in intermediate-energy heavy-ion collisions (HICs) provides a sensitive probe of the nuclear equation of state and of the isospin dependence of reaction dynamics. In particular, pion production near threshold is strongly affected by the nucleon-nucleon ($NN$) inelastic cross sections and by the high-momentum components of the nucleon momentum distribution. To explore the influence of these two ingredients on pion production and charged-pion ratios, the in-medium $NN$ inelastic cross sections calculated within the relativistic Boltzmann-Uehling-Uhlenbeck transport theory and the short-range-correlation-induced high-momentum tail (HMT) are introduced into the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model. By simulating Au+Au collisions at intermediate energies, we find that the in-medium modification of the $NN$ inelastic cross sections suppresses the pion multiplicity by reducing the probability of $N\Delta$ production in dense matter. The HMT, on the other hand, enhances the high-momentum components of nucleons and modifies the available energy in individual $NN$ collisions, thereby affecting $NN\rightarrow N\Delta$ reactions and the subsequent pion production. With the simultaneous inclusion of these two effects, the pion yields measured by HADES and the $\pi^-/\pi^+$ ratio measured by FOPI can be reasonably reproduced. These results highlight the need to incorporate both in-medium reaction cross sections and short-range-correlation-induced high-momentum components consistently in transport-model studies of pion production in heavy-ion collisions.

A boolean function $f$ has Fourier dimension $k$ if its nonzero Fourier coefficients span a subspace of dimension $k$. We consider the property testing task of determining whether a function has Fourier dimension at most $k$, or is $\epsilon$-far from being so. We show that there is a $O(k/\sqrt{\epsilon})$-query quantum property tester for this problem, which we show to be almost optimal. Combined with Gopalan et al.'s classical lower bound of $\Omega(2^{k/2})$, this demonstrates an exponential quantum advantage for this task \cite{DBLP:journals/siamcomp/GopalanOSSW11}. We complement this result with a $\tilde{O}(2^{k/2}/\epsilon)$ classical tester, giving a quadratic improvement over the previous best tester, and essentially settling the classical query complexity.

Fast radio bursts (FRBs) are millisecond-duration radio transients of extragalactic origin, whose emission mechanisms and progenitors remain unresolved. Statistical analyses of the rapidly growing samples provide a promising means to constrain the underlying physics. In this review, we synthesize the statistical properties derived from current FRB catalogs, encompassing constraints on dispersion measure, redshift, energy/luminosity functions, repetition rate, and host-galaxy demographics. For repeating FRBs, we examine the statistics of energy, fluence/flux, waiting time, and discuss time-series analyses that reveal memory effects and chaotic dynamics. We further discuss the observational discovery and theoretical interpretation of periodic activity, and survey polarization properties that probe the magneto-ionic environments of FRB sources. Throughout, we emphasize robust empirical trends, account for observational biases and selection effects, and outline outstanding open questions regarding the physical origin of these enigmatic bursts.