Papers

As Quantum Machine Learning (QML) transitions toward practical implementation, the field faces a critical architectural bottleneck that challenges the fundamental assumptions of classical statistical learning theory. In classical deep learning, increasing model capacity typically risks overfitting. However, this study advances a counter-intuitive paradigm: unstructured contemporary QML architectures suffer from a profound state of quantum underfitting, driven by the "expressivity-trainability paradox." We demonstrate that the vast Hilbert space capacity of Parameterized Quantum Circuits (PQCs)-traditionally chased as the source of quantum advantage is the direct mathematical cause of Barren Plateaus (BPs), where gradient landscapes become exponentially flat. By synthesizing recent breakthroughs in Dynamical Lie Algebras (DLAs) and Geometric QML, we establish a comprehensive framework linking the algebraic dimension of circuit generators to their optimization dynamics. Furthermore, we empirically validate this framework on a non-linear binary classification task, illuminating a uniquely quantum manifestation of the bias-variance tradeoff: while unstructured architectures achieve near-perfect training accuracy via unscalable parameterization (quantum overfitting), embedding group-theoretic geometric priors acts as a structural regularizer. By restricting the DLA growth to a polynomial regime, our symmetry-preserving approach sacrifices raw memorization capacity to guarantee scalable, gradient-rich training landscapes, offering a robust roadmap for "Trainability-by-Design" in scalable quantum neural networks.

Practical hardware limitations, including finite transmitter and receiver filter lengths as well as the finite resolution of digital-to-analog and analog-to-digital converters, lead to mode mismatch and degrade the performance of continuous-variable quantum key distribution systems. To address this, we develop a machine learning-based end-to-end optimization framework that jointly optimizes transmitter pulse shaping and receiver matched filtering. The approach employs reinforcement learning under realistic hardware constraints, including a limited number of filter taps, finite digital-to-analog and analog-to-digital converter resolution, analog low-pass filtering, and the optimal mean photon number. By mitigating mode mismatch and accounting for implementation constraints, the proposed method improves overall system performance. Simulation results demonstrate enhanced secure key rates compared to conventional approaches, demonstrating the effectiveness of the proposed framework.

Globular clusters (GCs) can act as gravitational lenses for gravitational waves(GWs) in the wave-optics regime, imprinting frequency-dependent signatures on the observed signal. We investigate whether such lensing effects can be used to probe intrinsic properties of GCs, in particular their central velocity dispersion. Modeling GCs as singular isothermal spheres, we simulate lensed GW150914-like signals and perform Bayesian parameter estimation using waveform templates that include both source and lens parameters. We show that the effective lensing mass can be recovered and, when combined with GW sky localization information and GC catalogs, allows for an estimate of the cluster velocity dispersion. For favorable source-lens alignments, the injected values are well recovered within credible intervals. Our results demonstrate that lensed GWs can provide a complementary probe of GC dynamics and motivate searches for such signatures in current and future observations.

Interference is commonly regarded as the most direct manifestation of the superposition principle. This association is natural for the linear Schrödinger equation, where coherent alternatives combine at the level of probability amplitudes. However, the situation becomes less transparent when nonlinear couplings are present, or when the field is only partially coherent. In this work, we argue that a more robust organizing principle is provided by the local flow generated by phase variations. In this sense, phase-induced flow acts as a unifying mechanism for interference-like dynamics in nonlinear and partially coherent Schrödinger systems. The discussion is developed from a hydrodynamic, or Bohmian, perspective, understood here as a practical probing tool rather than as an additional ontology. Three representative situations are considered: interfering Bose–Einstein condensates described by the Gross–Pitaevskii equation, nonlinear Schrödinger dynamics obtained by modifying the quantum-potential contribution, and partially coherent Airy beams described through their cross-spectral density. Although these systems differ in physical origin and mathematical implementation, they share a common dynamical structure: density-related observables are shaped by velocity fields determined by phase, or ensemble-phase, information. From this viewpoint, interference-like traits, localization, self-acceleration and coherence loss can be interpreted in terms of the preservation, deformation or breaking of the symmetries displayed by the underlying flow. This provides a compact way of connecting interference, nonlinear dynamics, classicality, coherence loss, and structured-light propagation within a single trajectory-based framework.

This study presents a systematic investigation of Mn$_{1-x}$Pb$_{x}$(Bi$_{1-y}$Sb$_{y}$)$_{2}$Te$_{4}$ crystals over a wide range of concentrations (x = 10-60%, y = 5-60%). It was found that the value of the bulk band gap is determined exclusively by the Pb concentration and it closes at Pb 40-50 %, which corresponds to a topological phase transition. The position of the Dirac point is determined by the Pb/Sb ratio, rather than the absolute Sb content. The magnetic properties depend on the dilution of the Mn sublattice by Pb and are weakly sensitive to Sb. We show that the simultaneous substitution of Mn and Bi allows independent control of the topological phase and the position of the Fermi level.

We generalize the linear matrix method for computing normal modes in collisionless stellar disks to distribution functions with sharp edges at zero angular momentum ($L=0$). The generalization adds boundary-integral terms to the matrix equation without increasing its size. We validate the method by computing $m=2$ modes for two Kuzmin–Toomre disk models (Miyamoto $n_{\rm M}=3$ and Kalnajs $m_{\rm K}=6$ families) and comparing the eigenvalues with those obtained from an independent nonlinear matrix method based on logarithmic-spiral expansions. A systematic convergence study over grid resolution and harmonic truncation yields eigenvalues accurate to ${\sim}\,0.003$ in both pattern speed and growth rate. Unlike the nonlinear method, the linear method naturally incorporates gravitational softening, enabling the computation of eigenmodes for softened disk models. The implementation in Julia with GPU acceleration is openly available.

The Sun is a surprisingly difficult radio source to observe and image, even with the SKA. It is multiple orders brighter than the typical radio sources, which sensitive radio telescopes like SKA are optimized for. So, configuring the signal chain to enable solar observations while maintaining linearity is the very first non-standard requirement to be met. Next, solar radio emission spans an impressive range along every single phase-space parameter that can be used to describe it – time scales from solar cycles to millisecond; spectral scales from smooth thermal emission to $\sim$100 kHz coherent emission; brightness temperatures from $10^4$ K for gyrosynchrotron emissions to $10^{13}$ K for bright type-III bursts; fractional polarizations from less than 1% to nearly 100%; and angular scales extending beyond a degree. Capturing the dynamics in solar radio emission in their full glory requires, on the one hand, that all the data that goes into making an image be acquired over very short temporal and spectral spans and, on the other, also imposes requirements for very high imaging dynamic range with high polarization purity. Extracting the information at the requisite temporal and spectral scales from SKA data will require a spectropolarimetric snapshot capability with high dynamic range and fidelity. Additionally, some of the most interesting insights into solar physics and space weather come from studying solar activity, which remains inherently unpredictable. This chapter discusses the various considerations that need to be addressed to help realize the promise of solar and heliospheric science from SKA.

A prevailing intuition holds that quantum protocols using only free states confer no operational advantage. This intuition is contradicted by free-state discrimination gaps in which restricted measurements fail to optimally distinguish even orthogonal free states. Known instances include nonlocality without entanglement and, more recently, nonstabilizerness without magic. We trace these examples to a single convex-geometric mechanism: whenever the set of free measurements is closed, convex, and strict subset the set of all measurements, and the free states is a convex set with an interior, a gap-witnessing ensemble can be drawn entirely from the free states. The resulting gap is operationally rigid: no finite-dimensional assistance – catalyst or quantum memory – can asymptotically improve the discrimination rate beyond the single-shot restricted limit. By contrast, non-free ensembles admit memory-assisted attacks that fully erase the gap, exposing a sharp operational asymmetry between free and resource-carrying ensembles.

Little Red Dots (LRDs) are a population of high-z sources discovered by JWST whose compactness, broad permitted lines, strong absorption features, continuum shapes and luminosities point to accreting supermassive black holes (SMBHs) embedded in dense gas. To date, the metallicity of the hosts of these systems has not been systematically measured. We determine the gas-phase metallicities of LRD host galaxies and test whether their narrow-line emission is consistent with metal poor star formation or AGN activity. We assemble a sample of 24 LRDs at z ~ 2.3-7 with medium and high-resolution JWST/NIRSpec data. We derive oxygen abundances and electron temperatures using the direct Te method applied exclusively to the narrow components of emission lines, and cross-check against widely used strong line calibrations. We derive a sample-averaged abundance of $Z_{T_\mathrm{e}} = 0.08_{-0.03}^{+0.11}\,\mathrm{Z_{\odot}}$ ($T_\mathrm{e} = 23000_{-7000}^{+17000}$\,K), placing LRDs firmly in the metal-poor regime of high redshift star forming galaxies. The R-hat calibration yields a consistent average of $Z_{\hat{\mathrm{R}}} = 0.07_{-0.04}^{+0.07}\,\mathrm{Z_{\odot}}$, with only 4% scatter relative to the direct Te method, providing a robust proxy for systems where the [O III]4363Å line is not detected. We also identify two extremely metal-poor LRDs with metallicities <1.3%. The general population of LRDs are among the lower metallicity galaxies found by JWST at this epoch; they exhibit a narrow range of metallicities with a range of about 0.6 dex, which remains remarkably stable over cosmic time. Such low metallicity may then be a defining property of the class. The fact that LRDs have substantial metallicity across most of the class poses a challenge to models that require formation via pristine gas collapse, while their generally low metallicity indicates that they are not standard AGN.

Understanding the mechanism for launching relativistic jets in active galactic nuclei relies upon measuring the magnetic field strength and emitting plasma number density, tracing their evolution along the jet, and determining the relation between their rest frame energy densities. This can be achieved using measurements of the size and brightness temperature of the compact region at the jet base (the “core”) obtained with very long baseline interferometry (VLBI) across frequencies from 2 to 230~GHz. We develop a framework for independently estimating the magnetic field B* and the emitting plasma number density N* as functions of the jet width $d$, using multifrequency VLBI observations of the core size and brightness temperature. We apply the standard model of self-absorbed synchrotron emission, assuming power-law dependencies of the jet Doppler factor, Lorentz factor, magnetic field strength, and plasma density on the jet width. For an arbitrary jet boundary shape, we derive the dependencies B*(d) and N*(d), and explore a possible relation between the rest frame energy densities of the magnetic field and the emitting plasma. Analysis of core widths and brightness temperatures measured at multiple frequencies points to the possible presence of a magnetic flux decay and effective plasma acceleration within the observed cores at least in some sources of the sample.

Motivated by the temporal dynamics identified in the $(1+1)$ Carroll-Schrödinger theory, we derive a post-Carrollian Schrödinger dynamics in flat Klein space with signature $(2,2)$. Starting from the tachyonic Klein-Gordon equation in double-polar coordinates and removing a spacelike carrier, the spatial radius behaves as an effective evolution parameter, whereas the temporal two-plane $(t_1,t_2)$ serves as the equal-radius configuration space. The additional time direction supplies an $SO(2)$ temporal angular momentum $J$, produces temporal vortex sectors, and gives the centrifugal contribution to the post-Carrollian momentum $P_{\mathrm{PC}}=E_{\tau}^{2}/(2M_{\mathrm{eff}})+J^{2}/(2M_{\mathrm{eff}}\tau^{2})$ in the Hamilton-Jacobi limit. We determine the regular Bessel modes, Gaussian packets, oscillator spectrum, radial $SU(1,1)$ tower, equal-$r$ continuity equation, $\mathfrak{sch}(2)$ symmetry algebra, radial-ordered propagator, and the metaplectic organization of the quadratic sectors. Effective flat connections on the temporal configuration plane give Aharonov-Bohm, Landau, and Fock-Darwin analogues, while the two-body relative sector admits anyonic boundary conditions on the punctured temporal plane. As a curved extension, we derive a branch-dependent carrier reduction and apply it to an illustrative $SO(2,1)$-symmetric Kleinian Schwarzschild exterior, where the Kleinian gravitational source produces a lensing-type angular deviation on the temporal plane.

Filamentary structures are ubiquitous in the interstellar medium and play a key role in the evolution of molecular clouds and star formation. Their morphology and relative orientation with respect to magnetic fields have been widely used as a diagnostic of magnetohydrodynamic processes, turbulence, and gravitational accretion. In recent years, the growing availability of large continuum, spectroscopic, and polarization data stimulated the development of various filament detection techniques. In this review, we present a systematic overview of filament detection methods applied to observations of the interstellar medium. We classify the existing approaches into methodological categories, discuss underlying principles, illustrate their application on a same observational field, discuss limitations and advantages, in particular with respect to the studies of the relative alignment between magnetic fields and filaments. We conclude with presenting a point of view on the perspectives for filament studies in the era of ever-growing astronomical data volume.

The large-scale distribution of galaxies in the Universe forms an intricate, interconnected network known as the cosmic web. Cosmological simulations within the standard Lambda-CDM framework successfully reproduce this filamentary structure and predict that the nodes and filaments are filled with tenuous plasma at temperatures ranging from 10^5-10^8 K. The hottest and luminous plasma in the nodes corresponds to the intra-cluster medium, while the cooler, more tenuous, gas extends along filaments and cluster outskirts. Galaxies and galaxy groups form and flow along these filaments before accreting onto galaxy clusters (the nodes), outlining the dynamical evolution of large-scale structures. During this process, an enormous amount of energy is dissipated through complex plasma processes that can be traced by radio emitting electrons. Despite strong theoretical support for this picture, observational validation remains limited. While massive clusters have been widely detected across various wavelengths, cluster outskirts and the diffuse intergalactic medium within filaments has remained elusive due to their extremely faint emission. The advent of highly sensitive radio facilities such as LOFAR, uGMRT, and MeerKAT has recently enabled a few successful detections of emission from comparatively denser regions of the cosmic-web. These include radio megahalos, permeating the entire cluster volume, as well as bridges of radio emission connecting cluster pairs. In this chapter, we summarize current theoretical insights into the cosmic web, discuss observational strategies and recent discoveries, and highlight how the forthcoming Square Kilometre Array (SKA) is expected to transform our understanding of the cosmic web and the distribution of baryons in the Universe.

We study Magic generation in elastic neutron-proton scattering within a leading low-energy spin-sector ansatz that retains the one-pion-exchange spin structures and treats each scattering direction as a conditional two-qubit spin map. We show that the direction-averaged Magic is locally minimized at the CP-conserving (CPC) point $\bar\theta=0$ at the Clifford point $f_{\rm CPC}=\pi/4$, and for the representative non-Clifford CPC backgrounds analyzed here. At $f_{\rm CPC}=\pi/4$, the CPC spin map reduces to SWAP up to a phase and therefore generates zero Magic from stabilizer inputs. We further evaluate the complete spin-sector Magic functional by averaging over all 60 two-qubit stabilizer inputs and over scattering directions, and find that the curvature at $\bar\theta=0$ is positive only within specific windows of the effective CPC phase $f_{\rm CPC}$. These results identify the CPC point as a local Magic minimum within the restricted low-energy spin sector considered here.

We develop efficient algorithms for evaluating higher-order terms in the hopping-parameter expansion of $\textrm{Tr}\ln M$ on $SU(N_\textrm{c})$ gauge configurations. The resulting algorithms, which exploit a trie data structure for the computation of high-order terms, evaluate the $\kappa^8$, $\kappa^{10}$, and $\kappa^{12}$ terms at computational costs of approximately $20$, $460$, and $8900$ times that of a single staple evaluation, respectively. The correctness of the algorithms is verified by comparison with a computationally expensive but reliable reference calculation. We emphasize that collaboration between human researchers and AI coding agents was essential to the development of these algorithms.

We investigate the dynamical role of internal vibrational modes in the Abelian Higgs model, focusing on how Derrick-type excitations modify vortex dynamics and scattering processes. We study the scattering of excited vortices and show that the interplay between spectral flow and mode excitation generates effective forces and enables resonant energy transfer between translational and internal degrees of freedom. As a result, vortex dynamics become strongly non-adiabatic, exhibiting super-elastic collisions, oscillatory dependence of the final state on initial conditions, and the emergence of fractal structures in scattering diagrams. Our results demonstrate that internal vibrational modes play a fundamental role in vortex interactions, going beyond the standard moduli space approximation and revealing a rich phenomenology driven by mode dynamics.

The evolution of the radio properties of high-redshift radio-luminous active galactic nuclei is well known to be strongly affected by inverse-Compton losses which increase rapidly at higher redshifts due to the higher energy density in the cosmic microwave background radiation. Dynamical models of these sources, however, generally neglect the effects of radiative losses on the dynamics and energetics of the sources themselves. In the framework of an analytical model I developed in a previous paper, I show that the assumption that these losses can be neglected becomes unsafe at high redshifts. The effects on the source dynamics and energetics can result in significantly lower predicted luminosities for high-redshift sources in both radio (synchrotron) and X-ray (inverse-Compton) bands. Modelling of the population of these powerful sources needs to take account of these results in order to infer jet powers at high redshift, and also to make a correct prediction of the number of sources that may be available to provide a background for studies of the 21-cm forest.

Non-collinear density functional theories were developed to extend the use of established collinear exchange-correlation functionals to systems with unpaired electrons in the presence of significant spin-orbit coupling. A comparison of different approaches and implementations is not straightforward, as the methods are often formulated using different fundamental variables and numerical approximations. A consistent review of the formal and numerical aspects of collinear and non-collinear schemes has recently been reported (Desmarais et al., J. Chem. Phys. 154, 204110 (2021)) in the context of two-component methods. In this work, we present an initial effort towards a unified formulation of collinear and non-collinear approximations, encompassing both canonical and Scalmani-Frisch schemes, within the relativistic four-component DKS formalism based on G-spinor basis sets. Our preliminary implementation of the collinear and canonical non-collinear formulations in the DKS module of the BERTHA code extends its applicability and provides a benchmark for a series of simple open-shell hydride molecules (namely, H$_2$X$^+$, with X = O, S, Se, Te, and Po). Finally, we show that incorporating the magnetisation vector into the reformulated non-collinear canonical LDA approach enables a description of H$_2$ dissociation - and open-shell systems more broadly - that closely parallels unrestricted non-relativistic approaches, notably without explicitly imposing the broken symmetry solution as is often required in non-relativistic collinear calculations. This unified formulation forms the basis for a rigorous comparison between different numerical approximations, which will be essential for obtaining stable results for the non-collinear GGA exchange-correlation functionals.

Pulse-resolved spectral phase measurement of mid-infrared (MIR) pulses is essential for many applications, from precise waveform control to ultrafast quantum optics. However, conventional MIR pulse characterization techniques are typically limited to sub-kHz-rate operation, leaving a substantial speed mismatch with MIR sources operating at kHz or MHz rates. Here, we introduce time-stretch upconversion-based mid-infrared pulse evaluation (TSUBAME), a technique that enables pulse-to-pulse spectral phase characterization of ultrashort MIR pulses at the laser repetition rate. TSUBAME combines MIR-to-NIR (near-infrared) upconversion, time-stretch, and spectral interferometry to achieve scan-free high-speed spectral phase measurements. We validated the technique by measuring MIR pulses spanning 4.98-5.30 um while introducing well-defined dispersion, obtaining excellent agreement with theoretical predictions. Operating at a measurement rate of 1 MHz, TSUBAME achieves the fastest single-pulse-resolved spectral phase characterization of MIR pulses reported to date. As a further demonstration, we captured dynamic spectral phase variations on a microsecond timescale. TSUBAME provides a powerful tool for real-time monitoring and optimization of high-repetition-rate MIR pulses, with potential applications in strong-field physics, high-harmonic generation, and coherent molecular control.

Isolated stellar-mass black holes (IBHs) are expected to be abundant in the Milky Way, yet their electromagnetic signatures remain largely undetected. We investigate the detectability of IBHs in molecular clouds using a 1D, multi-wavelength emission model that incorporates magnetic flux transport controlled by the magnetic Prandtl number $P_m$. We find that magnetically arrested disks (MADs) form for $P_m\gtrsim 1$, where the magnetic flux threading the black hole is in a saturation value. On the other hand, MAD formation is restricted to a limited parameter range for $P_m<1$, In our model, outer parts of accretion disks, around 100 gravitational radii, efficiently emit infrared photons detectable by WISE. This feature is not captured by the conventional one-zone model. X-ray emission depends strongly on $P_m$; For $P_m=1$ where MAD is formed, X-ray emission is dominated by nonthermal radiation, whereas inverse Compton emission becomes dominant for $P_m=0.5$ where the magnetic field is weaker than the saturation value. X-ray detection is plausible if they are in dense molecular-cloud filaments for $P_m\ge1$, although it is challenging for $P_m< 1$. These results demonstrate that magnetic flux transport plays a key role in shaping the multiwavelength observational signatures of IBHs.

We investigate the Landau-Zener description of resonant axion-photon conversion in neutron star magnetospheres. We find that this picture often fails for axion conversions to millimeter-to-optical band photons due to the characteristic resonance width exceeding the size of the conversion region. This comparison of scales yields a simple criterion for evaluating the validity of the Landau-Zener formula. We verify this criterion numerically, and show that when invalid, the Landau-Zener conversion probability may significantly deviate from the numerical result. In light of these findings, we revise constraints on axions from neutron star optical-band polarization searches.

Extreme events in financial systems, often captured by indicators such as volatility, remain difficult to identify close to their onset. Volatility shares many statistical properties with other natural, complex systems which experience extreme events, which we explore in this manuscript. We extend the analogy between rogue waves in optical and hydrodynamical systems to financial volatility by identifying rogue-wave-like peaks with similar statistical properties. We use a Schrödinger equation where the potential follows the shape of a Kerr nonlinearity to examine the properties of financial volatility indices within a moving time window. We see evidence of Anderson localisation as a rogue peak approaches in the VIX, and show that the numerical gradient of the system's minimum eigenvalue reliably spikes at the onset of an extreme event. We adapt our methodology to simulate the real-time arrival of data, and show that all but one of the VIX's major peaks can be detected given a reasonable amount of history. We then perform two out-of-sample tests, one for the VXO index, and one for the VSTOXX index, and successfully replicate our initial results, identifying all but one major peak (87.5% or 7/8) in both cases. This method of analysis shows considerable promise as a tool for identifying potential financial crises, aiding in their mitigation.

We consider a very general scale-invariant scalar-tensor theory of gravity and its flat cosmological solutions. We show that any stable configuration with non-degenerate gravitational dynamics carries a non-vanishing cosmological constant, unless the quartic self-coupling of the scalar field vanishes. Since this condition is not protected against radiative corrections, a residual cosmological constant is expected as a generic and robust prediction of this class of theories. This result suggests that dark energy may be a natural consequence of an early scale-invariant phase of the Universe.

We introduce a unified graph-spectral framework for quantifying multipartite entanglement, built upon an entanglement graph and its associated entanglement matrix. The framework accommodates general subsystem and partition structures of composite quantum systems, while offering a complementary geometric and network perspective on characterizing multipartite quantum correlations. We prove that the resulting graph-spectral entanglement satisfies the requirements of an entanglement measure. Furthermore, we derive a multipartite monogamy relation and, based on the resulting spectral hierarchy, introduce residual graph-spectral entanglement for arbitrary multipartite states. This establishes a general construction of residual entanglement beyond conventional qubit-based formulations and provides a new approach to investigating, quantifying, witnessing, and classifying multipartite entanglement in both theoretical and experimental settings.

This work presents a comprehensive analysis of coupled stochastic van der Pol oscillators, a paradigm for understanding synchronization, bifurcations, and chaos in nonlinear systems subject to random fluctuations. The system comprises two or more oscillators with nonlinear damping, linear diffusive coupling, and additive Gaussian white noise. We develop a unified framework that systematically connects global bifurcations, synchronization phenomena, and chaotic dynamics within a single coherent stochastic model. We explore the stochastic dynamics of coupled van der Pol oscillators by seamlessly blending theoretical principles with in-depth numerical simulations. This integrated approach forms a robust framework for analysis, with essential phenomena clearly depicted in the accompanying figures. We then extend this framework to a comprehensive investigation of large networks, focusing on their continuum limit, emergent pattern formation, the role of noise, and the onset of collective chaos.

We introduce the average confidence width $\Delta_{a} x=\int_0^1\Delta_{c} x (\theta)\,\mathrm{d}\theta$: the confidence width $\Delta_{c} x(\theta)$—the measure of the smallest region of position space carrying probability $\theta$—averaged over all confidence levels. It is the first moment of the decreasing rearrangement of the position density, an $L^1$ (mean-absolute-deviation) measure of localization, and $\Delta_{a} x\,\Delta_{a} p$ is dilation invariant. We study the uncertainty relation $\Delta_{a} x\,\Delta_{a} p\ge c^\ast\hbar$ for pure and mixed states. A mean–entropy argument with the Bialynicki-Birula–Mycielski relation gives $c^\ast\ge\pi/e$, while the ground state $\psi_0$ of the Fourier-invariant operator $|x|+|p|$, with $E_0=1.1040744$, gives $c^\ast\le E_0^2\approx1.2190<4/\pi$: Gaussian states, which saturate the Heisenberg–Kennard and entropic relations, are not optimal here. We prove that $\psi_0$ is nondegenerate, nodeless, even, self-dual, and symmetric decreasing, with algebraic tails, and that the sharp hybrid relations $\Delta_{a} x \cdot 2 \langle |p-p_0| \rangle \ge E_0^2\hbar$ and $2\langle|x-x_0| \rangle \cdot\Delta_{a} p\ge E_0^2\hbar$ hold for all states, so $\Delta_{a} x\,\Delta_{a} p\ge E_0^2\hbar$ whenever either density is symmetric unimodal; the second variation of $\Delta_{a} x\,\Delta_{a} p$ at $\psi_0$ is positive definite apart from the symmetry directions. Extensive numerical minimization, including coherent states, never finds a product below $E_0^2\hbar$ and consistently returns $\psi_0$, supporting the conjecture $c^\ast=E_0^2$. In two dimensions the relation is sharp and saturated by Gaussians, identifying the dimension as the origin of the non-Gaussian optimizer in one dimension. Finally, we discuss other complementary pairs and the relation of the width to interferometric predictability and visibility.

Coronal Mass Ejections (CMEs) are large expulsions of magnetized plasma from the Sun into interplanetary space and are the primary drivers of extreme space weather variations. The strength and topology of CME magnetic fields largely determine their impact on Earth. Although visible-light coronagraphs routinely observe CMEs and provide their geometric and kinematic properties, they cannot directly measure CME vector magnetic fields. These fields evolve from initiation through the inner heliosphere due to interactions with other CMEs, coronal structures, and the ambient solar wind, leading to significant structural deformation. Such evolution complicates predictions of the CME magnetic field at Earth. Accurate measurements of CME magnetic fields in the corona and heliosphere are therefore essential for advancing space weather forecasting. Radio observations spanning MHz to GHz frequencies provide a powerful remote-sensing approach for measuring CME magnetic fields from the ground. Recent observations with Square Kilometre Array (SKA) precursors and pathfinder instruments, as well as other new-generation facilities, have demonstrated the potential of these radio techniques for CME magnetic-field diagnostics. At the same time, these studies have highlighted several limitations of current instruments. The higher sensitivity, wider instantaneous bandwidth, and broader frequency coverage of the SKA will open a new observational window, enabling these techniques to be fully exploited for constraining SpWx models and improving predictive accuracy. However, such observations are non-standard and require special consideration in scheduling, calibration, and imaging. Developments achieved with SKA precursors and pathfinders are paving the way for robust CME magnetic-field measurements with the SKA.

Fast Radio Bursts (FRBs) are millisecond-duration radio transients that are widely believed to originate within magnetar magnetospheres. Large-amplitude radio waves associated with FRBs propagate through strongly magnetized plasmas, where nonlinear scattering can affect their propagation. By solving the relativistic motion of a single particle interacting with electromagnetic waves of arbitrary polarization and propagation angle $\theta_B$, we compute the scattering cross section and the corresponding optical depth. The scattering cross section of the O-mode can exceed that of the X-mode when $a\sin\theta_B < \omega_B/\omega$, and becomes comparable to that of the X-mode when $a\sin\theta_B > \omega_B/\omega$, where $\theta_B$ is the angle between the wave vector and the background field. In the strongly magnetized and quasi-parallel limits, the cross sections asymptotically recover the linear regime scalings and are strongly suppressed by relativistic particle motion, leading to optical depths well below unity. We also show that curvature radiation losses of O-mode waves are strongly suppressed for quasi-parallel propagation, allowing them to escape from the magnetosphere at moderate multiplicities. We propose that Alfvén waves excited by magnetar crust quakes can reach amplitudes comparable to the background magnetic field, thus straightening field lines and reducing $\theta_B$. This geometrical alignment enhances the ability of FRBs to freely propagate through the open field line region. These results suggest that large-amplitude waves propagating quasi-parallel to open magnetic field lines can avoid significant single-particle scattering losses, providing a possible condition for their escape.

We present a free-space plasmonic modulator based on a single heavily-doped semiconductor layer. We investigate its ability to modulate both the linear and nonlinear response at mid-infrared frequencies slightly below the plasma frequency of the semiconductor. We demonstrate electric control of the linear transmittance and reflectance, and of the efficiency of third-harmonic generation with a field-effect gate structure. We discuss further performance optimization of the device in terms of modulation speed and depth towards a fast modulator with very simple active material requirements. Our results establish a viable route toward practical plasmonic modulators and mixers operating in the mid-infrared atmospheric window available for free-space communications at wavelengths between 8 and 12 um.

The ground state of $^{12}\mathrm{C}$ has often been approximated by a mean-field picture. This conventional view has been challenged by recent nuclear theories suggesting non-negligible $\alpha$-cluster formation, but experimental evidence remains inconclusive. Here, we show that existing $^{12}\mathrm{C}(p,p\alpha)^{8}\mathrm{Be}$ data provide direct evidence for a pronounced $\alpha$ cluster formation in the ground state of $^{12}\mathrm{C}$. We analyze the data with distorted-wave impulse approximation using $\alpha$ preformation amplitudes from an unrestricted $3\alpha$ cluster model and harmonic-oscillator-based models. The results show that the former reproduces the measured cross sections, whereas the latter underestimate them by more than an order of magnitude. Thus, contrary to conventional expectations, the data support a nearly fully developed three-$\alpha$ cluster structure in the ground state of $^{12}\mathrm{C}$.