Papers

The interfacial structure and dynamics around a quenched impurity is far from understood till date. Here we explore the structural and dynamical properties of interface between colloidal fluid film and a quenched impurity by using computer simulation. We tune the size($\sigma_{imp}$) of a quenched pinned impurity and observe that the impurity surface is wetted by a fluid layer, giving rise to a finite-width interfacial region for sufficiently large impurities. Beyond this interfacial region, the host fluid exhibits quasi-long ranged orientational order(QLRO) due to the fluid- crystal phase coexistence. We find that the mean diffusivity becomes very low in the QLRO phase where the self van Hove function shows an exponential tail, signature of dynamic heterogeneity within the system. In the presence of second impurity the orientational order is suppressed if the fluid layers around the impurity particles overlap.

Among the various entanglement measures, the negativity stands out not only for its clear physical meaning but also for being directly computable from the spectrum of the partial transpose. However, the negativity captures only the total weight of the negative eigenvalues, whereas the finer structure of the negative spectrum remains largely unexplored. In this work, we fill this gap by introducing a hierarchical generalization of the negativity, the Ky Fan $k$-negativity, and developing a unified analytical framework for deriving spectral bounds on the partial transpose. To obtain the absolute bounds, we reduce the maximization problem to a spectral graph optimization, whose solution yields the exact bound for every $k$ through a single cubic equation. We further investigate these spectral bounds both analytically and numerically under a fixed-purity constraint. In particular, we solve the $k=1$ case completely and uncover a simple underlying graph structure. As two direct applications, we show that the Ky Fan $k$-negativity robustly certifies genuine multilevel entanglement and that it converts the $p_3$-PPT condition into a quantitative lower bound on the negativity.

The translational dynamics usually decouples earlier than the rotational in supercooled liquids as the temperature decreases, whereas the inverted scenario remains scarce reported. In this work, starting from the coarse-grained ortho-terphenyl model, we build a rigid tetrahedral structure model. It exhibits an earlier decoupling in rotation than in translation. The Stokes-Einstein-Debye relation breaks down while the Stokes-Einstein relation remains intact. The decoupling happens at approximately 2Tg similar as that observed in supercooled water. The rotation shows more heterogeneous dynamics than the translation at all temperatures. Our results suggest that the steric hindrance plays an important role in determining the decoupling between the translational and rotational dynamics.

We initiate the study of nonlinear wave equations on the Witten bubble spacetime (also known as the "bubble of nothing"), which is an $\mathrm{SO}(3,1)\times \mathrm{U}(1)$-symmetric solution to the Einstein vacuum equations in $(4 + 1)$ dimensions. This spacetime was introduced by Witten to model the semiclassical instability of the Kaluza–Klein spacetime $\mathbf{R}^{3+1}\times S^1$ (which is classically stable by work of Huneau–Stingo–Wyatt (arXiv:2307.15267)). We prove a small-data global existence result without symmetry assumptions and an improved decay result for $\mathrm{U}(1)$-symmetric solutions to a class of semilinear equations satisfying a version of the null condition. Key to the proof are novel estimates for the linear wave equation, which has been studied in the physics literature by Bhawal and Viveshwara and in the mathematics literature by Bachelot (arXiv:1601.03682).

Fast-light approximations neglect fluid evolution along rays, whereas slow-light modeling is indispensable for recovering the true magnetohydrodynamic state. However, full slow-light radiative transfer for extended general relativistic magnetohydrodynamic (GRMHD) sources requires simultaneous access to many fluid snapshots and is memory-intensive. We introduce CoportSL, the first contribution-constrained hybrid slow-light framework for time-dependent full-Stokes imaging. It uses emission, absorption, and Faraday contributions to identify where fluid evolution must be retained, applies fast light elsewhere, and loads only snapshots spanning the relevant delays. Tests with M87*-like magnetically arrested disk GRMHD data show that the contribution-based region and delay-based snapshot restrictions each keep normalized full-image Stokes differences below $4\times10^{-3}$ relative to the corresponding complete calculation. At this accuracy, CoportSL requires 75.3% and 44.7% fewer snapshot layers for near-horizon and jet images, respectively; its per-frame slow-light transfer time remains comparable to fast light. For the two configurations, source-code estimates place the capacities of the principal data structures at 255-657 GiB for a fixed public ipole version and 20.2-37.3GiB for CoportSL, bringing both configurations within workstation-scale memory. Fast–slow comparisons further show close agreement in near-horizon variability, whereas jet variability follows similar overall trends but differs in local peaks and amplitudes; in both cases, fast light misses substantial full-Stokes spatial structure. As the next-generation Event Horizon Telescope (ngEHT) advances toward dynamical imaging and spatially resolved polarimetry, CoportSL provides a computationally practical way to model full-Stokes finite-light-travel-time signatures in extended black hole systems.

Nanodiamonds hosting luminescent point defects, known as fluorescent nanodiamonds (FND), are a leading platform for quantum technology. The nitrogen-vacancy (NV) centre is the most intensively studied of these; its negatively charged state (NV$^-$) can serve as a qubit at room temperature, and its stability is governed by surface functional groups. We present two solution-phase fluorination routes for stabilising NV$^-$: direct C-F bond formation by decarboxylation with xenon difluoride via a radical mechanism, and the Balz-Schiemann reaction, which replaces surface amino groups with fluorine. The two routes were compared by infrared, X-ray photoelectron, energy-dispersive X-ray, Raman and photoluminescence spectroscopy. Both gave a high NV$^-$ fraction, up to $\sim$85% on average, which to our knowledge is among the highest reported for surface-terminated nanodiamonds of this size and, in particular, for fluorine termination. We attribute the stabilisation to the fluorination treatment, which removes acceptor-like carboxyl groups and forms C-F bonds that give the surface a positive electron affinity. Frequency-domain relaxometry shows that the fluorinated particles retain a long spin-lattice relaxation time, $733\pm56$ and $712\pm20$ $\mu$s for the XeF$_2$ and Balz-Schiemann routes, several times the values reported for commercial HPHT nanodiamonds, although shorter than the $1173\pm123$ $\mu$s of the as-received material. Fluorination thus activates near-surface NV$^-$ centres, which dominate relaxometric sensing, at the cost of a moderate shortening of $T_1$.

We investigate shortcut-to-adiabaticity protocols for the rapid compression of optical solitons in nonlocal media. Using a variational approximation, we derive an effective Ermakov-like equation for the soliton width and employ inverse engineering to design propagation-dependent control parameters. Three control strategies are compared, based respectively on modulation of the characteristic nonlocal length, the Kerr nonlinearity, and the external parabolic confinement. We show that all three protocols enable high-fidelity compression over strongly reduced propagation distances. By comparing control smoothness and final fidelity, we find that the relative performance of the protocols in the very short-distance regime depends on the chosen criterion, revealing a trade-off between implementation smoothness and target-profile accuracy. These results establish a practical and general route to fast soliton manipulation in nonlocal media.

We present the X-ray surface brightness maps of the jet from the quasar PKS 0637-752, using two epochs of archival Chandra observations (1999 and 2017). We present, for the first time, a model of the faint inner jet extending from 3.4 to 7 arcsec from the core, interpreting its X-ray emission as inverse Compton scattering of cosmic microwave background photons by the synchrotron-emitting relativistic electrons. The inner jet contrasts with the bright outer part of the jet, dominated by several discrete knots for which upper limits to the Fermi gamma-ray flux rule out the inverse Compton mechanism. It is the first detailed inverse Compton model published for this inner jet. We examine three physically motivated scenarios, distinguished by the high-energy cutoff of the electron distribution, that can account for the observed radio, millimeter/submillimeter, and X-ray emission while remaining consistent with optical and gamma-ray upper limits. We also report for the first time X-rays from the radio lobe at the end of the receding jet.

A physical learning network is read at a few accessible nodes. Every task and learning rule that uses only the steady voltages and currents there, at a fixed operating point, acts through the boundary response map. Changes in the kernel of its Jacobian are blind to first order. A walk along one fiber ran to a 600-step cap, one edge then at 15.2 times its start. A decomposition theorem splits the response Jacobian over the hidden components. The blind dimension adds over components whose surviving slots are disjoint. A boundary-to-boundary edge adds one parameter and deletes one slot. Exposing a hidden node changes only its component. For one hidden node the contribution counts the bipartite components of the non-adjacency graph of its neighbors. For a pocket of h hidden nodes a factor-analysis bound caps what outside electrodes can expose. It is attained when every pocket node meets every neighbor and no edge joins two of those neighbors, so past a threshold further electrodes outside such a pocket expose nothing. An electrode inside such a pocket, when its hidden nodes form a clique, is worth h-1 directions where one outside is worth none. Read as vector displacements rather than potentials, the same nodes left no deficit beyond counting in all 90 spring networks tested, each a pocket fully joined to five or more accessible nodes, and nothing blind in 88. What limits the reading is the quantity measured as much as the number of contacts. Maximum-weight spanning forests give a proved upper bound on the blind dimension. The matching equality is proved for one hidden node and conjectured beyond. It holds in all 5,343 components whose maximum could be attained and certified, and the forest count matched the certified blind dimension in 1,448 of 1,500 held-out networks, where the maximum must be searched. A self-learning circuit shows the split on hardware.

Bivariate bicycle (BB) codes of Bravyi et al.~\cite{Bravyi2024} are quantum low-density parity-check codes with weight-$6$ checks, exemplified by $[[144,12,12]]$ with $kd^2/n=12$. We develop the algebraic structure theory of BB-type codes with weight-$8$ checks (weight-$4$ generator polynomials) and use it, together with an exactly validated search pipeline, to construct and certify new codes. We prove an exact dimension formula $k=2\dim R/(A,B)$ (forcing even $k$), a $4\ell m$-element symmetry group on generator pairs, an $X/Z$ distance equality $d_X=d_Z$, and a family of subgroup-coset kernel vectors giving rigorous distance upper bounds and a design rule for high-distance constructions; all distances are computed exhaustively by a cross-validated bit-mask verifier. At $n=144$ the pipeline returns a census of $53$ codes whose strongest members surpass the BB benchmark: $[[144,6,d\ge 15]]$ exceeds the benchmark distance $12$ (certified $d\ge 15$), $[[144,10,12]]$ reaches it with weight-$8$ checks, and $[[144,16,10]]$ encodes a third more logical qubits at $kd^2/n=11.11$ ($7.4\%$ below benchmark) while decoding no worse. At $n=72$, $[[72,14,8]]$ attains $kd^2/n=12.44$—more than twice the same-length BB code—and decodes better; a circuit-level memory experiment places our weight-$8$ codes at $\approx 0.1\%$ pseudo-threshold versus $\approx 0.4\%$ for the BB reference under an identical model, quantifying the threshold cost of the heavier checks. All structural statements are verified numerically on the whole census.

The recent LUX-ZEPLIN (LZ) search reported a nuclear-recoil event near $248~{\rm keV}$. Such a high-recoil event can be interpreted in terms of endothermic inelastic dark matter scattering, which typically requires a mass splitting of order a few hundred keV between the initial and final dark states. The inert doublet model (IDM) provides a natural realization of this scenario through the $Z$-mediated transition $H+N\to A+N$. In this work, we systematically examine whether this interpretation can be consistently realized in the IDM under the relevant theoretical constraints and existing experimental bounds. We perform a detailed profile-likelihood analysis of the LZ event, and find a viable high-mass IDM region with a profile best fit at $m_H=1080~{\rm GeV}$ and $m_A-m_H=369~{\rm keV}$.

Rydberg atomic electric-field sensors, under the framework of optical excitation and readout, can overcome the size-to-wavelength constraint imposed by the Chu limit. However, their sensitivity for decametric-wavelength shortwave electric fields is substantially lower than that for microwave ones, stemming from the off-resonant nature of low-frequency signals with Rydberg transitions. Here, we demonstrate a high-sensitivity heterodyne shortwave sensor based on microwave-dressed Rydberg atoms, leveraging precisely modulated Floquet sidebands. Around local- and microwave-field-engineered Floquet sidebands, the steep response gradient, arising from the enhanced atom-shortwave interaction through additionally created coherent channels, induces pronounced amplification of the heterodyne intermediate-frequency signal. As a result, compared to the same atomic heterodyne setup without microwave modulation, such Floquet-sideband-enhanced shortwave measurement boosts the sensitivity by four orders of magnitude, yielding a sensitivity of -122.7 dBm/Hz for shortwave at 30 MHz. This work offers a potential route to high-sensitive portable shortwave receivers in radio astronomy, radar and long-distance communications.

We present a photometric and timing study of the near-period-gap SU~UMa-type dwarf nova YZ~Cancri, based on nearly continuous Transiting Exoplanet Survey Satellite (TESS) photometry and long-baseline ground-based observations. Our main observational result is that the positive-superhump (SH) waveform follows a repeatable, stage-dependent sequence during superoutbursts (SOs). In the two well-covered TESS SOs, and consistently in the long-baseline ground-based SO sample, the plateau waveform evolves from an early saw-tooth profile (ST), through a double-humped profile with unequal maxima (DHd), to a more symmetric double-humped profile with nearly similar maxima (DHs). The global and time-resolved Lomb–Scargle periodograms show that power near the positive-SH time scale and its harmonics is concentrated during SOs, whereas quiescent and normal-outburst intervals lack a comparably persistent SH-band signal. The dense TESS maxima–minima timing sequence shows different clock stability in different waveform stages: precursor modulations have slightly longer local periods, the middle-to-late DHs plateau is the most regular timing interval, and the post-plateau evolution is affected by phase switching and possible secondary/late-SH contamination. The TESS data also reveal profile-clock coupling, with SH amplitude and rise/decay durations evolving together with the timing residuals. As a secondary timing constraint, we obtain a common TESS-timing-based mean positive-SH period of $P'_{\rm sh}=0.09043(27)$~d, corresponding to a SH excess of $4.03(31)\%$ and an approximate mass ratio of $q=0.175(11)$. The repeatable ST–DHd–DHs sequence makes YZ~Cnc a useful system near the lower edge of the period gap, and may trace the growth, redistribution, stabilization, and decay of the light source associated with an eccentric, precessing accretion disk during SOs.

A Poincaré section replaces a flow by a return map, but for a chaotic system this map is usually known only from sampled crossings. We show that coarse transport can be read directly from Koopman spectral data, without fitting the map. Measure-preserving EDMD retains the isometric structure; riggedDMD then approximates spectral measures and constructs finite regularized wave packets. Packet phase supplies a finite-resolution transport coordinate; low modulus marks a singular skeleton where the phase becomes ill-conditioned. We demonstrate the idea on the Rössler system, a 32-mode Kuramoto–Sivashinsky Galerkin system, and the forced Duffing oscillator. The packets yield coarse symbolic models on sections ranging from an almost one-dimensional curve to a visibly thick set. Their graphs organize observed low-period orbits and guide targeted searches for others. In Duffing Regime~II, a seven-region rule accounts for $91\%$–$94\%$ of filtered one-step transitions, while failures in the lowest retained modulus decile occur at $5.08$–$5.20$ times the overall rate. The packets are not Koopman eigenfunctions, nor are the regions exact Markov partitions. Together these computations show how spectral information beyond isolated eigenpairs can expose chaotic transport directly from trajectories.

We develop a theoretical model for self-generated magnetic islands in relativistic laser-driven channels in near-critical-density plasmas. The islands arise from the nonlinear superposition of the quasi-static magnetic fields generated by the longitudinal channel current $j_x$ and the laser-front driven transverse current $j_y$. By deriving the critical conditions among laser depletion, transversely symmetric channel formation, and magnetic-island formation, we identify the laser-plasma parameter window in which the magnetic island structures can exist. Within this window, the balance between the laser ponderomotive force and the charge-separation force, expressed through an effec tive electron density $n_\mathrm{eff}$, determines the transverse island width $H$, whereas the mismatch between the laser group and phase velocities determines the longitudinal period $L$. Large-scale particle-in-cell simulations over a broad range of laser intensities and plasma densities validate the resulting scaling laws. The model turns the island geometry from a qualitative feature of the channel field into a predictable quantity, providing a basis for tailoring electron transport, particle acceleration, high-energy radiation, and novel fusion ignition schemes in relativistic laser-plasma interactions.

The extreme magnetoresistance of compensated semimetals is governed by both the Fermi-surface geometry and carrier relaxation, but these contributions are difficult to disentangle in finite-size structures. Here, we combine longitudinal and Hall magnetotransport measurements with temperature- and angle-dependent Shubnikov–de Haas oscillations in single-crystalline Sb flakes grown by chemical vapor deposition (CVD), with thicknesses ranging from 110 to 783 nm. As thickness increases, the non-saturating MR at 2 K and 14 T rises nearly 30-fold, reaching $7.13\times10^{5}\%$, while the primary frequency $F_{\alpha}$ remains approximately 99 T without any systematic shift. A joint three-channel analysis of $\rho_{xx}(B)$ and $\rho_{xy}(B)$ reveals that this evolution is driven by an increase in the mobility of a nearly compensated electron–hole pair, rather than by a reconstruction of the primary pockets. Angle-dependent measurements confirm the existence of a closed three-dimensional $\alpha$ pocket, and a reproducible high-frequency sector (335-377 T) is consistent with the electron $\beta$ orbit of the $L$-point pockets in bulk Sb. Together, the transport and quantum-oscillation results show that thickness tunes extreme MR through dimension-dependent scattering while preserving bulk-like fermiology.

We uncover and prove a general class of hidden zeros in tree-level amplitudes with massless fermions. For arbitrary even numbers and arbitrary arrangements of massless real adjoint fermions and gluons, color-ordered gauge-theory amplitudes in $D=4,6,10$ vanish on general rectangular kinematic loci supplemented by species-dependent bridge conditions. The fermion–fermion bridge is governed simply by the vector current $\chi_i\gamma^\mu\chi_j$, while mixed and gluonic bridges are fixed by the corresponding gauge-covariant contractions. A worldsheet analysis proves the result at arbitrary multiplicity and traces its universality to the local fusion channels $ff\to g$, $fg/gf\to f$, and $gg\to g$, with no new primitive bridge structures appearing at higher fermion multiplicity. The same mechanism extends to ten-dimensional amplitudes with gravitons and arbitrary even numbers of gravitinos in factorized gamma-traceless polarizations, and to single-trace Einstein-Yang-Mills amplitudes with adjoint gluinos and gravitons. These results expose a finite local structure underlying fermionic hidden zeros across gauge and gravitational amplitudes.

Radio surveys provide exponentially increasing amounts of observational data, which requires the development of novel data reduction and analysis methods. To this end, realistic simulations of observational data provide controlled environments for testing and developing new methods. Diffusion models excel at synthesizing realistic image data, but are limited by size constraints and high computational demands. We implemented a latent diffusion model (LDM) to synthesize realistic radio survey map cutouts. Further, we developed a technique for sampling radio survey maps of arbitrary size with the LDM. This is done by sampling in multiple sequential steps, whereby consistency is provided through context vectors and image inpainting. We trained our model on observations from the LOFAR telescope obtained from the third data release of the LOFAR Two-Metre Sky Survey. We implemented a LDM composed of a vector-quantized variational autoencoder and a diffusion model operating on the resulting latent representations. We added information on source locations, brightness and sizes by extracting parameters from the public source catalog and encoding them into a vector format passed as context to the LDM. We trained the model for image inpainting to facilitate continuous sequential sampling. We were able to generate realistic cutouts of 512 pixel side length, corresponding to ~5.7 arcmin, with precise control over source locations and brightness. Control over source extension was achieved at lower precision. Sampling of arbitrary-sized maps was made possible, showing realistic results with seamless combination of individual samples and limited only by occasional sampling artifacts.

We apply a thin metal rod (copper rod) as a probe in the alternating magnetic field generated by a Helmholtz coil, and measure the variation of the induced electromotive force (EMF) on the metal rod at different radial positions of Helmholtz coil. Experimental results show that the induced EMF is zero when the center of the metal rod passes through the center of the cylindrical magnetic field inside the Helmholtz coil. When the metal rod is displaced from the center of field to different radial positions, the induced EMF gradually increases from zero, reaches a maximum at a certain position, and then decreases monotonically as the radial distance continues to increase. At the position where the induced EMF reaches its maximum, the metal rod intersects the radial cross-section of the internal magnetic field of the Helmholtz coil at two points, with a small central portion of the rod located inside the Helmholtz coil and the two end portions outside the coil. To explain the experimental phenomena, we construct four simplified models of the magnetic field distribution based on the actual field distribution of the Helmholtz coil to quantitatively investigate the radial variation of the induced EMF along the metal rod. Our theoretical results show that the four models yield similar results and can all qualitatively explain the experimental data curves, particularly reproducing well the variation trend of the induced EMF and the position of the extremum point. The result of piecewise function fitting model is quantitatively in good agreement with the experimental data. This work is also very much helpful and instructive for undergraduate-level students.

The evolution of modern-day communication networks towards enhanced capacity and robustness is driving interest in topological light wave as a next-generation information carrier. However, harnessing its potential is hindered by the lack of an effective topological reader, particularly when strong disorder renders conventional readout intractable. Here we address this by introducing TOPO$^{2}$, an artificial intelligence framework that leverages on topological learning to recover topological information from light. We demonstrate it on highly distorted optical fields with embedded Skyrmion topologies, showing that we can extract the topological numbers in a single shot with just a conventional camera. We showcase its capability in a TOPO$^{2}$-based communication scheme, sending and recovering information encoded in a topological alphabet, confirming that it outperforms conventional approaches. Our connection of topological photonics with topological AI as a powerful paradigm for robust high-capacity information encoding and processing opens a new path towards topological information optics.

This article systematically examines the effects that must be taken into account when modeling the dechanneling of highly ultrarelativistic charged particles caused by incoherent scattering by electrons of crystal atoms. Changes in the particle electromagnetic field that occur in condensed matter at highly ultrarelativistic energies are taken into account. The excitation of both collectivized electrons and inner-shell electrons of atoms is considered, taking into account thermal vibrations and the inhomogeneous periodic distribution of atoms in crystals. Differences in the calculations of stopping power and mean square scattering angle by electron of channeled particles are described. The need to separate both of them into diffuse processes, accompanied by the transmission of a transverse momentum which does not exceed the transverse momentum of the channeled particles, and instantaneous dechanneling processes with a greater transmitted momentum, the variation range of which reaches several orders of magnitude, is substantiated. The main result of the present work is expressions for the mean square projected scattering angles per unit length in planes parallel and perpendicular to the atomic plane, which also allow for the introduction of effective minimum momenta for incoherent scattering. Expressions of both types take into consideration completely the nonlocal effects of momentum transfer from crystal electrons to particles moving along classical trajectories, and allow for the formulation of simple methods for modeling the incoherent scattering of ultrarelativistic positively charged particles.

We report transmitted conductance measurements between a source and reflection-less contacts connected to a compressible quantum Hall fluid with filling fraction $\nu$. We observe that total sum of transmitted conductances universally approaches Hall conductance $\nu(e^2/h)$. The universality of this sum rule is established experimentally across integer and fractional quantum Hall regimes, remaining invariant under variation in temperatures, sample geometries, material qualities and quasi-particle interactions. Chiral transport in compressible quantum Hall fluids, characterized by suppressed dissipative transport with a distinct handedness, is confirmed by floating contact measurements. Consequently, this sum rule emerges as a conduction law of the chiral metal phase. Theoretically, we argue that time-reversal-symmetry breaking under a strong magnetic field within this chiral metal gives rise unidirectional trajectories of carriers in a nearly flat potential landscape with point-like disorder potentials, a regime realized when the screening length is smaller than the magnetic length. Within this chiral framework, longitudinal resistance does not originate from bulk dissipation but primarily from the equilibration of electrochemical potentials at the contacts. Our study introduces a new paradigm of chiral transport across a broad class of gapless two-dimensional systems characterized by short-range screening and broken time-reversal symmetry.

Random unitaries are fundamental to quantum information and many-body physics, with widespread applications ranging from quantum learning and metrology to device benchmarking. A central pursuit is to minimize the space and circuit depth required to generate them. However, existing methods for generating low-depth random unitaries rely heavily on an extensive number of ancillary qubits, imposing severe spatial overhead. In this work, we prove that random unitaries can be generated in optimal depth without ancillae. For multiplicative-error approximate $k$-designs on $n$ qubits, our circuits achieve a depth of $\widetilde{O} (k) (\log n)^{1/\delta}$ on $\delta$-dimensional architectures and $\widetilde{O}(k) \log \log n$ with all-to-all connectivity. Furthermore, by introducing a general exactification lemma, we lift our construction to optimal-depth exact $k$-designs, yielding an exponential resource reduction over state-of-the-art exact constructions. Our results minimize the space-time costs for a wide range of quantum protocols.

We prove a uniform shifted anticoncentration theorem for the hafnian of a real Gaussian Gram matrix under an explicit condition on the row dimension. After normalization by its root mean square, the law has a bounded continuous density, maximal at zero, and every interval has probability bounded by an explicit coefficient times its radius. Under suitable growth conditions on the row dimension, this coefficient grows at most polynomially in the hafnian order, meaning half the dimension of the Gram matrix. We also compute the exact second moment. The proof exploits the perfect matching structure, combining conditional Gaussian representations, row suspension, and bilinear interpolation to control an inverse moment of the conditional variance. At fixed hafnian order, a rescaled limit as the row dimension grows yields corresponding bounds for the hafnian of a real symmetric Gaussian matrix with independent entries above the diagonal.

A nonlinear EM inversion method regularized by $\ell_1 / \ell_2$-norm of the model gradient is proposed. The $\ell_1 / \ell_2$-norm, defined as the ratio of $\ell_1$-norm to $\ell_2$-norm, exhibits a scale-invariant property that enables it to more accurately characterize sparsity in the solution compared with the conventional $\ell_1$-norm. To address the nonconvexity and nonsmoothness introduced by the quotient structure of $\ell_1 / \ell_2$-norm, the inversion problem is reformulated and solved using the alternating direction method of multipliers, resulting in an efficient optimization algorithm comprising five sub-steps. The Gauss–Newton method is incorporated into the first sub-step to linearize the nonlinear inversion. The proposed method is validated by a series of numerical examples using both synthetic and experimental datasets, and is compared against standard regularization methods such as Tikhonov and total variation. The results demonstrate that the proposed method yields superior reconstructions of permittivity profiles, particularly in preserving sharp edges and suppressing artifacts, without incurring additional computational cost. Furthermore, the method exhibits strong robustness to measurement noise and reduced sensitivity to the choice of the regularization weight.

Active quantum matter has very recently emerged at the intersection between bio- and quantum many-body physics, combining the self-organization of living systems with the coherence of the quantum world. Active quantum systems have been shown to exhibit flocking - a collective phenomenon with no precedent in equilibrium quantum physics. In this work we uncover an unexpected layer of quantum order in active quantum flocks: they can become superfluid. We show that, in addition to the symmetry breaking associated with their directed motion, these flocks can also break an additional U(1) symmetry, giving rise to off-diagonal long-range order. For a microscopic model of active hard-core bosons governed by Lindblad dynamics, we derive an effective long-wavelength description of the single-particle density matrix and demonstrate that the flocking phase develops an instability toward off-diagonal long-range order characteristic of superfluid behavior. Our findings reveal active quantum matter as a promising research direction for discovering exotic nonequilibrium phases of quantum matter.

A time fractional extension of the Hunter Saxton equation is examined, in which the temporal derivative of u_x is replaced by a Caputo derivative of order 0 < alpha <= 1. This modification introduces memory effects into a model traditionally associated with director field dynamics in nematic liquid crystals. By employing a fractional separation of variables strategy together with the exponential spatial profile phi(x) = exp(b+x), which cancels the nonlinear structure exactly, the governing nonlinear partial differential equation is reduced to a fractional relaxation ODE, whose closed form solution is the one-parameter Mittag Leffler function. The exact analytic solution is derived algebraically from the separation process. This appears to be the first exact closed form solution of the Caputo time fractional Hunter Saxton equation. The result is validated symbolically using the MathHandbook computer-algebra system. Quantitative analysis in both the fractional (0 < alpha < 1) and classical (alpha -> 1) limits demonstrates how fractional-order memory slows temporal relaxation relative to the exponential baseline. The solution provides a reliable benchmark for numerical schemes and clarifies how fractional dynamics influence nonlinear wave propagation in orientationally ordered fluids.

In low-energy heavy-ion collisions, baryon stopping is an important process, in which protons from the initial colliding nuclei are stopped at mid-rapidity region. Quantifying such stopping can reveal information on the properties of the nuclear medium, such as net-baryon density. Though experimental measurement of net-proton rapidity spectra provides constraints, microscopic origin of such protons is not fully accessible. Transport model studies can therefore provide deeper insight into the microscopic origin of protons transported from initial nuclei, complementing experimental measurements. This article presents an investigation of baryon stopping in minimum-bias Au+Au collisions over a wide range of beam energies, $\sqrt{s_{NN}} = 2.4-17.3$ GeV ($E_{\rm lab} = 1.23A-158A$ GeV). Final-state protons are classified based on their origin by analyzing their interaction history in the UrQMD model. A significant fraction of transported protons at mid-rapidity originates from initial neutrons rather than initial protons, referred to as isospin-converted protons, and their contribution as a function of collision energy and centrality is quantified. Anisotropic flow coefficients of different proton categories are estimated and compared with experimental measurements. Furthermore, a comparison between the $\pi^{-}/\pi^{+}$ ratio and isospin conversion rate is performed. The latter is further compared with the $\alpha$ parameters of the Kitazawa-Asakawa formalism, revealing a significant deviation from the chemical equilibrium assumption $\alpha_N = \alpha_\pi$ below $\sqrt{s_{NN}} \lesssim$ 10~GeV. Finally, the saturation of the isospin conversion rate is found to coincide with the onset of nuclear transparency, demonstrating that isospin randomization and baryon stopping are coupled phenomena in hadronic transport across the NICA/FAIR energy range.

As the Artemis program advances toward the lunar south pole and permanently shadowed regions (PSRs), understanding lunar charging is increasingly important for protecting astronauts, robotic systems, instruments, and infrastructure. Persistent darkness, cryogenic temperatures, low regolith conductivity, and long charge-relaxation times may allow energetic-particle-induced charge to accumulate beneath the surface. This Technical Memorandum addresses a key unresolved question: how is electrostatic charge generated, separated, retained, and accumulated within lunar regolith? Existing models predict that solar energetic particles and galactic cosmic rays may produce subsurface electric fields approaching dielectric breakdown thresholds, but the microscopic connection between incident particles and macroscopic volumetric charge sources remains unclear. Energy deposition alone does not determine retained charge. Incident particles and their secondary particles may stop, implant, backscatter, transmit, recombine, become trapped, or escape. This memorandum therefore defines the required microscopic input as the average signed retained-charge distribution per unit depth and incident particle, resolved by particle species and energy. Combined with incident flux and energy spectra, this response provides a depth-dependent volumetric charge-source rate that can be coupled with charge continuity, conduction, dielectric relaxation, and Poisson's equation. Key uncertainties include the effects of mineralogy, grain and pore geometry, temperature, and pre-existing potential on charge retention. Particle-resolved modeling and cryogenic high-vacuum irradiation experiments are needed to constrain these processes and assess subsurface electric fields, dielectric breakdown, dust transport, contamination, and charge-mitigation requirements for sustained lunar polar exploration.

We propose a concrete theoretical framework for the double inverse seesaw mechanism within an alternative gauged $U(1)_{B-L}$ model, where the tiny neutrino masses emerge radiatively at the loop level in accordance with the 't Hooft naturalness criterion. By assigning non-universal $B-L$ charges of $(-4, -4, 5)$ to the right-handed neutrinos, we introduce vector-like fermions and two inert singlet scalars that circulate in the loop to generate the required mass terms. The spontaneous breaking of the $U(1)_{B-L}$ symmetry leaves a remnant $Z_2$ symmetry, which naturally stabilizes these new particles as dark matter (DM) candidates. We systematically investigate both fermionic and bosonic DM scenarios, assuming their interactions are predominantly mediated by the $B-L$ gauge boson ($Z'$). Our comprehensive analysis of the relic density, direct detection, and collider bounds reveals that the fermionic DM scenario is strongly favored. In contrast, the bosonic DM via the $Z'$ portal is severely constrained and largely ruled out by the latest direct detection experiments such as LZ, PandaX-4T, and XENONnT.