Papers

We present a comprehensive ab-initio study of the elastic properties of the IV-period transition metal nitrides, highlighting the correlation between their mechanical behavior and electronic structure. By analyzing the electronic density of states, we reveal how the occupation of bonding or antibonding orbitals determines the evolution of elastic properties along the period. Furthermore, we examine trends across different crystal structures, specifically comparing rocksalt, zincblende and wurtzite phases, to uncover how variations in crystal symmetry and atomic coordination influence their elastic properties.

It has been over fifty years since Kenneth Wilson had his Nobel-prize-winning ideas on the renormalization group. In this time frame, despite many attempts, no mathematical results have implemented Wilson's vision to a satisfactory degree. Although a number of predictions stemming from the renormalization group framework have been proven to date, these proofs usually rely on alternative ideas and do not cover the full predictive power of Wilson's renormalization group. The discovery of pathologies within rigorous implementations of renormalization group transformations have further reduced the enthusiasm of the mathematics community for this subject. This paper presents a novel framework to implement Wilson's original idea in a rigorous manner based on inverse limits of finite systems. Doing so, one avoids these pathologies and hence obtains a mathematically sound framework for Wilson's renormalization group. This opens up a completely new path to tackle some of the existing problems in rigorous renormalization group theory like the existence of non-trivial fixed points.

EuAgAs is an antiferromagnetic topological material exhibiting intriguing magnetic behavior. We investigate its structural, magnetic, and local electronic properties using X ray diffraction, Mössbauer spectroscopy, dc magnetization, ac susceptibility, and heat capacity measurements. The results confirm antiferromagnetic ordering below $T_\text{N}$ and reveal pronounced magnetic anisotropy and several field induced metamagnetic transitions. We construct the magnetic phase diagram of EuAgAs, identifying several distinct magnetic regions. The field and temperature dependent behavior observed suggests a noncollinear magnetic structure in the low field regime. The sequence of field induced transitions resembles that observed in centrosymmetric rare earth compounds hosting skyrmion phases, suggesting that competing magnetic interactions may play an important role in stabilizing the observed magnetic states.

We show that a transverse electric field applied to a zigzag graphene nanoribbon opens a band gap whose energy can be tuned through the terahertz (THz) range. The field breaks the reflection symmetry of the ribbon, allowing optical transitions that are forbidden in its absence. The relative strengths of transitions polarized parallel and transverse to the ribbon depend strongly on excitation frequency and become equal at a particular frequency. At this frequency, each helicity selectively excites carriers in only one of the two field-induced edge-state valleys, with the selected valley reversed for the opposite helicity. Since this excitation occurs away from the valley minima, the photoexcited carriers have finite group velocity, giving rise to a circular photogalvanic response. Van Hove singularities enhance radiative recombination at the band edge, providing a route towards compact, tunable THz emitters.

Phonon angular momentum, characterized by circular or elliptical motion of atoms, plays a decisive role in diverse phenomena, ranging from the phonon Hall effect, phonon magnetic moment, Einstein-de Haas effect, Weyl phonons, and driven chiral phonons. The phonon modes with an antisymmetric Raman tensor, which carry an intrinsic phonon angular momentum in a pseudovector symmetry channel, have been overlooked in the past in the chiral phonon community. Here, we report the detection of this type of phonon mode using polarization-resolved Raman spectroscopy. We observe a phonon at 266cm$^{-1}$ in the antiferromagnetic chiral phase of Cr$_2$O$_3$ in the $A_2$-pseudovector symmetry channel. This $A_2$ mode's frequency and the elliptical motion are captured by first-principles phonon calculations, which treat both lattice and spins on an equal footing as 'slow' degrees of freedom. This mode gets Raman activity due to the presence of Cr vacancies in Cr$_2$O$_3$ that locally break the twofold rotational symmetry perpendicular to the threefold axis. Our results provide a new way to detect the novel symmetry-forbidden $A_2$ phonon modes with an antisymmetric Raman tensor in a pseudovector symmetry channel.

A framework for quantum electrodynamics of equilibrium systems is proposed that takes the Maxwell equations as foundational and links them to the structure of density-functional theory for the quantum system. By switching from purely internal observables like the one-particle density to combined internal and external quantities, the external sources and their energy are taken into account. A fully regularized functional theory emerges that avoids the usual representability problems. With the Kohn-Sham construction that links to an auxiliary uncoupled system, the ultra-violet cutoff can be removed and one arrives at a fully renormalized and non-perturbative light-matter description. Regularized forms of density-functional theory with and without magnetic fields appear as boundary cases, while the emergent physical picture reproduces the macroscopic Maxwell equations.

We study statistical variants of the classical largest average submatrix problem. For small submatrices (where the dimension is less than linearly proportional to the original matrix), the problem is typically well understood and believed to exhibit the statistical-computational gap (SCG). However, analytical treatment of both the information-theoretic and algorithmic aspects of the linear regime remains challenging, and no mathematically rigorous results have yet arrived anywhere close to proving or disproving SCG existence in this setting. Focusing on the linear regime, we make strong progress in several key directions: 1) We develop a generic Random Duality Theory (RDT) framework to characterize largest average submatrix values. 2) Using the plain RDT variant, we obtain closed-form upper bounds as explicit functions of dimensionality proportionality parameters. 3) We demonstrate that a lifted RDT variant strictly improves upon the plain RDT within a certain linear range of submatrix dimensions. 4) For small submatrices where the dimensional proportionality constants approach zero, we prove that our results match both the replica results from [34] (obtained via one-step replica symmetry breaking) and the sublinear results from [18,45].

Can quantum entanglement continue to grow even after the entanglement entropies of subsystems have saturated? We address this question using genuine multi-entropy, which probes multi-partite entanglement structure beyond bipartite entanglement. In a two-sided BTZ black hole, this quantity grows linearly with time after every subsystem entropy of a fixed tripartition has saturated, extending the interval in which entanglement detects Einstein-Rosen bridge growth. The result refines the ER=EPR relation by identifying multi-partite structure invisible to ordinary entanglement entropies. Some spin-chain models and the spatially partitioned Sachdev-Ye-Kitaev (SYK) model exhibit distinct transients, while the late-time plateau values in holography, the SYK model, and Haar-random states share a universal behaviour.

We study the Loschmidt echo in a system of N non-interacting spinless lattice fermions released from a double-domain-wall initial state. In the large-N limit, the return probability is characterized by a large-deviation rate function known as the dynamical free energy. The Loschmidt echo is dominated by a complex instanton configuration, and the dynamical free energy develops a logarithmic singularity at the dynamical quantum phase transition. We obtain analytical results in the short-time and long-time regimes and support them with numerical computations. We show that the transition can be understood as a topological change of the dominant instanton configuration, analogous to the emergence of a cut in random matrix theory. We further show that post-selection can drive the system through two successive DQPTs, associated with successive topological changes of the dominant instanton configuration in complex time.

Recently, momentum-space nonsymmorphic symmetries have attracted considerable attention. However, their realizations typically rely on fine-tuning hopping phases to satisfy the required projective symmetry algebras. Here, we show that such symmetry algebras arise naturally on bipartite lattices through the interplay of crystalline and sublattice symmetries. Unlike previously studied cases, these symmetry operators can anticommute with the Hamiltonian and are therefore referred to as momentum-space nonsymmorphic chiral symmetries. Although the free actions of these symmetries reduce the Brillouin torus to more elementary manifolds, the resulting manifolds are twisted in the Atiyah–Segal formalism. In particular, chiral glide reflection (screw rotation) gives rise to a twisted Klein bottle (dicosm) in two (three) dimensions, and this twisting dramatically alters the topological classification. Unlike the untwisted Klein bottle, whose nonorientability forces the Chern number to vanish, the twisted Klein bottle can host nonzero Chern numbers, corresponding to even Chern numbers on the torus. At open boundaries, the corresponding topological invariant manifests itself through chiral edge states exhibiting a glide-reflection structure in energy–momentum space. Our results establish momentum-space nonsymmorphic chiral symmetry as a new organizing principle for discovering and engineering topological phases beyond conventional crystalline classifications.

Spatial inhomogeneity breaks translational symmetry and prevents conventional Bloch-band topological invariants from directly answering a practical question: do Majorana zero modes survive in a given inhomogeneous superconducting device? In this Letter, we develop a real-space landscape approach to address this question. Rather than solving the zero-energy equation as a boundary-value problem, we treat the spatial coordinate as an evolution parameter and recast the equation as a first-order dynamical system. A Majorana zero mode is then identified with a stable trajectory that satisfies the physical boundary condition and approaches the origin at large distance. We show that the landscape geometry fixes the dimensions of the stable and unstable subspaces, while the intersection of the stable subspace with the physical boundary subspace determines the number of Majorana zero modes. In the homogeneous limit, the topological phase transition is manifested as a geometric transition of the landscape. Applied to one-dimensional spinless $p$-wave superconductors and nanowire–superconductor systems, the approach yields sufficient bounds on both the amplitude and spatial gradient of the inhomogeneity, providing quantitative criteria for the design of Majorana devices.

Discovery and study of superconducting electrides have opened new avenues in condensed matter physics, driven by their intriguing multifunctional features spanning ambient and high-pressure regimes. This work investigates the ternary nitride superconductor Nb5Ir3N under pressure ranging from 0 to 20 GPa via density functional theory based simulations. Estimated structural parameters agree well with the available data, confirming their reliability and supporting the validity of this analysis. Negative formation enthalpy, together with evaluated elastic constants and phonon spectra, confirm the structural, thermodynamic, mechanical, and dynamical stability of Nb5Ir3N over the entire pressure range. Pressure dependent elastic constants and polycrystalline elastic moduli are investigated. The compound is categorized as ductile in light of estimated mechanical indices. Elastic anisotropy factors indicate that Nb5Ir3N remains anisotropic, with the degree of anisotropy gradually decreasing as pressure increases. Electronic band structure and density of states are calculated with and without spin orbit coupling to investigate its influence on the electronic structure. Calculated optical response reveals substantial intraband contributions in the low energy region, intense ultraviolet absorption, and strong reflectivity. The spectra exhibit optical anisotropy and a broadening at higher pressures. Pressure induced superconducting features are also discussed qualitatively.

We present a general method for estimating entropy differences between arbitrary probability distributions using stochastic interpolants. The marginal distributions which bridge the base and target obey a continuity equation, which allows a straightforward calculation of the entropy difference in terms of an inner product of the probability flow velocity and score fields. This formulation has several advantages: (i) no computationally expensive divergence calculations of either field are required, (ii) the score field need not even be learned directly if model transferability is not required, and (iii) on-the-fly estimates are produced nearly for free during training. When tractable base distributions are chosen (e.g. Gaussian chain, ideal gas, etc.), statistical thermodynamic entropies are then immediately recovered. Notably, the analysis relies only on the definition of the Gibbs-Shannon entropy, rather than any particular statistical mechanical ensemble, so that generalized non-equilibrium entropies may be computed. The method is demonstrated on several systems of increasing complexity: (i) a 40-dimensional Gaussian mixture model, (ii) the classical XY model of N spins arranged in one dimension, (iii) the 13-atom Lennard-Jones cluster, and (iv) an active Brownian polymer.

We develop a microscopic theory of spin-torque ferromagnetic resonance (ST-FMR) in nonmagnetic-metal/ferromagnetic-metal heterostructures. Tracing out the conduction-electron degrees of freedom in the FM, we derive an effective interfacial exchange coupling between the localized spins and the conduction electron spins in the adjacent electron system. Based on this interaction, we calculate the current-induced driving torque, resonance-frequency shift, damping modulation, and resulting dc voltage. As a concrete example, we apply the formulation to a disordered Rashba two-dimensional electron gas and demonstrate that the ST-FMR spectrum reflects the dynamical spin responses of the adjacent electron system. Our formulation applies to a broad class of heterostructures and establishes a unified microscopic framework connecting ST-FMR spectra directly to the electronic spin responses of adjacent systems.

The anomalous Hall effect (AHE) reported in epitaxial RuO2/TiO2 has been attributed to a strain-stabilized magnetic state, but strain can be entangled with Ru-Ti intermixing and interfacial charge redistribution, which can produce Ti3+ and potentially localized moments. Here, we disentangle these contributions using Ti-alloyed RuO2 heterostructures in which abundant Ti3+ states are retained while epitaxial strain is independently changed. The strained and relaxed films have nearly identical Ti/Ru compositions and comparable Ti3+ fractions, yet a pronounced nonlinear AHE appears only in the coherently strained film, while the relaxed heterostructure exhibits an almost linear Hall response. Spectroscopic ellipsometry further shows that the AHE-active strained state is accompanied by a reconstruction of the itinerant electronic response, including enhanced metallicity and longer carrier relaxation times. These results show that Ti3+ formation alone is insufficient to generate the anomalous Hall state and identify epitaxial strain, through its modification of the itinerant RuO2 electronic structure, as the dominant control parameter.

Valley-layer coupling (VLC) two-dimensional (2D) materials define a distinct class of quantum systems in which valleys are related by crystal, rather than time-reversal ($\mathcal{T}$) symmetry, enabling gate-controlled valley-contrasted layer polarization. Here we extend this concept to excitons. Using TiSiCo as a prototype VLC material, we show that a perpendicular electric field $E_{\perp}$ controls exciton- dispersion anisotropy and thereby generates unconventional linear transverse exciton transport in both monolayer and twisted bilayer structures. In the monolayer, this response is characterized by anisotropy-induced transverse conductivities, arising from the antisymmetric combination of diagonal elements in the conductivity tensor and strongly tunable by $E_{\perp}$. In the twisted bilayer, symmetry additionally permits transverse responses from the symmetric part of the conductivity tensor. Since intralayer excitons in different layers are connected by the Förster coupling, these symmetric and antisymmetric responses coexist and compete with the recently proposed $\mathcal{T}$-even layer Hall and Nernst exciton counterflow. This interplay is highly tunable by twisted angle, temperature, and the direction of the in-plane driving force, providing a route to disentangle distinct transverse exciton transport signals experimentally. Our results establish $E_{\perp}$ as a powerful knob for controlling exciton transport via VLC and identify VLC 2D materials as a promising platform for engineered excitonic phenomena.

Contemporary memory technologies are increasingly constrained by the fundamental trilemma of storage capacity, access latency, and power consumption. Among the emerging technologies, spin-orbit torque magnetic random-access memory (SOT-MRAM) shows promise to circumvent these challenges, owing to its fast switching dynamics and high endurance. However, the application of SOT-MRAM is hindered by the relatively low write and read efficiencies, resulting in a large bitcell area and an insufficient sensing margin. Meanwhile, the involvement of an ultrathin spin-source channel, typically within a few nanometers, imposes technological challenges for mass production. Here, we resolve these issues on a 300-mm wafer platform by exploiting the emerging orbital degree of freedom and the resultant orbital torque (OT) from the relatively thick Ti/W bilayer. In particular, OT memory nanodevices exhibit a giant tunnel magnetoresistance (TMR) of 182%, nanosecond-scale response, 1012 endurance, together with an enhanced switching efficiency (E_b/I_c), which consequently enables an ultra-low write energy of less than 0.1 pJ/bit. Our findings demonstrate that orbital angular momentum can be implemented for building energy-efficient MRAM devices, offering a practical pathway towards low-latency memory that is demanded for high-performance computing and AI applications.

Accurate thermal properties of metal thin films are essential for microelectronic thermal modeling and for interpreting thermoreflectance measurements when signals are sensitive to film thermal transport. In practice, film thermal conductivity is commonly inferred from electrical resistivity via the Wiedemann-Franz (WF) law with the Sommerfeld-Lorenz number L_0, neglecting phonon contributions and microstructure-dependent scattering. Here, we combine square-pulsed source (SPS) thermoreflectance with van der Pauw measurements to characterize thermal and electrical transport in Al, Ti, and Ta thin films prepared by thermal evaporation, e-beam evaporation, and magnetron sputtering. SPS measurements from 80 to 300 K yield the film thermal conductivity k_m and volumetric heat capacity C_m, with C_m agreeing with bulk values within +/-8%. Compared with WF-based estimates using L_0 and a modeled resistivity, h̊o}_model (T)=h̊o}_bulk (T)+h̊o}_0, k_m deviates by 5-20% for Al and Ti and up to 40% for sputtered Ta at 300 K. While the smaller deviations are comparable to experimental uncertainty, the large mismatch for Ta demonstrates the limitation of applying the bulk L_0 to highly resistive metal films. Apparent Lorenz numbers L_app=k_m h̊o}_meas/T from 150 to 300 K further reveal that deposition-induced disorder, grain-boundary scattering, and possible phase-related effects can modify the correlation between heat and charge transport in thin metal films. These results clarify the applicability of the WF law to deposited metal thin films and offer practical guidance for thermal modeling and thermoreflectance analysis.

The quantum Mpemba effect is the counterintuitive phenomenon whereby a quantum state initially farther from equilibrium relaxes faster than one initially closer to it. We demonstrate this effect in random Clifford circuits with a conserved $\mathrm{U}(1)$ charge, using the entanglement asymmetry to characterize relaxation through dynamical symmetry restoration. Exact numerical simulations show that an initially more asymmetric state can become locally more symmetric than an initially less asymmetric one. We explain this behavior by mapping the dynamics onto a charge-conserving quantum automaton, in which the decay of the entanglement asymmetry is controlled by the statistics of encounters between two particle species evolving according to a symmetric simple exclusion process. This mapping yields an analytic expression for the entanglement asymmetry and provides a simple microscopic mechanism for the quantum Mpemba effect: stronger initial symmetry breaking corresponds to a denser particle configuration, which enhances the frequency of particle encounters and thereby accelerates symmetry restoration.

Can the terminal macroscopic outcome of a many-body system be inferred from its microscopic initial data without simulating the full trajectory? Rather than construct such a shortcut, we address a more fundamental question for Gaussian microscopic inputs: can any fixed Wiener-Hermite degree retain a nonvanishing fraction of the variance of the terminal outcome as the system grows? We consider homogeneous systems with independent Gaussian disorder in which all microscopic coordinates are symmetry-equivalent, the terminal event is monotone in each disorder variable, and a uniform disorder shift is exactly equivalent to a control-field shift with a size-independent conversion factor. Using forward and inverse Gaussian influence bounds together with a Gaussian Russo formula, we derive a directly measurable criterion that is both necessary and sufficient for noise sensitivity. Specifically, the correlation between the original and coordinate-perturbed terminal outcomes vanishes asymptotically for every fixed nonzero level of coordinatewise noise if and only if the slope of the outcome probability with respect to the control field at the balanced threshold grows more slowly than the square root of the system volume. Event-driven simulations of the three-dimensional driven random-field Ising model up to linear size 192 find that both the normalized response and the correlations between perturbed samples decrease overall, consistent with the noise-sensitive regime at finite size. For spatial Stag-Hunt dynamics with prescribed seeds, the criterion generalizes through an effective number of influential coordinates. Separately, simulations of a path-dependent best-response game show, over the sizes studied, that the terminal equilibrium can depend on the update schedule while still carrying substantial finite-order predictive information.

We test whether the maximum penetration depth of a circular intruder into a two-dimensional granular bed can be predicted from its early trajectory using machine learning, without giving the intruder density. From 100 DEM simulations with varying density, we extract kinematic features from the first 50 ms. Ridge and Random Forest predict the maximum penetration. A single feature (the intruder height at 50 ms) concentrates almost all predictive power, showing that density information is already encoded in the early impact response.

We report the synthesis and comprehensive investigation of iodine-incorporated $Cr_2Se_3$, a non-van der Waals quasi-two-dimensional magnetic material, using structural, magnetic, transport, spectroscopic, and first-principles methods. Magnetization and electron spin resonance measurements reveal an antiferromagnetically ordered state below $T_N \approx 52$ K. At higher temperatures, a second, broader anomaly emerges near $T^* \approx 150$ K, coinciding with a shallow minimum in the temperature-dependent resistivity that resembles a metal-to-insulator-like crossover. Hall measurements indicate predominantly hole-like conduction at high temperatures ($\geq$ 150 K), while the nonlinear Hall response below T*, together with an anomaly in the third-harmonic electrical signal, suggests the emergence of mobility-dependent multichannel and spatially inhomogeneous transport. A large, non-saturating negative magnetoresistance reaching approximately -78% at 25 K and 12 T further demonstrates strong coupling between charge transport and the magnetic state. Temperature-dependent Raman spectroscopy reveals no symmetry-changing structural transition near T*, whereas angle resolved photoemission spectroscopy (ARPES) measurements show no major reconstruction of the electronic structure occupied across the crossover. Taken together, these results identify the high-temperature anomaly as a broad magnetically coupled transport crossover arising from the interplay of short-range magnetic correlations, chemical disorder, and redistribution among competing conduction channels. These findings demonstrate that anion incorporation provides an effective route to tuning the coupled electronic and magnetic properties of non-layered Cr$_2$Se$_3$, establishing this system as a promising platform for investigating correlated transport and emergent spintronic functionalities in transition-metal chalcogenides.

In this paper, we study Renyi and Tsallis information entropies for a Hamiltonian system with position-dependent mass confined in harmonic oscillator potential. Gegenbauer polynomials are used to obtain the position eigenfunction of such a system, and the modified Bessel function of the second kind is used to determine the equivalent momentum eigenfunction. By means of probability densities of both representations, we analytically and numerically evaluate the Heisenberg-like uncertainty of this system. Because the Renyi and Tsallis information entropies in position representation are described by integral functionals of the Gegenbauer polynomials, these quantities are much more difficult to calculate. To get around this problem, we evaluate these information entropies at the system s asymptotical limit, which corresponds to the behavior of an undeformed harmonic oscillator. Nevertheless, no approximation method is used to obtain the Tsallis and Renyi information entropies in momentum representation. In both representations, we find that these information entropies approach the Shannon entropy when the entropic parameter alpha-> 1 and are closed to the results of similar models of the literature. Finally, we evaluate the related entropic uncertainty relations numerically to validate the latter obersevations.

The free-energy principle (FEP) and active inference describe adaptive systems through probabilistic generative models and free-energy functionals, whereas integrated information theory (IIT) characterizes intrinsic cause-effect organization. We separate two questions: whether revised IIT quantities admit local free-energy-like representations and whether scalar expected free energy can determine system integrated information. We show that the 2026 IIT intrinsic-differentiation and specification terms admit exact surprisal representations, and hence variational-free-energy representations under exact inference. We then construct noisy binary permutation networks whose causal topology varies while local transition reliability is fixed. In a homogeneous state, all permutations yield the same one-step predictive distribution and state-risk expected free energy under common preferences and observation models, yet revised IIT distinguishes them: multicycle permutations have zero whole-system integration, whereas a single noisy cycle has positive integration at intermediate reliability. For an n-unit noisy single cycle, we derive a closed-form expression for revised system integrated information, prove that the minimum-information partition cuts exactly two causal edges, and show that as n grows the optimal reliability approaches unity, the joint specified-state probability approaches one half, and the maximum integration approaches one ibit. Numerical IIT calculations for n = 2-5 and exhaustive partition enumeration through n = 8 reproduce the analytical results. Thus, local surprisal/free-energy correspondence coexists with global non-equivalence: equal expected free energy does not imply equal revised IIT system integrated information. Any synthesis of IIT with FEP/active inference must retain counterfactual causal information beyond a scalar free-energy value.

Young's law on a rigid solid and the Neumann balance at a three-fluid junction describe different admissible motions. We connect them through an ordered continuum construction. An affine viscoelastic third phase first acquires permanent deformation memory in the no-relaxation limit at fixed modulus. Independently specified material-surface laws distinguish surface free energy from mechanical surface stress. On the deformable support, displacement of solid material and migration of the wet-dry partition give separate equilibrium conditions. Stiffening an anchored support suppresses displacement at a fixed macroscopic observation distance but leaves reversible migration possible. The surviving variation gives Young's law; the constrained mechanics remains as a reaction carrying normal and, in general, tangential capillary loads. Two complementary results substantiate this reduction. A clamped finite-strain model with circular liquid interfaces yields uniform convergence of reduced energies and recovery of the spatial Young angle for global almost minimisers. A separate quadratic half-space model gives convergence of stationary migration derivatives and a nonzero limiting traction distribution. The results explain how a local Neumann-like ridge can coexist with a Young angle measured against the distant wall, while distinguishing geometric convergence from the control of migration and reaction forces.

Power magnetic materials are characterized on the sinusoidal and triangular waveforms that excitation hardware conveniently produces, whereas deployed converters expose cores to trapezoidal, PWM-shaped flux trajectories, so loss models must predict exactly where their training data are thinnest. The final test of the MagNet Challenge embeds a deliberately extreme instance of this characterization-deployment mismatch: for material D, trapezoids form 16.4% of the test set but only 1.4% of the training set. The 95th-percentile relative error, hereafter p95, of the best submission, built on sequential transfer learning, stalled at 15.9%, the worst among the five materials. This paper shows that the obstacle is missing information under covariate shift rather than class imbalance, and that the missing support can be borrowed from sibling materials instead of being extrapolated. Controlled experiments first refute the imbalance reading: four standard remedies fail, and raising the trapezoidal share to the test-set level degrades accuracy further. The proposed material-identity support transfer, MIST, then trains one 2784-parameter predictor jointly on all five challenge materials. Material identity enters through feature-wise linear modulation, or FiLM, the scarce material's true-label loss is reweighted, and material D receives no fine-tuning, so that the bias of its trapezoid-free training set is never re-installed. MIST lowers the five-seed material-D p95 from 20.39+/-2.03% to 12.38+/-0.92% and the trapezoidal-class p95 from 37.4+/-8.8% to 15.16+/-1.69%, surpassing the best submission with one-sixth of its parameters and no fine-tuning stage; removing material identity at matched capacity inflates the error by an order of magnitude. These results argue that scarce materials should be characterized jointly with their siblings.

For the neutral periodic one-dimensional Riesz gas with pair potential locally $-|x|^a$, $0<a<1$, we prove a particle-displacement variance bound of order $\beta^{-1}$, uniformly in the number of particles. Log-concavity also gives exponential displacement tails. Every stationary periodic thermodynamic limit is simple, has intensity one, and admits a stationary ordered matching to the unit lattice with the same bounds. Each limit satisfies the canonical Gibbs equations for the full-line interaction, with an ordinary symmetric spatial principal value for the exterior potential. The matching implies uniformly bounded interval number variance and a positive limiting second moment of the reciprocal-lattice Fourier average at sufficiently low temperature. The main estimate compares the inverse random Hessian, through deterministic electrical flows, to a transient long-range network.

For the hard-sphere Boltzmann equation, we derive an exact nonlinear generating vertex for collisional stress and heat-flux production. The complete two-input Hermite hierarchy for stress resums to a universal traceless tensor times one scalar radial law, while the heat-flux vertex follows from the same law by an exact contraction. Taylor differentiation yields universal bilinear collision tensors with exact stress and heat-flux gradings, without a finite moment closure. DSMC tests, including wall-driven flows and a bimodal Mach-5 shock, recover independently sampled Boltzmann productions and the predicted convergence, while the converged production is independent of the thermal Gaussian foot used for its Hermite representation.

The exploration of non-hexagonal two-dimensional topologies has opened new possibilities for tailoring the properties of group III-V monolayers beyond those accessible through conventional honeycomb phases. In this context, we have investigated the structural, mechanical, electronic, and optical properties of T-GaN, a two-dimensional tetragonal gallium nitride monolayer composed of alternating four- and eight-membered rings featuring coexisting homoelemental (Ga-Ga, N-N) and heteropolar (Ga-N) bonds, using density functional theory (DFT) within the generalized gradient approximation (GGA/PBE) and the hybrid HSE06 functional. The dynamical stability of T-GaN was confirmed by phonon dispersion calculations, which revealed the absence of imaginary frequencies throughout the Brillouin zone, and was further supported by ab initio molecular dynamics (AIMD) simulations. The mechanical characterization reveals a pronounced in-plane anisotropy, with critical strains of approximately 16.5% and 7.0% along the $x$- and $y$-directions, respectively. The electronic band structure analysis indicates that T-GaN is a nonmagnetic semiconductor with an indirect band gap of 0.35~eV (PBE) and 1.15~eV (HSE06), with the valence band maximum dominated by nitrogen 2p orbitals and the conduction band minimum governed by gallium 4s and 4p states. The optical response was evaluated along three crystallographic directions, exhibiting considerable anisotropy in the absorption coefficient, refractive index, and reflectivity. These findings provide new insights into the physical properties of tetragonal group III-V monolayers and suggest that T-GaN may serve as a promising candidate for anisotropic nanoelectronic and optoelectronic applications.

Atomic vacancies and vacancy aggregates control the thermodynamic stability and the functional response of graphene, yet the configurational space spanned by many vacancies at variable concentration and separation is too large to be mapped exhaustively by first-principles methods. Here, we map and rationalize this stability landscape by combining semiempirical atomistic thermodynamics, interpretable machine learning, and symbolic regression. Several hundred defective supercells, built from a 72-atom cell by varying the vacancy concentration and the inter-vacancy distance up to the fourth neighbor, were relaxed with the PM7 Hamiltonian in MOPAC, and the heat of formation was adopted as the stability metric. Each structure was encoded with the Dynamic Collision Fingerprint, a translationally and rotationally invariant descriptor that maps the local topology onto transport-like statistics of virtual probe particles. A gradient boosted decision tree model, optimized by Bayesian hyperparameter search, reproduces the heat of formation of an independent test set with a root mean squared error of approximately 23.5~kcal/mol and no evidence of overfitting, and a SHAP analysis identifies the defect concentration and the inter-vacancy distance as the two variables that dominate the stability. Symbolic regression then condenses the learned mapping into a compact closed-form expression that reproduces the heat of formation with a coefficient of determination of $R^{2} = 0.9966$, a mean absolute error of 15.51~kcal/mol, and a root mean squared error of 24.18~kcal/mol. The workflow turns a high-dimensional structure–stability problem into an interpretable analytical law, providing a transferable route to rational defect engineering in two-dimensional materials.