Papers

We train a pair of autoregressive models to construct zero-mean control variates to mitigate the sign problem in quantum Monte Carlo simulations. The two autoregressive networks are confined to the positive- and negative-sign sectors with strictly disjoint support, and each is exactly normalized over its sector. Their difference is therefore structurally zero-mean, providing an unbiased auxiliary observable whose correlation with the sign estimator controls the variance reduction. We implement the method within the stochastic series expansion framework, which we extend to frustrated lattices by developing an incremental loop-topology update. Sign-ergodic sampling is achieved through a twist channel, which is the unique sign-changing mechanism on non-bipartite lattices. We implement the control variates as autoregressive transformers with an end-of-sequence parity mask that enforces exact sign-sector resolution, while the incremental loop-count change and cumulative frustration parity are incorporated as topological features. On the triangular-lattice Heisenberg antiferromagnet, we benchmark the method in the small-$N$ limit. The control variate reduces the standard error of the average sign by up to an order of magnitude and that of the energy estimator by a factor of three to five, remaining effective even when the average sign drops below $10^{-3}$. This work lays out the framework and provides a proof-of-principle demonstration that autoregressive control variates can effectively mitigate the sign problem. Scaling to larger systems with physics-informed architectures is the subject of future work.

We consider the non-Hermitian XY spin chain with open boundary conditions when the anisotropy parameter is extended to complex values. By analyzing the quasi-Hamiltonian matrix, we demonstrate that the free-fermion structure of the quasi-energy spectrum coincides with that of the Hermitian model and construct the corresponding biorthogonal fermionic basis away from exceptional points (EPs). We make use of an explicit Chebyshev-polynomial representation of the open-boundary eigenvectors in which the quasi-energy $\varepsilon$ is the natural spectral variable. This quasi-energy polynomial form is particularly useful at EPs, because EPs correspond to repeated roots of the same boundary polynomial, making the construction of generalized eigenvectors by $\varepsilon$-differentiation transparent. At EPs, where the quasi-Hamiltonian becomes defective, we derive the Jordan normal form and construct the associated generalized eigenvectors, which yields the correct counting of independent many-body eigenstates. We further show that EPs act as branch points in the complex anisotropy plane, leading to the characteristic permutation of eigenenergies and eigenstates upon encirclement. The branch-cut structure of the biorthogonal eigenstates provides direct evidence for the exchange of eigenstates when an EP is encircled. These results provide an analytically controlled many-body platform for studying EP physics and non-Hermitian topology beyond momentum-space descriptions.

Understanding coherent optical responses of topological surface states (TSSs) requires disentangling excitation pathways from the electronic band structure. Here, using angle-resolved two-photon photoemission spectroscopy, we identify two distinct excitation pathways in the TSSs of Bi$_2$Te$_3$: an off-resonant transition via virtual states and a resonant transition via unoccupied intermediate states. A pronounced modulation of the spectral response is observed, revealing a competition between the two coherent pathways. This competition is tunable via temperature-induced shifts of the chemical potential, which selectively modify the resonant channel. These results provide microscopic insight into the optical excitation mechanisms of TSSs and highlight the potential for controlling their optical responses, relevant for future spintronic devices.

We theoretically investigate the properties of phonon angular momentum in the superconducting state, using fulleride compounds in an external magnetic field as a model system. The electron orbital angular momentum injected by an external field is transferred to the phonon subsystem via electron–phonon coupling. We show that this field-induced phonon angular momentum is significantly enhanced and undergoes a sign reversal upon entering the superconducting state. In the normal state, the dominant energy scale governing the response function is the electronic bandwidth $D$. In the superconducting state, the phonon energy scale $\omega_1$ enters the denominator, leading to an enhancement of order $D/\omega_1$. The observed sign change in the response can be explained by the competition between Fermi surface and Fermi volume contributions.

The low-temperature fate of the spin-liquid regime in the classical kagome Heisenberg antiferromagnet has been debated for over three decades. Using an expansion in the number of spin components, we show that, contrary to earlier Monte Carlo simulations, the spin liquid terminates at a weak first-order phase transition into the $\sqrt{3}\times\sqrt{3}$ phase which ordered moment saturates at zero temperature. Adding second-neighbor interactions, this transition belongs to a line of first-order phase transitions that ends at a critical point. For comparison, the pyrochlore antiferromagnet remains disordered at all temperatures.

We performed parallel measurements of heat effects and shear modulus relaxation for glassy Te$_{75}$Ge$_{15}$Ga$_{10}$ taken as a representative of practically important non-metallic glasses with covalent bonding. It is shown that the heat effects occurring upon heating are quantitatively linked to the shear moduli in the glassy and crystalline states and their temperature derivatives as implied by Eq.(1), which was originally derived for metallic glasses. This relationship provides a good description of exo- and endothermal reactions using shear modulus relaxation data as an input. This is the first application of this approach to a non-metallic glass with directional interatomic bonding. The obtained results suggest that relaxation phenomena are governed by elastic dipoles – atomic configurations with the symmetry lower than that of surrounding matrix.

Inverse design of materials has significantly advanced target-driven formulation optimization, yet existing materials machine learning benchmarks remain limited to forward property prediction, failing to systematically evaluate inverse optimization and generation algorithms, a critical gap that hinders the progress of target-driven materials design. To address this limitation, we propose MatFormBench, a novel benchmarking ecosystem tailored to evaluate and guide generative strategies for target-driven formulation. MatFormBench integrates a physics-driven formulation generation scheme to generate synthetic samples that faithfully emulate realistic materials structure-property response relationships, complemented by five escalating difficulty levels to quantify the complexity of these relationships. To rigorously assess algorithm performance, we further propose MatFormScore, a multi-dimensional metric that comprehensively quantifies performance across five critical axes: target success, search efficiency, exploratory capacity, robustness, and stability. We validate MatFormBench by evaluating 39 diverse inverse design algorithms, covering classical surrogate-assisted black-box search, state-of-the-art deep generative models, and increasingly popular Large Language Model (LLM)-based recommendation strategies. Across 1170 standardized algorithm-task evaluations, diffusion-based models demonstrate the strongest overall performance, while Variational Autoencoder (VAE)-based and Genetic Algorithm (GA)-based methods exhibit distinct advantages in specific scenarios. By establishing a unified evaluation standard for target-driven materials formulation, MatFormBench enables reproducible benchmarking, principled algorithm comparison, and diagnostic analysis of inverse design strategies, providing a foundational tool for advancing materials inverse design.

Operando microscopy has unveiled key mechanistic insights in battery materials during early cycling, but long-term characterization to unveil material evolution, degradation, and failure remain limited. To address this gap, we develop a custom operando optical microscope that captures images across hundreds of cycles and hours using optically accessible, anode-free pouch cells. We image through-plane, bulk-representative electrodeposition behavior of aqueous tin metal anodes, which are promising due to their high energy density but whose reactivity limits practical cycle life. We show that substrate governs the morphology and stability of plated tin, particularly at high plated capacities. Specifically, copper substrates exhibit a multi-stage tin growth mode, which results in high overpotentials and irreversible active material loss at high plated capacities. In contrast, graphite substrates display a single-stage growth mode with slower kinetics. Using this insight, we balance performance and stability to demonstrate a high-utilization (70%, 630 mAh g$^{-1}_{Sn}$) porous graphite substrate Sn anode with high efficiency and long lifetime. Our results underscore the importance of material and device optimization guided by operando characterization across device lifetime with broad applicability to electrochemical systems.

Chirality plays a crucial role in determining the structure of many systems in nature. Twisted or helical aggregates as a consequence of self-assembly can be seen in many biological and synthetic materials. Despite extensive theoretical and experimental efforts, how molecular-scale chirality gives rise to complex twisted morphologies in amphiphiles still remains unexplored. Here we study the interplay between molecular hydrophobicity, shape anisotropy and chirality using molecular dynamics simulation. Variation of relative molecular concentration and intrinsic chirality of molecules drive a sequence of twisted liquid crystalline variants of lamellar, cylindrical and vesicular phases. These structures emerge spontaneously under equilibrium conditions and are characterized by orientational correlation functions. We demonstrate that variation in molecular chirality gives rise to the development of hierarchical chiral order within the system. Further increment of chirality competes with hydrophobic interactions, leading to morphological instabilities. Our findings establish a direct link between microscopic chirality and mesoscale structure formation and their instabilities. Qualitative comparison of liquidity and pitch of the observed phase morphologies with the amount of chirality has been reported.

We theoretically investigate the effects of parametric driving on the one-dimensional Frenkel-Kontorova model, a nonlinear many-body lattice system. It is numerically found that a parametric vibration induces spatiotemporal ordering characterized by the subharmonic frequency $\omega_{\mathrm{ex}}/2$ and wavenumber $k$ which takes nontrivial values depending on the vibration strength $P_{\mathrm{ac}}$ and frequency $\omega_{\mathrm{ex}}$. With increasing $P_{\mathrm{ac}}$, $k$ gradually increases and discontinuously jumps up to $k=\pi$. Based on an extended linear stability analysis, we show that the former $k$ resonance (the latter $\pi$ resonance) corresponds to the unstable (stable) mode and that the $k$ resonance is made possible by the interplay between the parametric amplification and the collective fluctuation developing through the nonlinear effect.

We provide an extended acount of the recent statistical mechanical theory of gauge invariance against operator shifting in quantum many-body systems (arXiv:2509.20494). The gauge transformation is enacted by a shifting superoperator that displaces the fundamental position and momentum degrees of freedom. The shifting superoperator constitutes a map between Hilbert space operators and it features Lie algebra commutator structure. Averages of general observables remain invariant under the shifting both in and out of thermal equilibrium, as well as in groundstates. The gauge invariance induces exact sum rules that interconnect global observables and associated locally resolved correlation functions. In particular we describe the resulting one-body force, hyperforce, product, and two-body sum rules. We relate the shifting superoperator to a previously formulated quantum canonical transformation and present the generalization of quantum shifting to multi-component systems. The gauge theory respects fundamental fermionic and bosonic particle properties, as we demonstrate by proving the compatibility of operator shifting and exchange symmetry. We formulate the quantum version of hyperdensity functional theory to provide formal access to hyperforces as well as to general averaged quantum observables via universal density functionals. For time-dependent situations, we describe quantum dynamical gauge invariance and prove exact dynamical sum rules for nonequilibrium situations, as generated by Hamiltonian time dependence. We argue for the fundamental status of statistical mechanical gauge invariance based on the compliance of the underlying geometry with canonical quantization according to Dirac's correspondence principle. Analogies and differences of the quantum mechanical sum rules with their classical counterparts remain indicative of the respective levels of description.

We determine the bipartite entanglement bounds of two interacting electrons in deeply interlocked Hopf-linked quantum rings via exact diagonalization of the unexpanded 3D Coulomb interaction. This identifies an exact continuous spatial symmetry that geometrically isolates the positive-parity Bell state, preventing classical interaction-driven localization. A non-coplanar geometric tilt ($\alpha > 0$) is essential to lift the exchange degeneracy and maintain this maximally entangled manifold as a state of frozen entanglement. However, a higher-order Schrieffer-Wolff transformation demonstrates this geometric protection is fundamentally bounded; uncancelled inter-orbital momentum transitions inevitably induce dynamical parity mixing. This defines a critical interaction threshold ($\lambda_{crit}$) for irreversible entanglement collapse. Our analysis shows that the resulting bounding conditions reveal scaling limitations in mesoscopic semiconductor architectures, dictating the necessity of synthetic macroscopic platforms to achieve robust topological protection.

The pyrochlore iridates R2Ir2O7 have emerged as a unique playground for exploring exotic quantum phenomena arising from the intricate interplay of strong spin-orbit coupling, electron correlations, and geometric frustration. While bulk crystals of these materials have revealed a rich landscape of correlated and topological states, recent breakthroughs in epitaxial thin-film synthesis and heterostructure engineering unlocked an entirely new dimension of discovery. This brief Perspective reviews recent advancements highlighting how new tuning knobs such as dimensional confinement, epitaxial strain, and interfacial coupling can be used to manipulate the delicate balance of competing interactions. We discuss several key discoveries enabled by this approach including the realization of the magnetic Weyl semimetal phase in (111) oriented films, strain-engineered magnetic multipolar orders, the emergence of a chiral spin liquid-like state in the quasi-2D limit, and the discovery of novel electronically anisotropic states at interfaces between pyrochlore iridates and other quantum materials, such as spin ice pyrochlores. These findings showcase that low-dimensional pyrochlore iridates provide ample opportunities for both theory and experiment to unravel, control and ultimately design novel quantum states of matter. We conclude by outlining key open questions and future directions ranging from the synthesis of new heterostructures to the application of advanced probes and the exploration of non-equilibrium phenomena.

Analytic continuation from imaginary-time Green's functions to real-frequency spectra is a central ill-posed inverse problem in quantum many-body physics. We show that the thermal kernel admits an analytical generalized singular-value structure once its purely dynamical part is separated from the statistical weight imposed by the heat bath. The dynamical kernel is the imaginary-bandwidth continuation of Slepian's finite Fourier transform and is governed by the same Sturm-Liouville algebra that yields prolate spheroidal wave functions. Fermionic and bosonic statistics then enter as gauge transformations of the frequency-space inner product, producing self-adjoint effective potentials but no numerical kernel diagonalization. The Shannon number, $N_c=\beta\wmax/\pi$, fixes the upper information capacity of this pure Laplace channel. Finally, the optimal sampling points are obtained as eigenvalues of a Legendre colleague matrix, giving a deterministic compressed-sensing grid without iterative root searches.

We present a numerical study of the ultrametric properties of the set of RNA secondary structures with the maximum number of base pairs (energetically degenerate minima) within the maximum matching model (Nussinov algorithm). Using 18 natural small nuclear RNAs as examples, we show that the degree of nontrivial ultrametricity varies widely. We consider the optimization problem for the degree of nontrivial ultrametricity of RNA secondary structures with the maximum number of base pairs under a fixed nucleotide composition. It is found that permuting the nucleotide sequence can strongly change the degree of ultrametricity, indicating the key role of nucleotide order in shaping the hierarchical properties of RNA secondary structures.

Antimicrobial photodynamic therapy (aPDT) is a promising modality for inactivation of antibiotic resistant bacteria, relying on the activation of a photosensitizer (PS) by light of a specific wavelength. This process results in the formation of reactive oxygen species, which ultimately induce cell death. However, aPDT in its conventional form, is limited by the shallow penetration of visible light, restricting its effectiveness for treatment of soft tissue and orthopaedic tissues. To overcome this limitation, near-infrared (NIR) absorbing PS can be used. However, poor stability in vivo after injection, ineffective microbial targeting due to hydrophilic nature and off-site tissue damage are the issues with use of NIR absorbing bare PSs. This issue can be mitigated by combining NIR light with a upconverting nanoparticles (UCNPs), which mediate in conversion of NIR into visible light for effective PS activation. In this study, LaF$_3$:Er$^{3+}$,Yb$^{3+}$ nanoparticles were synthesized using a hydrothermal method and coated with Rose Bengal (RB), a promising hydrophilic PS for aPDT, to evaluate the potential for NIR-triggered aPDT. Characterization of the synthesized UCNPs confirmed the crystalline structure, size distribution and successful RB functionalization. Photophysical studies demonstrated efficient energy transfer between UCNPs and RB, leading to singlet oxygen ($^1$O$_2$) generation in vitro. Antibacterial studies against Methicilin resistant Staphylococcus aureus (MRSA), a superbug of implicated soft tissue and orthopaedic infections, revealed significant photo-bactericidal efficacy upon NIR irradiation, indicating the potential of RB-coated UCNPs for aPDT applications.

Randomly connected neural networks have long served as a theoretical tool for studying collective dynamics in neural populations, yet quantitative comparisons to experiments remain limited. Recent technological advances have made it possible to resolve population-wide correlations across neurons, and minimal models such as random neural networks predict their generic structure. Whether the two agree quantitatively remains untested. In this work, we examine whether a minimally structured random neural network can account for the low dimensionality of activity in neural population recordings by building on recent developments in Dynamical Mean-Field Theory and incorporating two additional experimentally relevant features into the model: finite measurement time and variability across behavioral contexts. We show that, when these factors are included, the dimensionality measured from large-scale recordings is consistent with the values predicted by random models. However, current recording durations make it difficult to use dimensionality to discriminate among connectivity structures. We further show that analytically predicted dimensionality varies non-monotonically with external input strength, and that the orientation similarity between neural manifolds recorded under different behavioral contexts can be more sensitive to network structure than dimensionality is. Together, these results provide quantitative guidance for experimental design to infer the connectivity structure underlying population activity.

The super-Arrhenius dynamic slowdown in fragile supercooled liquids remains one of the central unresolved questions in condensed matter physics. In this study, we analyze particle jump dynamics in a prototypical fragile glass-forming liquid, the Kob-Andersen Lennard-Jones (KALJ) model. Using the displacement of jumping particles as the reaction coordinate, we demonstrate the emergence of non-Poissonian dynamics as the temperature decreases. In the mildly supercooled regime, the outer region of the first coordination shell of a jumping particle exhibits a significant distribution shift during the jump motion. By comparing the survival probability with its slow-fluctuation limit using this distribution as a slow variable, we confirm that particles in this region modulate the jump dynamics, enhance the jump rate fluctuations, and thereby induce the dynamic slowdown as supercooling proceeds. As the temperature decreases, this behavior extends to the outer regions of the second coordination shell and beyond, intensifying the dynamic slowdown. This spatial growth of the slow variables responsible for dynamic disorder exhibits close correspondence with an increase in the static correlation length. These results provide a microscopic mechanism for the super-Arrhenius dynamic slowdown in the KALJ model.

While negative capacitance has been demonstrated in ferroelectric-dielectric heterostructures in the form of capacitance enhancement, all experimental evidence, to date, suggests the existence of domains therein. Here, we address the question: what are the conditions to achieve ideal, domain-free negative capacitance in ferroelectric-dielectric heterostructures? Our main claim is that for given thicknesses of the ferroelectric and the dielectric layers, there is a critical value of domain wall energy parameter – above which the system would be stabilized in an ideal and robust domain-free negative capacitance state and would be robust against domain formation. Our analyses suggest that to achieve ideal negative capacitance, efforts should lie in understanding the means to control the domain wall energy on all fronts, both theory and experiments via high throughput design, discovery, and engineering of ferroelectrics.

Thermal transport in low-dimensional semiconductors is important for nanoelectronics, quantum devices, and thermoelectrics. Recent molecular dynamics (MD) studies reveal a nonmonotonic diameter dependence of thermal conductivity in ultrathin silicon nanowires (NWs), but classical MD is limited at low temperatures and under strong confinement. Here, we investigate this anomaly using anharmonic non-equilibrium Green's function (NEGF) simulations combined with density functional theory-trained neuroevolution potentials. All transport results are expressed as effective thermal conductivities ($\kappa_{\mathrm{eff}}$) for NW devices with a finite channel length of $L=10$ nm. At 300 K, $\kappa_{\mathrm{eff}}$ decreases with diameter to minima at 6.24 and 5.50 nm for [001]- and [110]-oriented NWs, respectively. At 10 K, the corresponding minima occur at 7.33 and 5.50 nm. At room temperature, dominant momentum-conserving normal scattering relative to Umklapp processes enables Poiseuille-like hydrodynamic phonon flow that competes with boundary scattering. At cryogenic temperatures, Bose–Einstein statistics restrict heat transport to low-frequency confined acoustic-like modes. Comparison with the harmonic Landauer limit reveals a finite correction to $\kappa_{\mathrm{eff}}$ from anharmonic phonon–phonon scattering. Classical MD neglects quantum suppression and overexcites high-frequency vibrations, leading to overestimated thermal conductivity in thinner, strongly confined NWs at low temperatures. The NEGF framework incorporates quantum statistics and anharmonic scattering, providing a quantum-mechanical description of thermal transport down to 10 K.

Twisted moire superlattices in van-der-Waals heterostructures provide a powerful platform for engineering correlated states through moire-band reconstruction. However, whether globally coherent electronic orders can be continuously manipulated at the nanoscale remains largely unexplored. Reconstructed moire structures in small-angle and near-commensurate regime feature continuously varying local environments, offering new opportunities for nanoscale manipulation of correlated phases. Here, we report the modulation of charge density wave (CDW) states in a twisted vortex moire superlattice formed between monolayer VTe2 and superconducting NbSe2. Scanning tunneling microscopy/spectroscopy reveals that the intrinsic long-range CDW of monolayer VTe2 is reconstructed into inequivalent local phases with distinct stability and coherence within a single moire unit cell, including suppressed CDW order and enhanced short-range CDW correlations persisting to room temperature. First-principles calculations show that the reconstructed CDW landscape originates from strong local strain variation, where compressive strain substantially stabilizes the charge order. Furthermore, the modulated CDW states exhibit competing interplay with proximity-induced superconductivity. Our results establish vortex moire superlattices as a versatile platform for nanoscale manipulation of correlated electronic orders in low-dimensional quantum materials.

Quantum light provides opportunities for controlling multiphoton absorption beyond classical limits. Here, we investigate biexciton generation in nanocrystal quantum dots driven by energy-time-entangled photon pairs generated via spontaneous parametric down-conversion. We show that frequency-time correlations between pairs of photons increase the population of biexcitons over excitons, thereby lending specificity to the excitation of many-body states. By employing a three-level model, we demonstrate that biexciton generation depends nontrivially on the photon entanglement time and the pump bandwidth. We find that maximizing efficiency requires an optimally shaped entangled photon field rather than simply scaling parameters for a monotonic improvement. Extending to a realistic CdSe/CdS core-shell quantum dot containing many excitonic states coupled to the quantum field, we demonstrate that increasing the bi-photon arrival-time entanglement (closer arrival time) enhances constructive pathway interference and expands accessible excitation channels while preserving better energy-conservation excitation than classical light when generating biexcitons. Furthermore, tuning the time correlation properties enables selective excitation of closely spaced biexciton states. These results establish entangled photons as a tool for selective excitation and control of higher-order excited states in quantum-confined systems.

Harnessing active matter calls for strategies that break the directional symmetry of self-propelled motion without altering the propulsion mechanism itself. Here, we show that magnetically inert spherical active colloids can be steered through the anisotropic viscous response of a ferrofluid under a uniform magnetic field. Self-propelled Janus colloids exhibit robust cross-field motion transverse to the magnetic field, although the applied magnetic field directly controls neither the particles nor their propulsion speed. Quantitative measurements reveal an emergent reorientation torque that grows with both propulsion speed and magnetic field strength. A squirmer model in a magnetoviscous medium captures these observations and shows that the torque arises from the coupling between swimmer-generated flow and anisotropic rotational viscosity. Our findings establish a hydrodynamic basis for converting viscous dissipation into directional symmetry breaking through anisotropic rheology, providing a route to field-controlled material transport by active matter.

The discovery of altermagnetism has shown that crystal symmetry can generate momentum-dependent internal polarization without net magnetization. Whether an analogous form of symmetry-organized momentum-space order can exist for spinless lattice vibrations remains unresolved. Here we identify a structural mechanism for $alter$-$phononics$, in which phonon eigenmodes formed from structurally equivalent sublattices acquire momentum-dependent sublattice polarization and frequency splitting in nonmagnetic crystals. The central quantity is the sublattice-resolved dynamical asymmetry $\Delta(\mathbf q)=D_{AA}(\mathbf q)-D_{BB}(\mathbf q)$, which controls the associated eigenvector polarization. We show that this effect requires an alter-generator that maps equivalent sublattices onto one another while rotating the wave vector, together with the absence of inversion exchange and little-group sublattice-exchange constraints that would otherwise enforce sublattice equipartition. These symmetry rules generate nematic $d$-wave, tetragonal $d/g$-wave, and tripartite six-lobe phonon textures. First-principles calculations demonstrate the mechanism in representative nonmagnetic crystals and show how a symmetry-preserving structural distortion can unlock a hidden $d_{x^2-y^2}$-type texture by removing glide-induced equipartition traps while retaining the screw-axis alter-generator. We further show that the eigenvector texture is inherited by sublattice-projected electron-phonon coupling and anharmonic response functions. Our results establish structural alter-phononics as a spinless counterpart to altermagnetic momentum-space order and provide experimentally testable signatures in finite-$\mathbf q$ phonon spectra and displacement patterns.

Defect modes localize vibrations within phononic-crystal bandgaps. Prescribing their frequencies alone does not ensure separation from competing modes. We use frequency-dependent selection weights to combine attraction of target-adjacent modes with repulsion of competing in-gap modes. Only the central defect cell is optimized within a previously designed, fixed host bandgap. Cell-level Craig–Bampton reduction retains physical interface coordinates, allowing the host contribution to be assembled once while the defect basis and matrices are updated. Across three numerical cases, the reduced-order method accelerates defect optimization by approximately 13–20 times. A comparison with attraction-only optimization shows that the combined objective moves competing modes away from the target and increases the minimum target-to-non-target frequency separation. Full-order reanalysis shows that the optimized modes remain close to the prescribed frequencies and localized around the defect. A finite-array calculation shows enhanced response near the target relative to the defect-free host under the prescribed loading.

Orbital order describes a quantum state where occupied orbitals line up in a periodic pattern. While orbital physics plays a fundamental and universal role in strongly correlated electron systems, the existence and particularly the band structure fingerprint of orbital order remain a long-standing mystery. Here, we report the discovery of rare earth 5d-orbital order developed by the surface states of intermetallic compound Tb2CoAl4Ge2. Angle-resolved photoemission spectroscopy reveals characteristic nematic features like Fermi surface deformation and band split. These experimental observations can be described by a ferro-orbital order term in the mean-field Hamiltonian. The structural and magnetic origin of such order is excluded by systematic high-resolution neutron powder diffraction and scanning tunnelling microscopy measurements. Our results provide strong evidence for a pure surface orbital order scenario avoiding complications from structural distortion as in colossal magnetoresistance manganites, magnetic order as in iron-based superconductors, and charge transfer p-orbital order in cuprates.

Structural and dynamic correlations in the ground state of the one-dimensional Fermi one-component plasma are studied by Quantum Monte Carlo simulations. Results are presented for the pair correlation function, static structure factor, the one-particle density matrix and the momentum distribution, for the cases of full, partial and no polarization. {Within the precision of the calculation, the results conform to the fundamental scaling prediction of the Tomonaga-Luttinger Liquid Theory}. Evidence is reported of density correlations slowly decaying with distance, with the concurrent emergence of quasi-crystalline order even in the weakly correlated regime. Effects of quantum statistics in the momentum distribution are discussed.

Many problems in nonlinear and statistical physics are formulated through represented flows, including physical-space vector fields, phase-space drift fields, and truncated renormalization-group beta functions. We introduce a complementary representation-dependent diagnostic for testing whether finite-separation flow geometry is stable across observational resolution. For two separated points, states, or theories, the method compares the direction of the corresponding vector-field increment after the field has been smoothed at two resolutions. Averaging this normalized comparison over sampled separations gives a coherence matrix tied to the chosen variables, coarse graining, metric, and sampling protocol; it is a consistency test, not a coordinate-invariant quantity. We demonstrate the diagnostic in three settings. Synthetic divergence-free fields with identical Fourier amplitudes, spectra, and scalar two-point correlations nevertheless produce distinct coherence matrices, showing that second-order statistics do not determine cross-resolution increment geometry. Lorenz phase-space tests show that a smooth coordinate wrinkling changes represented drift geometry without changing the underlying dynamics, and that a weak model perturbation lowers finite-separation coherence even when local stretching proxies remain closely matched. Finally, for functional renormalization-group flows of the three-dimensional \(O(1)\) scalar theory, projected \(M=4,5,6\) LPA beta fields remain internally coherent, while cross-truncation coherence decreases as higher-order coupling directions are activated. The diagnostic provides a practical field-level check of how representations, models, and truncations preserve finite-separation flow geometry, complementing rather than replacing standard local, spectral, or fixed-point diagnostics.

The topological gap $\Delta$ – the excess $H_1$ total persistence of a critical point cloud over a density-matched null – scales as $\Delta \sim L^{d+\eta}$. We derive this analytically: the spectral integral $I(\alpha) = \sum_{k\neq 0} S_{\mathrm{conn}}(k)\,|k|^{\alpha}$ scales as $L^{2-\alpha-\eta}$ when IR-dominated, giving $I(-2\eta) \sim L^{d+\eta}$. The decomposition $I(-2\eta) = I_0 \cdot I_{\mathrm{shape}}$ separates volume ($I_0 \propto N(1-m^2) \sim L^d$) from anomalous dimension ($I_{\mathrm{shape}} \sim L^{\eta}$); the volume factor accounts for the magnetization-driven per-configuration variance of $\Delta$. We prove the mechanism requires $d < 2 + \eta$ (IR dominance), confining it to $d = 2$ for physical systems; in $d = 3$ the spectral integral is UV-dominated, explaining why density normalization is needed. An $\alpha$-sweep for Potts $q = 4$ at $L = 32$–$256$ finds $\alpha_{\mathrm{opt}}$ in $[-0.75, -0.5]$, consistent with $-2\eta_{\mathrm{Ising}}$ and inconsistent with $-2\eta_{q=4} = -1$; we flag this as tentative pending $L \geq 1024$ confirmation. The $\langle m^2 \cdot I(-2\eta)\rangle$ hyperscaling product is dominated by the correlation $r(m^2, I) \approx -0.98$ via the shared $I_0$ amplitude, so we report it as a covariance-correction analysis. Under a heuristic argument extending Divol–Polonik to inhomogeneous Poisson intensities, the bare PH kernel is flat; the effective kernel acquires $k$-dependence only at criticality. The per-configuration agreement between $\Delta$ and $I(-0.5)$ is primarily a magnetization correlation: $R^2 = 0.91$ at $L = 256$ collapses to $R^2 \approx 0$ once $|M|$ is partialed out. Per-configuration evidence corroborates the $I_0$ Parseval identity but not the $|k|^{-2\eta}$ shape factor; the latter is established by ensemble $L$-scaling.

Reducing coating thermal noise in future gravitational-wave detectors requires identifying the atomic motifs that control mechanical loss in amorphous optical coatings. We combine grazing-incidence X-ray pair distribution function measurements with atomic-structure modeling to study amorphous TiO$_2$-doped GeO$_2$ films over Ti cation concentrations from $\sim$11 % to $\sim$48 %, before and after annealing. The structural analysis reveals systematic composition- and annealing-dependent changes in short- and intermediate-range order. Increasing Ti content raises the average Ti coordination and promotes edge- and face-sharing polyhedral connections, while Ge remains predominantly fourfold coordinated. Annealing reduces these compact shared-polyhedron motifs and sharpens the first sharp diffraction peak, indicating a more relaxed intermediate-range network. Among the structural descriptors examined, the clearest correlation with the annealing-induced reduction in mechanical loss is the decrease in edge- and face-sharing polyhedra. These results connect composition, annealing, atomic structure, and mechanical dissipation in TiO$_2$-doped GeO$_2$, providing microscopic guidance for optimizing low-noise mirror coatings.