Papers

We show that a traveling modulation of the polarization-gradient stiffness in a ferroelectric material induces an effective flow in its collective polarization dynamics. Within a controlled local approximation, small polarization fluctuations, or ferrons, obey a massive Klein-Gordon equation with flow. Unlike conventional analogue-gravity platforms, the effective flow originates from the modulation of the material parameters rather than from the physical transport of the medium. This mechanism enables mobile analogue horizons separating sub-ferronic and super-ferronic regions, the latter supporting negative-norm antiferron modes. Their coupling to positive-norm ferrons gives rise to superradiant-like amplification, while the effective mass gap can be tuned independently through an external electric field. Ferroelectric systems therefore provide a novel and experimentally controllable platform for analogue gravity with massive scalar excitations.

We study local marginals in one-dimensional translation-invariant quantum systems that may hide finite-period structure. Given an $n$-site reduced density matrix, we ask whether it can be obtained by repeating a finite $p$-site block state along the chain and averaging over the $p$ lattice translations. This defines a symmetrized block-product periodic marginal problem, which provides a route both to diagnosing hidden periodic order from local data and to upper bounding ground-state energy densities of infinite translation-invariant local Hamiltonians. We develop two complementary methods. The first is a semidefinite-programming relaxation based on block permutation symmetry and positive partial transpose constraints, which outer-approximates the convex hull of such marginals and yields certified infeasibility tests. The second is a symmetrized matrix product state ansatz, which constructs explicit block-product periodic states and gives variational upper bounds. We benchmark the framework on the Majumdar-Ghosh model, transverse-field Ising, XX, XXZ, and contextuality-related spin models. The results show that the method captures the expected finite-period structure in exactly solvable cases and gives systematically improving variational energies as the period and bond dimension increase. We also formulate a periodic-NPA relaxation for translation-invariant contextuality witnesses and recover the known quantum limits in the tested examples.

A systematic first-principles investigation of the structural, electronic, mechanical, and optical properties of the cubic C15 Laves-phase intermetallic compound LaMg2 is performed within density functional theory. The calculated elastic constants satisfy the mechanical stability criteria for cubic crystals, confirming the intrinsic stability of the C15 phase. LaMg2 exhibits relatively low bulk, shear, and Young's moduli, indicating enhanced compressibility and elastic softness compared with transition-metal-based Laves phases. Direction-dependent elastic analysis reveals moderate anisotropy in Young's modulus, shear modulus, and Poisson's ratio, whereas linear compressibility remains nearly isotropic, consistent with the high crystallographic symmetry. The ductile nature of LaMg2 is supported by Pugh's ratio and Poisson's ratio, suggesting resistance to brittle failure and the dominance of metallic bonding. Electronic structure calculations confirm metallic behavior with a finite density of states at the Fermi level, primarily originating from La-5d states, accompanied by delocalized charge density characteristic of metallic interactions. The optical response further reflects the metallic nature through high reflectivity, strong optical conductivity at low photon energies, and pronounced absorption in the ultraviolet region. The combination of mechanical compliance, ductility, and metallic optical response highlights LaMg2 as a promising lightweight intermetallic material for applications requiring structural stability, damage tolerance, and efficient electromagnetic shielding or reflective components.

Obtaining equilibrium distributions of nonlinear systems is essential for accurately computing macroscopic observables. Conventional theoretical corrections are typically limited to weak nonlinearities, where interaction terms can be treated as effectively uncorrelated perturbations and the random phase approximation applies. In this Letter, we develop a framework to determine equilibrium distributions based on the generalized energy equipartition principle. Our approach recovers existing corrections in the weakly nonlinear regime and, crucially, remains valid for strong nonlinearities, where perturbative contributions become correlated and conventional approaches break down. Numerical simulations of the nonlinear Schrödinger equation, the Majda-McLaughlin-Tabak model, and the Fermi-Pasta-Ulam-Tsingou model demonstrate accurate corrections for nonlinearities more than an order of magnitude stronger than those accessible to conventional theories.

Determining microscopic interactions from spectroscopic and scattering measurements is central to understanding quantum materials, yet it often remains unclear which interactions can be reliably revealed by the available experimental data and how additional experimental modalities should be designed to resolve the remaining ambiguities. Here we present an artificial intelligence-enabled framework for uncertainty-aware Hamiltonian inference and adaptive experimental design. By combining Hamiltonian-conditioned neural surrogates with Bayesian inference and observation geometry, the framework characterizes how measurements constrain Hamiltonian parameter space, quantifies the identifiability of microscopic interactions, and propagates posterior uncertainty directly in the physical Hamiltonian parameter space rather than an abstract learned representation. Using multimodal powder and single-crystal inelastic neutron scattering measurements of the quantum magnet NiPS$_{3}$, we demonstrate physically interpretable Hamiltonian inference, modality-aware uncertainty quantification, and adaptive experimental design. The framework provides a general strategy for uncertainty-aware microscopic characterization and multimodal experimental design across quantum materials.

Thermo-mechanical compliant devices are commonly designed with small-strain linear elasticity and temperature-independent material properties, even though they might operate hundreds of kelvin above ambient where both assumptions are questionable. In this work, we quantify the effect and cost of each assumption in multi-material topology optimization of thermally actuated compliant devices. To this end, we introduce a physics-informed, simultaneous analysis-and-design framework with (i) a finite-strain quadratic-Hencky (logarithmic-strain) constitutive model whose isotropic thermal eigenstrain admits an exact additive split in log-strain space, and (ii) temperature-dependent conductivity, thermal expansion, and elastic moduli for a titanium–copper–steel material system. We optimize a thermal actuator and a thermal gripper at three design temperatures under both a baseline model and the full physics, subject to mass and manufacturability constraints. Every converged design is re-evaluated by verified nonlinear finite element solvers in the full factorial of constitutive law and property model. The comparison between the two factors reveals that the constitutive law is the decisive modeling choice: These devices work as linkages where linear kinematics mistakes rotation for compressive strain; its error therefore grows with the design temperature and concentrates on the very layouts that exploit rotation best. Because a linear optimizer also steers away from the rotation-rich mechanisms that would expose this bias, the model can deceptively appear trustworthy when validated against its own designs. Designing with the full physics yields consistently stronger and more temperature-robust devices at a modest increase in design-time cost.

Radial vortex is a topological spin texture stabilized by the interfacial Dzyaloshinskii-Moriya interaction (DMI) in ferromagnetic disks. Previous investigations have shown that the doublet splitting of azimuthal modes in traditional circular vortices arises from the coupling between azimuthal spin waves and vortex core (VC), an effect occurs only for azimuthal indices $m=\pm1$ and is absent for higher-order modes. Here, we present a giant mode splitting of azimuthal spin waves in radial vortices, even in the absence of the VC. This mode splitting arises from the DMI, which can be an order of magnitude larger than that induced by the VC. Moreover, the DMI-induced frequency splitting increases with both the DMI constant and mode index, reaching tens of GHz for higher-order azimuthal modes. Our results reveal a robust mechanism for mode splitting in chiral magnetic textures and deepen the fundamental understanding of the DMI effect on the spin-wave dynamics in confined magnets.

Starting from the constrained variational formulation of Larché and Cahn for solids in contact with fluids, a unified thermodynamic framework for such systems is developed. Both bulk and interfacial equilibrium conditions arise as stationarity conditions of a single thermodynamic functional. While earlier theory neglects a full treatment of interfacial contributions and therefore cannot describe systems in which surface effects are significant, the present formulation incorporates interfacial thermodynamics directly into the variational principle. The framework is introduced first for fluid-fluid systems to establish the underlying mathematical structure, and is then extended to solid-fluid interfaces. Within this setting, classical equilibrium relations for heterogeneous systems emerge naturally from different classes of admissible variations, providing a common theoretical basis for bulk, interfacial, and configurational thermodynamics.

Long term operation of semiconductor spin qubits requires active stabilization of quantum dot potentials against low-frequency charge noise. Previous work demonstrated a gradient-descent feedback (GDFB) approach on a silicon double quantum dot utilizing transport current measurements. We extend such a GDFB approach in a silicon double quantum dot device with high-bandwidth rf-reflectometry readout by utilizing a field-programmable gate array, the OPX by Quantum Machines, for digital signal processing. The OPX enables continuous multi-parameter gradient calculation and quick gate voltage updates, significantly increasing the effective feedback bandwidth compared to previous work. By operating with 8 steps per feedback cycle and an integration time of 25.6 $\mu$s, this high speed stabilization scheme achieves a -6 dB noise suppression up to a bandwidth of 5 kHz. This effectively suppresses low frequency 1/f noise, maintaining device stability over longer time periods, and potentially enables real-time control in large-scale quantum dot arrays.

Angle-resolved photoemission spectroscopy (ARPES) can measure electrons' energy vs momentum relations in solids via photoelectric effect. This pedagogical paper experimental results from this technique as a tool for visualizing the Fermi gas model in quantum statistical mechanics. This model is an important starting point for understanding more complex electronic behaviors in real metals.

The generation and manipulation of spin waves at the nanoscale via magnetic vortices are of considerable importance because of their broad applications across magnonic and quantum technologies. Previously, fixed nitrogen-vacancy (NV) centers in diamond have been used to locally characterize vortex dynamics, and scanning NV magnetometry (SNVM) has been used to image vortices' static stray fields. Here, we demonstrate SNVM imaging of both the static and microwave fields generated by vortices in mesoscopic permalloy structures with $\sim$50 nm spatial resolution, achieving excellent agreement with micromagnetic simulations, while revealing the effects of disorder. We further demonstrate a 40$\times$ microwave field enhancement near a vortex core and image the disorder-dependent, spatially varying, evanescent decay of these microwaves. Our ambient, tabletop technique surpasses diffraction-limited techniques' resolutions by at least 5$\times$, with far greater accessibility and throughput than synchrotron radiation-based techniques, offering new opportunities in the study and development of magnonic devices.

Auxetic behavior, characterized by a negative Poisson's ratio, is a counterintuitive mechanical response exhibited, among other systems, by certain polymer networks. Here, through in silico simulations we investigate the mechanical response of thermoresponsive microgels across the volume phase transition upon varying crosslinker concentration down to ultralow conditions, a regime so far unexplored. After refining the method to estimate the elastic moduli based on equilibrium shape fluctuations for the challenging case of ULCs, which are very sparse networks with rather anisotropic shape, we are able to show the onset of auxetic behavior near the volume phase transition for microgels with crosslinker concentration of ~ 1%. In addition, we find that ULC microgels exhibit a slightly negative Poisson's ratio across the whole swollen regime. Further examining the auxetic response within the inner region of the network, we also demonstrate that, for ULC microgels, this extends at all length scales, suggesting that it is an intrinsic property of the weakly connected polymer network. The present findings should likely stimulate novel experimental investigations, aiming to measure the Poisson's ratio of individual low and ultralow crosslinked microgels, to verify these intriguing numerical predictions.

CrBr$_2$ and CrI$_2$ are promising platforms for studying the effect of dimensionality on magnetic order, having been isolated in a 3-, 2-, and 1-dimensional form as bulk crystals, monolayers, and individual chains encapsulated in carbon nanotubes. However, the interactions that give rise to their helimagnetic order are unknown. Via inelastic neutron scattering on single crystals, we have determined the exchange interactions of these compounds from the spin wave dispersions, finding that the helimagnetic order arises primarily from competing antiferromagnetic interactions between intrachain and interchain nearest-neighbors. Single-ion anisotropy is substantial, modulating the helical spin rotation and gapping the inelastic intensity at points of branch crossings. As temperature increases, long-range order vanishes but intralayer correlations remain detectable up to at least 50 K.

Most materials with high thermal conductivity belong to one of two classes: metals, where heat is carried predominantly by electrons, and insulators, where heat transport is dominated by the phonon contribution. Materials that combine substantial electronic thermal conductivity and lattice thermal conductivity are rare, because the mechanisms that favor electron transport typically suppress phonon transport, and vice versa. Here, we report the theoretical prediction and experimental realization of such a material, metallic $\varepsilon$-TaN. Our calculations predict a total thermal conductivity at room-temperature of 273$\pm$5Wm$^{-1}$K$^{-1}$ in single crystals and 145$\pm$5Wm$^{-1}$K$^{-1}$ in polycrystals with 0.5$\mu$m grains, with an unusually large lattice contribution (79%) for a metal. The latter value is in agreement with our local transient thermoreflectance measurements on polycrystalline samples yielding $\sim$130Wm$^{-1}$K$^{-1}$. We show that the balanced electronic and lattice thermal conductivities of $\varepsilon$-TaN originate from a combination of large Fermi velocity and small Fermi density of states on the electron side, and large speed of sound and wide phonon gap on the lattice side.

In this letter, we examine how the presence of flat band leads to the formation of a high-temperature superconductor even in the case of repulsive pairing interactions. We also show that in the case of flat bands, the high-temperature superconducting state deforms the flat band, tilting it and making the effective mass finite. As a result, neither the superfluid weight nor the supercurrent disappear. Our results are in good agreement with experimental data.

The electronic structure of the spin-ladder cuprate Sr14Cu24O41 challenges the presumed universality of the Zhang-Rice singlet (ZRS) framework and models based exclusively on Cu-O hybridized orbitals. Combining polarization-dependent resonant soft X-ray scattering at the O K-edge with inelastic neutron scattering, we show that doped holes in the Cu2O3 ladders localize predominantly in planar non-bonding O 2pz (p{\pi}) orbitals of rung oxygen sites rather than forming conventional ZRS states. Polarization-resolved RSXS uniquely identifies this orbital assignment, while lattice and magnetic excitations reveal its coupled consequences, establishing a unified microscopic picture that excludes the conventional {\sigma}-bonded singlet. This oxygen-sublattice charge order produces an anomalous diagonal stretching phonon and explains the absence of incommensurate magnetic fluctuations and anomalous magnon splitting. These findings motivate a reassessment of hole pairing in ladder cuprates and the sufficiency of copper-centric models for cuprate superconductors.

NiO/Ga$_{2}$O$_{3}$ heterojunctions have garnered significant attention for use in power electronics due to the ultrawide bandgap and wafer-scale availability of Ga$_{2}$O$_{3}$ and the controllable p-type doping of NiO. However, the structure of NiO/Ga$_{2}$O$_{3}$ interfaces remains underexplored, largely due to the complexity of the junction between their dissimilar cubic and monoclinic crystal structures. Here we investigate the atomistic structure of the NiO/Ga$_{2}$O$_{3}$ interface for (100), (-201), and (001) oriented Ga$_{2}$O$_{3}$ substrates using aberration-corrected scanning transmission electron microscopy (STEM) in combination with interface modeling and image simulations. We evaluate the abruptness and consistency of the interfaces and compare them to calculated interface models, proposing precise atomic structures and assessing potential structural variation arising from complexity of the monoclinic Ga$_{2}$O$_{3}$ crystal structure. Our interface analysis supports increased focus on (100) oriented Ga$_{2}$O$_{3}$ as a candidate for fabricating high quality, low defect density NiO/Ga$_{2}$O$_{3}$ heterojunction devices. Importantly, we consider the effects of specimen thickness and 3D-to-2D projection during the STEM imaging process to differentiate such effects from real crystal variations. This work provides insight into the effect of substrate orientation on NiO film and interface quality, creating a pathway to improving heterojunction properties. It further highlights important considerations for interpretation of stability and interlayer phase formation in these interfaces, which is crucial for their integration into reliable and robust power electronic devices.

Let $x_1,\ldots,x_n$ be independent standard Gaussian vectors in $\mathbb{R}^d$. An ellipsoid fit is a matrix $S \succeq 0$ such that $x_i^\top S x_i =d$ for every $i$, so that all the points lie on the boundary of the centered ellipsoid $\{ x : x^\top S x = d\}$. Saunderson, Parrilo and Willsky conjectured that, as $n,d \to \infty$, this semidefinite feasibility problem undergoes a sharp transition at $n \sim d^2/4$. We prove this conjecture. If $\lim \sup n/d^2 = \alpha^* <1/4$, then, with probability tending to one, an ellipsoid fit exists; moreover, one can choose $S$ with all eigenvalues in a fixed interval $[\lambda_- , \lambda_+] \subset (0,\infty)$ depending only on $\alpha^*$. Conversely, if $\lim \inf n/d^2 > 1/4$, then, with probability tending to one, no ellipsoid fit exists, without any spectral restriction. Our proof builds on the Gaussian-equivalence framework developed by Bandeira and Maillard (2025) and closes the two gaps left open in their work: establishing exact fitting and removing the operator-norm constraint. On the satisfiable side, the new ingredients are a head-tail decomposition of the dual vector, exact correction of the sparse head constraints, and a Gaussian comparison principle for the low-influence tail. On the unsatisfiable side, we split a candidate into a low-rank spectral head and a Schatten-3 diffuse bulk, Gaussianize the bulk conditionally on the head, and apply a projected Gordon escape argument. The threshold is governed by the statistical dimension $d(d+1)/4$ of the positive semidefinite cone.

Van der Waals (vdW) ferroelectric semiconductors provide a unique platform for exploring the interplay between spontaneous polarization, electronic transport, ion migration, and photocarrier generation at the nanoscale. Here, we establish a room-temperature ferroelectric state in SnS2 and its sensitivity to structural polytype by directly contrasting the centrosymmetric 2H-phase with the polar 4H-phase. Raman spectroscopy distinguishes the 2H and 4H polymorphs of SnS2 through their characteristic phonon fingerprints. Piezoresponse force microscopy confirms room-temperature ferroelectricity in the 4H phase, while the 2H phase exhibits no ferroelectric response. The built-in polarization in a three-terminal transistor device of the 4H-SnS2 is modulated significantly by electrostatic gating and on exposure to linear and circularly polarized light. This device reveals polarization-controlled output characteristics with distinct gate-voltage induced hysteretic response and thermally activated carrier transport, confirming p-type semiconducting behavior strongly coupled to ferroelectric polarization. The photoresponse likewise exhibits polarization-assisted carrier separation, sublinear power-law scaling, a nonmonotonic temperature response correlated with the characteristic Raman modes, ferroelectric hysteresis, and a pronounced dependence on the circular and linear polarization states of the incident laser beam. These results establish 4H-SnS2 as a promising material system for polarization-driven electronic and optoelectronic technologies, including nonvolatile memory and photoferroelectric functionalities.

Fast Fourier transform (FFT) is widely used for thick-film reflectometry because of its simplicity and computational efficiency. However, its performance under practical thick-film measurement conditions has received limited experimental evaluation. In this work, FFT, Linearized Reflectance Zero-Crossing (LRZ), and optical model fitting were compared using reflectometry measurements from a nominal 52 {\mu}m dielectric film acquired on a production wafer, with White-Light Interferometry (WLI) serving as an independent reference. Although FFT exhibited excellent repeatability, it showed systematic deviation from WLI (RMSE = 0.62 {\mu}m), whereas LRZ significantly improved accuracy (RMSE = 0.20 {\mu}m). Simulations and theoretical analysis indicate that the observed systematic deviation is consistent with spectral leakage caused by finite measurement windows and non-integer fringe periodicity. These results demonstrate that excellent repeatability does not necessarily imply high accuracy and highlight the advantages of zero-crossing-based approaches for thick-film thickness metrology.

We demonstrate the existence of at-$\Gamma$ degenerate hybrid bound-states in the continuum (BICs) with high-order topological charges and quadratic band degeneracy in periodic photonic structures with $C_{6v}$ symmetry above the diffraction limit. The degenerate BICs are realized by combining symmetry protection, which suppresses radiation into zeroth-order diffraction channel, with quadratic band degeneracy and parameter tuning to eliminate radiation into first-order diffraction channels. An effective Hamiltonian is used to investigate the band structure around the degeneracy point, and the topological dynamics in all diffraction channels are characterized. This work reveals a novel mechanism for realizing degenerate BICs above the diffraction limit, opening up opportunities for new physics and applications.

Motivated by the discovery of bimetallic MXene compounds with Janus metal sites, we investigate Janus MXenes TiM"CO2, where M" = Mo, W. Our computational analysis reveals that broken inversion symmetry in the Janus structure, coupled with strong spin-orbit coupling at M", generates diverse and remarkable functionalities. These include pronounced Rashba spin splitting, non-trivial Z2 topology, Berry-curvature-dipole-driven nonlinear anomalous Hall effect, and strain control of the Berry curvature dipole. Notably, the 4d transition-metal-based TiMoCO2 and 5d transition-metal-based TiWCO2, with M" elements from the same column of the periodic table, display markedly different behaviors. While TiMoCO2 is a Z2 topological insulator, TiWCO2 is a trivial semimetal. Both compounds, however, exhibit compelling quantum properties. TiWCO2 shows a robust Rashba effect with a large Rashba coefficient of 1.35 eV. Angstrom and a large nonlinear anomalous Hall conductivity of 120 x 0.0001 G0. TiMoCO2, a Z2 narrow-gap semiconductor with weaker Rashba splitting and moderate nonlinear anomalous Hall conductivity, exhibits a strain-driven transition from semiconductor to semimetal. This transition modulates both the sign and magnitude of the Berry curvature dipole, yielding a sizable nonlinear anomalous Hall conductivity of 17 X 0.0001 G0 under 2% tensile strain. Our findings underscore the potential of MXenes as a platform for investigating and tailoring multifunctional quantum phenomena.

Negative stochastic entropy production is commonly called an apparent violation of the second law. In general quantum-trajectory dynamics, however, the physical entropy production $\sigma$ need not obey a forward detailed fluctuation theorem. A general arbitrary-coupling formulation identifies a dynamical-asymmetry term $\sigma^\ast$ that completes it into $\Omega=\sigma+\sigma^\ast$, whose mean is $\langle\Omega\rangle=\Sigma+\Sigma^\ast$. We prove that the likelihood-ratio sign is optimal among reversal-odd trajectory observables and use this fact to transfer an established sharp fluctuation-theorem floor to the tie-corrected physical sign statistic $\Pi_\sigma=\Pr(\sigma<0)+\Pr(\sigma=0)/2$. When $\Pr(\sigma=0)=0$, the result reads $\Pr(\sigma<0)\ge[1-\langle\Omega\rangle/g(\langle\Omega\rangle)]/2$, where $g$ is the inverse of $a\mapsto a\tanh(a/2)$. The physical integral fluctuation theorem simultaneously suppresses large negative events, producing a quantitative “frequent but mild” law, while the sign imbalance lower-bounds the hidden mean $\Sigma^\ast$. We formulate the measured-record protocol explicitly and illustrate and numerically audit the tie-corrected theorem in random finite-coupling collision models and a coherently driven qubit interacting with thermal ancillas.

A recent work introduced the Simulator Collection for Atomic-to-Continuum Scales (SCACS) toolkit, a framework for improving finite element predictions of heat flow by mapping atom-resolved thermal conductivity into the stiffness matrix of the Galerkin finite element formulation [Ugwumadu et al., Phys. Rev. Materials 10, 053804 (2026)]. Here, we demonstrate that SCACS-derived conductivity fields are solver-independent and can be transferred to existing continuum simulation platforms. As a proof of concept, we map SCACS-derived conductivity fields from complex silicon structures onto finite element meshes in Abaqus and compare the resulting heat-flow solutions with that obtained using conventional uniform-conductivity assignment within Abaqus. Comparison of the two implementations shows that atom-informed conductivity fields can be incorporated into existing finite element workflows and improve realistic prediction and the accuracy of its solution. This work supports broader efforts to improve the predictive capability of continuum simulations for efficient materials design and property prediction.

Practical implementations of quantum error correction (QEC) require rapid measurement and continuous processing of the syndrome information in order to prevent a backlog of unprocessed data. While “static” QEC is theoretically well understood via mappings to equilibrium statistical mechanics models, such an understanding of “real-time” QEC is currently lacking. Here, we study the kinetics of sliding window decoding (SWD), an implementation of real-time decoding that acts on temporally local windows of noisy syndrome information and commits to corrections irreversibly at a nonzero rate. We propose an effective description of SWD in terms of a stochastic kinetic process, where $\mathbb{Z}_2$-charged point particles undergo parity-conserving reaction and diffusion. This model describes dynamics at length and time scales large compared to the window size $W$, whereas physics at scales smaller than $W$ leads to nontrivial $W$-dependent scaling of the effective parameters. We identify the rate of decoding $1/W$ as a relevant perturbation to the decodable phase. We also show broad applicability of our results by changing many microscopic details of SWD without affecting the effective description.

Time delays are ubiquitous in physical and biological networked systems, playing a fundamental role in the emergence and stability of collective behavior. Yet, existing theoretical methods for synchronization analysis of delay-coupled systems are largely limited to networks with homogeneous degree distributions. Here, we extend the master stability function framework to a broad class of degree-heterogeneous, weighted, and directed delay-coupled networks. The analysis reveals that synchronization can be enhanced in heterogeneous networks compared to homogeneous ones, including all-to-all networks, which are known to be optimal in non-delayed systems. To identify optimal heterogeneous structures, we develop a network optimization method that finds directional, edge-weighted configurations maximizing synchronization stability. Our results show that, in delay-coupled networks, heterogeneity and nonreciprocity are key resources for synchronization.

Product codes are an important class of quantum error-correcting codes constructed from multiple input codes, which can give rise to asymptotically good quantum low-density parity check codes. In previous work, we showed how the product between two codes can be physically implemented by coupling layers of the first code using checks of the second code. In this work, we further unify product code constructions with coupled-layer constructions of phases of matter by introducing coupled-layer codes. The essential strategy is to condense general excitations created by Pauli operators among multiple decoupled layers of the first code. The condensation is specified by an excitation algebra, which encodes the excitations, along with an algebra-preserving map. This coupling between layers generalizes the notion of gauging in physics as well as the mapping cone in homological algebra, and can be used to produce non-CSS codes. As examples, we show how coupled-layer codes reproduce the X-cube and Chamon models. We further generalize the balanced product code by allowing a unitary transformation in addition to a group action by free permutation and describe its corresponding coupled-layer construction. In particular, we show how balancing by a ZX-duality can reproduce non-CSS codes such as the fermionic toric code and the 3-fermion Walker-Wang model in 3D.

Understanding correlated quantum matter starts with an accurate model of the single-particle states that interact at low energies: their dispersion, band geometry, orbital content and charge density. In many cases, notably the topological bands of moire materials, it is not straightforward to find a real-space description with a few local orbitals that accomplishes this task. Here we provide a systematic way to identify the local degrees of freedom that best capture the band geometry and charge density of any chosen set of bands. We use the unit-cell one-particle reduced density matrix (UC-1pRDM), obtained by restricting the projector onto the target bands to a single unit cell. Its eigenstates, which we call cell natural orbitals (CNOs), form a local, symmetric basis uniquely determined by the Bloch wavefunctions and the choice of real-space partition. Their eigenvalues measure the occupation of each CNO in the target bands, quantifying entanglement across unit-cell boundaries and the importance of multi-orbital character. A set of CNOs that maximizes total spectral weight and reproduces the target band symmetries provides optimal trial states for Wannierization. We exemplify this by constructing a lattice model for twisted bilayer WSe$_2$ that tracks the orbital content across twist angles.

The crossover between topology and nonequilibrium dynamics has emerged as a rich frontier, in which quantum systems can exhibit unique dynamical phenomena that lie beyond the reach of equilibrium. Of particular interest are quench dynamics across topological phase, as it may reveal the information about the underlying Majorana zero-energy states. Here, we investigate the fate of Majorana boundary modes in a quenched fermionic superfluid using self-consistent time-dependent Bogoliubov-de Gennes theory. For quantum quenches within the topological regime, Majorana boundary modes survive but undergo coherent boundary oscillations arising from the nonadiabatic deformation of their wave functions. Furthermore, a pronounced ripple pattern appears in the post-quench density distribution following a sudden topology-changing quench. Here we identify that these ripple structures originates from the coherent hybridization and interference of the initially separated Majorana boundary states. Our findings establish nonequilibrium boundary dynamics as a new approach for probing Majorana physics, which is complementary to conventional equilibrium measurements.

We establish a global, worst-case non-identifiability theorem for periodically driven finite-dimensional quantum systems. On the unrestricted smooth periodic Hamiltonian class, we show that the period-averaged Fubini-Study metric component of a fixed initial state cannot, in general, be reconstructed from exact one-period propagators indexed by every starting time and external parameter. Thus, even complete starting-time-resolved endpoint data are insufficient to determine this intra-period geometric quantity. The obstruction is characterized exactly. The starting-time-indexed endpoint data determine the conjugation path of the monodromy, but not its particular unitary lift. On each fixed-monodromy slice, the observational fibres are precisely the right orbits generated by smooth parameter-dependent based loops taking values in the pointwise centralizer of the monodromy. The Fubini-Study functional is not invariant under this fibre action and therefore does not factor through the endpoint observation map. An explicit real-analytic two-level witness demonstrates the obstruction within a commuting, one-generator Hamiltonian family, so neither non-Abelian time ordering nor Floquet-logarithm ambiguity is required. A continuous family of Hamiltonians produces identical starting-time-indexed one-period endpoint data while yielding different, and on the unrestricted class arbitrarily separated, period-averaged Fubini-Study geometry. Non-identifiability persists under any prescribed uniform bound on the parameter derivative of the Hamiltonian. The result is a deterministic global statement, not a claim of generic non-identifiability or experimental impossibility. It identifies a precise information gap between complete one-period endpoint data and full intra-period dynamics: the missing information is the unitary lift of the observed monodromy path rather than ordinary scalar phase freedom.