Papers

A single oblique metallization step gives conventional gratings one-sided silver decoration, established by electron microscopy and elemental mapping. Opposite-face reversal measurements yield finite-aperture red/green/blue transmission ratios up to 1.74 for a 1-$\mu$m grating and 1.5-1.8 for a 30-$\mu$m grating, with reference-normalized transmittances for the latter. Flat-side coating and reduced silver dose give ratios near unity. Maxwell calculations on self-shadowed growth profiles reproduce the directional sign qualitatively and attribute the contrast to diffraction-channel redistribution. The structure remains reciprocal, including its normal-incidence zeroth-order transmission. These results establish directional metallization as a route to direction-selective optical transmission without multilayer alignment or overlay lithography.

We investigate how sensory coupling mediates phase coherence between spatially separated, confined active systems. Using two fish schools separated by a water-filled transparent gap, we isolate vision as the primary interaction channel. Under boundary confinement, each school's center-of-mass heading exhibits noisy bistable dynamics, spontaneously switching between two antiparallel directions along the partition wall. Turning events in one school bias the orientation of the other, driving distance-dependent phase synchronization. We model this behavior using two coupled stochastic bistable oscillators whose exact solution quantitatively reproduces the empirical results. Our work establishes a precise connection between nonequilibrium active systems and coupled stochastic oscillators, offering insight into boundary-spanning information transfer in living collectives.

Recently, we introduced a geometric object analogous to an orthonormal frame in the Cartan formalism to study the parameter space of quantum systems; we called it $\mathcal{N}$-bein, with $\mathcal{N}$ being the number of parameters that characterize the quantum system. Acting as the “square root” of the quantum geometric tensor (QGT), the $\mathcal{N}$-bein allows us to define new tensors to improve our understanding of the structure beneath the parameter space of quantum mechanics. In this work, we extend this mathematical framework surrounding the $\mathcal{N}$-bein to analyze the parameter space of quantum systems with degenerate spectra. As in the non-degenerate case, we define a non-Abelian two-state QGT to identify possible transitions between degenerate states after two consecutive parameter variations. Additionally, using the Wilczek-Zee connection, we introduce a torsion-like tensor as the covariant derivative of the $\mathcal{N}$-bein. This torsion captures the noncommutativity of successive parameter variations and coincides with the antisymmetric part of the two-state QGT. We also present a geometrical formulation using differential forms and discuss the physical implications of the newly defined tensors. Furthermore, we construct several gauge-invariant observables from the $\mathcal{N}$-bein and its derivatives to highlight the utility of the new tensors. Finally, to illustrate the convenience and applications of this formalism, we apply the theoretical framework to a system of coupled harmonic oscillators immersed in an electric field. The coupling between the oscillators results in a degenerate system. Thus, using the new formalism, we found correlations among the quantum states quantified by the new invariants.

Excitons are composite quasiparticles: beyond a center-of-mass position, each carries an internal electron-hole dipole governing its coupling to electric fields and other excitons. Exciton Wannier functions locally represent exciton bands, but resolving this dipole requires localizing the electron and hole simultaneously. We show that, in one dimension, the projected electron and hole position operators fail to commute when the covariant derivative of the quantum geometric dipole (QGD) matrix (the difference between the hole and electron non-Abelian Berry connections) is nonzero. This precludes a common eigenbasis and bounds the joint electron-hole spread from below. For one band, the internal dipole is gauge invariant and center-of-mass methods suffice; for multiple bands, no existing construction yields a gauge minimizing both position uncertainties. We introduce an “exciton spatial localizer,” a Hermitian operator embedding both projected positions in a Clifford-algebra structure. Its spectral minima locate the exciton's center-of-mass and dipole coordinates, while its eigenvectors yield exciton Wannier functions jointly localized in electron and hole coordinates without gauge fixing, an ansatz, or iterative optimization. In an interacting bilayer model, combined reflection–time-reversal symmetry or a nonsymmorphic particle–hole symmetry forces the QGD matrix to be traceless at every momentum while allowing it to remain nonzero. A two-band exciton subspace with zero net internal dipole then decomposes into a symmetry-related pair of exciton Wannier functions with opposite center-of-mass positions and internal dipoles. Adding the interlayer dipole as a Clifford component further separates intralayer and interlayer exciton Wannier functions in a six-band subspace.

We study bilinear order-parameter correlations in a general class of sign problem-free systems that are described by what we call Fluctuating Gaussian States (FGS) with anti-unitary symmetries, where the weight of each Gaussian measurement in the space-time path integral is positive-definite. Supported by Monte Carlo simulations on fluctuating Gaussian fermionic and bosonic examples, we argue that such systems generally exhibit two types of broken-symmetry phases: a saddle point phase and a non-local contraction phase, with the competition between the two determined by the stability of the fluctuation saddle point of FGS. Due to the Fermi liquid instability in fermionic FGS with anti-unitary symmetries, we also discuss the possibility of representing fermionic FGS with a particular Projected Entangled-Pair State (PEPS) ansatz, which we argue a certain construction provides an efficient description for the saddle point phase, but not for the non-local contraction phase. Finally, we discuss the potential implication of our result in non-equilibrium systems and stabilizing a target bilinear order.

Programmable quantum annealers can realize real-time dynamics of frustrated transverse-field Ising models on large, nontrivial graphs. Recent work by King et al. argued that the classical simulation of such experiments would require exponential computational resources for classical methods such as tensor networks and neural quantum states. Here, we numerically simulate the D-Wave spin-glass annealing protocol with time-dependent variational Monte Carlo (t-VMC) using a correlator state tailored to spin-glass dynamics. For the two-dimensional cylinder, three-dimensional dimer, diamond, and biclique instances considered, at annealing times of 7 and 20 ns, we show that systematically increasing the variational ansatz size enables t-VMC to approximate the final two-spin correlation errors of the quantum processing unit (QPU). We also perform an accurate large-scale simulation of a challenging biclique instance for which no other variational method is known to work, and we find close agreement with the quantum annealer. Through ablation studies, we identify poor Markov-chain mixing, high-variance local-energy estimators, and stochastic Runge-Kutta error estimates as the principal numerical failure modes. We address these numerical issues by using parallel tempering, blurred sampling and an importance-weighted differential equation solver, thereby clarifying the numerical requirements for stable, large-scale t-VMC simulations. Our results extend the frontier of classical simulation while providing a realistic assessment of the computational costs of simulating quantum dynamics at this scale.

Prethermalization describes long-lived intermediate regimes that precede equilibrium and can dominate experimentally accessible dynamics. Here, we show that a separation of spectral energy scales, despite giving rise to a hierarchy of dynamical timescales, does not by itself guarantee the appearance of a prethermal plateau. Under the same Hamiltonian, some observables may exhibit prethermal behavior, while others relax directly toward equilibrium. We uncover the mechanism governing this selectivity, showing that the emergence of a prethermal plateau depends not only on the Hamiltonian, but also on the observable and the initial state. Our results apply broadly to systems close to a fully permutation-symmetric limit and are illustrated with a long-range interacting spin model. We further prove that the Loschmidt echo provides a lower bound on the prethermal lifetime of any bounded observable whenever the prethermal and exact dynamics are unitary.

We construct a constant-degree and constant-gap quantum expander on $n$ qubits where each unitary can be implemented by a depth-$1$ and 1D circuit of Pauli or CNOT gates. We provide two applications of this expander. First, we use it to construct a family of frustration-free 1D Hamiltonians whose ground states obey the entanglement-gap relation $S = \Theta(\Delta^{-1/2})$; this is believed to be optimal, but achieving it had been open. Second, we use it to provide a streaming protocol that tests for closeness to a class of 1D volume-law entangled states. Moreover, we extend our quantum expander to a constant-degree and constant-gap expander on the unitary group where each unitary is a single $T$ gate, a single $T^{\dagger}$ gate, or a depth-$1$ Clifford circuit. This implies that a random sequence of unitaries from the expander yields a gapped walk on a dense subgroup of the unitary group. This improves upon previous work by Bourgain and Gamburd which did not control the dependence of the gap on the dimension.

In a bulk 3D type-II superconductor, the lower critical field at which an isolated vortex becomes thermodynamically favorable is a size-independent material property. We show that the situation is different in 2D superconductors: the larger the superconductor, the weaker the field needed to create its first vortex. The lower critical field in 2D is always size-dependent. For a disk of area $\mathcal A$, the lower critical field $B_v(\mathcal A)$ scales as $\mathcal A^{-1}\ln(\mathcal A/\mathcal A_0)$ in the weak-screening regime and as $\mathcal A^{-1/2}$ in the strong-screening regime. We derive these results from an analytically tractable microscopic model that admits many-body wavefunctions for both the uniform and singly quantized vortex states in a magnetic field, and incorporate screening by coupling their long-distance 2D supercurrents to 3D Maxwell equations. These results motivate organizing the weak-field ground-state of a 2D superconductor in the $(1/\mathcal A,B)$ plane. The origin represents the zero-field thermodynamic limit and it is singular. Approaching the origin along the $B$ axis leads to an increasingly dilute vortex lattice, whereas approaching along the $1/\mathcal A$ axis yields the uniform vortex-free state. Our theory shows that every trajectory carrying fixed finite flux ultimately approaches the vortex-free state in the thermodynamic limit and provides a firm microscopic foundation for the weak-field thermodynamics of 2D superconductors.

Superconductor-semiconductor hybrids host emergent states of matter and offer a platform for new qubits, but the superconducting metal shunts electrical transport, which rules out conventional semiconductor characterization and leaves the hybrid parameters to speculation. Here we determine density, mass, $g$-factor, mobility and subband occupation beneath the superconductor, from Shubnikov-de Haas oscillations of a buried InAs quantum well under Al, Sn, V, Nb, Ta and Re films, with a Dingle analysis that accounts for the shunt. Every metal adds an interface subband whose occupation falls into one of two classes, whereas the mass and $g$-factor of the buried well are unchanged to within 10%. Within the uncertainty set by the transport mobility, no film shortens the quantum lifetime of the buried well, and Al and Sn lengthen it. Quantum lifetimes bound the hybridization of the interface subband to 2-4~meV. These measurements supply the normal-state parameters that tunnelling spectroscopy renormalizes but cannot measure.

Additive functionals $\overline{J}_t=\frac{1}{t}\int_0^tU(X_s)\circ dX_s$ of Stratonovich-type recently attracted much attention in the context of inference of thermodynamic properties of complex systems from observations $U$ of individual fluctuating paths $(X_s)_{0\le s\le t}$, whereby $X_0$ is initiated from some general measure. Concentration results on $\overline{J}_t$, albeit desirable, are virtually nonexistent. They turn out to be significantly more challenging to prove than for classical Lebesgue-type functionals $\overline{\rho}_t=\frac{1}{t}\int_0^t V(X_s)ds$ because the tilt deforms the full second-order structure of the Feynman-Kac generator instead of contributing an additive potential. This renders the generator generally non-self-adjoint even under detailed balance. We overcome this by working with a symmetrized Dirichlet form with a new effective potential that now couples the observable to the non-equilibrium character of the dynamics. We prove concentration inequalities for $\overline{J}_t$ for any bounded, sufficiently smooth vector-valued function $U$ of a general geometrically ergodic diffusion process $X_s$, including explicit sub-gamma and Bernstein-type inequalities, and we obtain explicit upper bounds on ${\rm Var}(\overline{J}_t)$. Strikingly, under detailed balance the concentration of $\overline{J}_t$ is distinctively sub-Gaussian at all times and all deviations, with a variance proxy fixed by the noise alone and independent of the spectral gap, which has no analog for $\overline{\rho}_t$.

Odd viscosity is a nondissipative component of the viscosity tensor that arises in fluids with broken time-reversal symmetry. Despite conserving energy, we show that odd viscosity can qualitatively alter hydrodynamic stability by generating exponentially growing modes that are absent in conventional fluids. For plane Poiseuille flow, we derive the odd-viscous generalization of the Orr–Sommerfeld–Squire equations and find a new instability that first emerges for spanwise perturbations and extends to oblique modes through the amplification of odd-viscous forces in critical layers. The instability originates from the non-normal dynamics of shear flows: conventional fluids support transiently growing disturbances through the lift-up mechanism, while odd viscosity provides a feedback between wall-normal velocity and vorticity that converts this transient growth into a self-sustaining exponentially growing mode. More generally, we show that an energy-conserving perturbation can destabilize a non-normal dynamical system only when the unperturbed system supports transient growth. Our results establish a direct connection between transient growth, non-normality, and instability induced by nondissipative forces, with implications extending beyond odd-viscous hydrodynamics.

The source-free condition, $\nabla\cdot\mathbf{B}_{\mathrm{xc}}=0$, where $\mathbf{B}_{\mathrm{xc}}=\delta E_{\mathrm{xc}}/\delta\mathbf{m}$ is the exchange-correlation (xc) magnetic field of non-collinear spin-density functional theory (SDFT) and $\mathbf{m}$ the magnetization, is widely believed to be exact. Recent studies report that projecting the field of a parent functional onto its source-free part improves the predicted magnetic moments. We show that the condition violates the global spin-rotation symmetry of $E_{\mathrm{xc}}$ and therefore cannot be exact. A source-free field is exact only in a transverse theory whose xc functional differs from $E_{\mathrm{xc}}$ and is itself not invariant under spin rotations. We examine a source-free (SoF) construction, an exchange-correlation energy given by a parent SDFT functional evaluated at the transverse magnetization $\mathbf{m}_{\perp}$. Its field is divergence-free, remains a functional derivative and exerts local torques, but still, it breaks global spin-rotation symmetry. With the LSDA as parent we examine the \ce{Mn2} molecule. The SoF and the locally collinear (LoC) LSDA both give too short a bond and too large a bond energy, but SoF finds a broken-symmetry antiferromagnetic solution, consistent with the experimentally observed $^{1}\Sigma^{+}_{g}$ ground state, with a coupling of the right sign and roughly the right size, while LoC finds a high-spin $^{11}\Pi_{u}$ ferromagnet and the wrong sign. The broken symmetry of SoF, however, produces severe errors in directional properties: a rigid spin rotation of the magnetization changes the energy by about $1\,\mathrm{eV}$, in a weak uniform field the magnetization points perpendicular to the field instead of antiparallel to it, and the molecule develops a spurious magnetic anisotropy.

We investigate the refractive index $n$ of LiF using DFT+G$_0$W$_0$+BSE, with ionic-temperature effects included through QMD. We calculate photon-energy dispersions $n(\omega)$ and $k(\omega)$ at ambient pressure and $n(\rho,T)$ at 532 and 1550 nm under shock compression, where $\rho$ and $T$ vary together. Quasiparticle band structures at ambient and compressed conditions and the ambient-pressure orbital-projected density of states connect the optical response to the electronic structure. At ambient pressure, G$_0$W$_0$ yields a quasiparticle gap of 14.25 eV, close to the experimental 14.2 eV, while BSE reproduces the main excitonic feature at 12.5 eV, close to the observed 12.6 eV. Quasiparticle and excitonic effects are thus essential for accurate optical dispersion; the hybrid HSE functional does not reproduce the optical spectra. Along the principal Hugoniot up to 140 GPa, $n(\rho)$ agrees closely with shock data at 1550 nm and acceptably at 532 nm, and agrees better overall than earlier first-principles calculations. Above approximately 110-120 GPa, QMD produces a downturn relative to cold $n(\rho)$ curves, suggesting that ionic dynamics may contribute to deviations from the linear $n$-$\rho$ Gladstone-Dale relation. QMD-sampling and finite-k-grid uncertainties are estimated, and transition-peak broadening is assessed using a recently proposed criterion. The gap increases under pressure, with a transition to a $\Gamma\to\mathrm L$ indirect gap near 50 GPa. An exploratory calculation at approximately 1400 GPa finds a gap of about 24 eV, disfavoring gap-closure metallization. Structural and elastic benchmarks of the underlying models are also provided.

Resistive random access memory (RRAM) devices, also known as memristors, are highly dependent on fabrication, location on the wafer, and measurement protocols. However, openly available large-scale memristor datasets remain scarce, particularly those that combine experimental metadata with electrical measurements and preserve explicit links across the experimental workflow. Here, we present a comprehensive relational database of automated electrical characterization data from oxide-based memristors. The database links 6,190 memristor devices across TiN/HfOx/TiN, Pt/TiOx/AlOy/Pt, and Pt/TiOx/Pt stacks to 161,006 validated experiments and over 169 million electrical point records. It integrates fabrication, wafer mapping, electrical characterization, and modeling to describe electroforming, current-voltage non-linearity, memory windows (R_off/R_on), switching dynamics, and short-term volatility. Released as a normalized and indexed SQLite database with schema documentation, graphical user interfaces, and examples of empirical modeling, this resource supports provenance-aware querying, statistical analysis, and data-driven applications for the development of future memristor technologies.

Nonadiabatic coupled electron-nuclear dynamics upon electronic excitation underpin the microscopic mechanism and rational modulation of diverse photoinduced functional phenomena in materials, yet their direct first-principles simulations remain computationally demanding. Here we develop a framework for nonadiabatic excited-state machine-learning molecular dynamics (EMLMD) simulations, where the nonequilibrium electronic information upon photoexcitation such as electron temperature is rigorously calibrated from high-precision real-time time-dependent density functional theory (rt-TDDFT) benchmark simulations, enabling accurate reconstruction of excited-state potential energy surfaces (PES). This framework natively incorporates the excited-state electron-phonon couplings and intrinsically captures photoinduced phonon anharmonicity, both of which are missing in standard machine learning molecular dynamics, thus delivering first-principles-level accuracy for excited-state atomic evolutions. Large-scale EMLMD simulations resolve time- and momentum-resolved phonon dynamics in photoexcited materials, directly uncovering the competition between photogenerated coherent phonons and thermal phonons during photoinduced phase transition of bismuth. It also simultaneously resolves elusive atomic-scale microscopic dynamics and global structural rearrangement for selenium photoamorphization. Balancing high accuracy and efficiency, EMLMD offers a versatile paradigm to tackle key challenges in the study of complex excited-state molecular dynamics.

The in-plane critical field of Ising superconductors exceeds the Pauli limit by an order of magnitude because the Ising spin-orbit coupling locks the electron spins out of the basal plane. The same locking converts an in-plane Zeeman field into a source of equal-spin triplet Cooper pairs, so that the field-driven condensate acquires an $s+if$ character. We show that this conversion channel also generates Lifshitz invariants, the odd-in-momentum terms of the Ginzburg-Landau expansion responsible for the superconducting diode effect. When the basal mirror symmetry of the monolayer is lifted by a substrate or a gate, the field-induced triplets couple linearly to the Cooper-pair momentum, and an intrinsic diode response develops whose strength is set by the ratio of the Zeeman and spin-orbit energies rather than by the small ratio of the spin-orbit and Fermi energies familiar from parity-mixing mechanisms. We construct the symmetry-constrained two-component Ginzburg-Landau theory of the coupled singlet and triplet order parameters and derive all of its coefficients from the microscopic model of an Ising superconductor; the complete functional, including all gradient and quartic terms, is generated by a single pair-breaking function of temperature, field, and Cooper-pair momentum. An attractive triplet channel reshapes the diode response: at weak fields it suppresses the efficiency through destructive interference between the direct and the collective-mode conversion paths, while at strong fields it extends the diode regime well beyond the singlet-only critical field, with the maximal efficiency reached along the triplet-enhanced phase boundary. The diode effect thereby serves as a transport probe of a hidden triplet pairing channel and of the field-induced $s+if$ state.

Recent real-space imaging in quantum paraelectric SrTiO$_3$ [Nature 656, 54 (2026)] reveals that local polar textures do not continuously grow upon cooling, but reach a maximum intensity at intermediate temperatures around 60-65 K and weaken again toward the quantum paraelectric ground state. Such a reentrant-like weakening of local polar textures challenges the conventional paradigm in which ordering tendencies generally continue to strengthen as temperature decreases. Here we employ a self-consistent phase-field theory showing that this anomalous behavior naturally arises from the coupling between intrinsic polar and antiferrodistortiv (AFD) fluctuations. We demonstrate that the flexoelectric-like coupling strongly hybridizes the polar and AFD modes. As the uncoupled polar and AFD modes cross near 52 K, their hybridization is maximized, driving the lower hybridized branch to develop a minimum on a finite-wave-vector shell. This finite-$q$ softening triggers a Brazovskii-type instability, strongly enhancing polarization correlations and producing nanoscale polar textures. Away from the crossing temperature, the two modes become increasingly detuned, weakening their hybridization and the associated finite-$q$ softening. These results reaveal the origin of the formation of polar nanoregions in SrTiO$_3$, naturally explaining the unexpected confinement to an intermediate-temperature window and providing a mechanism beyond the quantum-fluctuation-based interpretation suggested by experiment. Furthermore, we predict an unconventional reentrant-like sequence in weakly strained SrTiO$_3$, evolving from ferroelectric to paraelectric, polar-nanoregion, and eventually paraelectric regimes upon heating from zero temperature.

Hyperuniform materials occupy an intermediate regime between periodic order and conventional disorder, characterized by a suppression of long-wavelength density fluctuations, commonly quantified by the structure factor. This characterization, however, relies on the statistical properties of an extended configuration or supercell representation and does not directly describe the resonant response of a finite structure, as typically encountered in scattering experiments. Here, we introduce the quasi-normal-mode spectrum as a complementary framework for characterizing the wave properties of finite stealthy hyperuniform materials. We analyze the complex eigenfrequencies of both periodic and stealthy hyperuniform structures over a range of the stealthiness parameter ($\chi$), and investigate how the spatial organization of scatterers is encoded in both frequency and spatial profiles of their quasi-normal modes. We find systematic changes in the quasi-normal modes spectrum as the degree of hyperuniformity is varied, revealing signatures that are not captured solely by the structure factor. In particular, the evolution of the resonant states provides a direct connection between structural correlations and the scattering response of finite systems. Our results establish quasi-normal modes as a real-space and open-system characterization of hyperuniformity and provide a unified framework for comparing discrete heterogeneous materials from the perspective of their scattering and resonant dynamics.

Asymmetric cell division – in which a mother cell divides into two daughter cells of unequal size – is a fundamental problem in biology. It is believed that the asymmetry originates from the prior polarization of the mother cell. Here we show that division asymmetry can occur spontaneously even in unpolarized mother cells. Specifically, curvature-dependent active stresses in the cell cortex can lead to this symmetry breaking without any molecular polarity cue if the mother cell is confined within a restricted space. Either reducing the cell size or tightening mechanical confinement triggers the same spontaneous symmetry-breaking instability, in which the contractile ring slips off the equator to yield daughters of unequal volume. In the presence of a polarity cue, this instability cooperates with the cue to program the division asymmetry. The model prediction is compared with the imaging data of C. elegans embryogenesis, in which successive cell divisions in a confined eggshell lead to smaller and smaller cell sizes. The measured division asymmetry indeed increases as the cells shrink, and is further amplified when the embryo is mechanically compressed, both in agreement with the model prediction.

To improve the agreement between measured and calculated intensities of three-dimensional electron diffraction (3D ED) experiments, a simulation pipeline is needed to assess and quantify the influence of various structural and experimental parameters. We present a computational pipeline, built upon the abTEM Python package, to simulate continuous-rotation 3D electron diffraction data based on either the Bloch wave or the multislice formalism. Multislice calculations in arbitrary orientations are achieved through large supercells and windowing. We investigate the convergence of key simulation parameters and test their consistency, establishing suitable parameters for accurate and efficient simulations. The pipeline's applicability and robustness are demonstrated through case studies on cubic silicon as well as stretched and sheared variants, analyzing the influence of electron kinetic energy, sample thickness, orientation, and symmetry on simulated diffraction intensities. Finally, we investigate a representative selection of seven compounds, including cubic $\mathrm{SrTiO_3}$, monoclinic $\alpha$-glycine $\mathrm{C_2H_5NO_2}$, and triclinic kyanite $\mathrm{Al_2SiO_5}$ to validate the method. This framework for the simulation of 3D electron diffraction data establishes an approach to investigate the dependence of diffracted intensities on experimentally relevant parameters which are difficult to systematically investigate in experiments.

We demonstrate that Wannier-Stark ladders (WSLs) in one-dimensional Su-Schrieffer-Heeger (SSH) chains manifest as antiresonance signatures in the electron transmission. We study the quantum transport in the SSH chain in the presence of a periodic potential profile plus a uniform electric field. By employing the global matrix method with non-trivial matching conditions, we find that these WSL antiresonances correspond to states that are exponentially localized at the potential's incident boundary. These findings provide a robust, unified framework for identifying WSLs across diverse scales, ranging from electronic transport in trans-polyacetylene to classical-wave analogs in phononic crystals and surface water waves.

Sensory adaptation provides a concrete setting in which low-order system identification can fail qualitatively. We show that one fixed higher-order adaptive system composed entirely of real first-order relaxation modes can be reduced to opposite sides of the second-order pole boundary: low-frequency moment matching gives $\rho_{\rm moment}=4.50$, whereas finite-window fitting gives $\rho_{\rm window}=3.31$, and the inferred pole class changes further with sampling protocol. Thus the real-versus-complex classification of a reduced model is not itself reduction invariant. We then use the general two-state spectrum to connect stochastic identifiability to adaptation: for nontrivial coupling and one-state observation, cross diffusion drops out of the scalar spectrum when the hidden state has no self-relaxation. In the adaptive model, this condition is precisely the integral-memory limit that produces exact adaptation, while leaky memory restores spectral sensitivity. For the exact-adaptation model, the Gaussian path-space irreversibility nevertheless depends on the hidden cross-diffusion channel. Hence $\{H,S_x\}$ does not determine the irreversibility rate. Independently, for a specified all-even reduced two-state drift with $\rho<4$, the drift-only lower bound is $\sigma \ge \tau_x^{-1}(4/\rho-1)$. Published E.~coli and C.~elegans responses provide biological examples of these limits. The distinction established here between transfer-function invariants, reduction-dependent properties, and hidden-state quantities provides a concrete framework for evaluating the limitations of low-dimensional models of adaptive biological dynamics.

We investigate the electronic properties of binary tight-binding chains generated by the cut-and-project method for rational slopes $\alpha=p/q$, leading to periodic and inversion symmetric chains with $n=p+q$ sites. The binary structure is encoded in two hopping amplitudes $t_a$ and $t_b$. For fixed $t_a \neq t_b$, the support of the energy spectrum as a function of $p/n$ gives rise to a "Cut-and-Project butterfly". We concentrate on insulators with $M$ filled bands among a total of $n$ bands and vary $t_a/t_b$. Inversion symmetry constrains the electric polarization $P$ to $0$ or $P_q/2$ modulo a polarization quantum $P_q = \gcd(M,n)/n$. A topological transition, between two insulators that differ by their quantized polarization, occurs if and only if $n/\gcd(M,n)$ is odd. When $n/\gcd(M,n)$ is even, the two insulating regimes have a vanishing polarization and no topological transition occurs, despite the gap closing at $t_a=t_b$. When $n$ is even and $M$ odd, we find an adiabatic path between $t_a>t_b$ and $t_a<t_b$ that maintains inversion symmetry and a gap.

We studied orbital-torque generation in Cr(10nm)/Gd($t_{\mathrm{Gd}}$)/Co(3nm)/TaO$_x$ and the inverted stack Co(3nm)/Gd($t_{\mathrm{Gd}}$)/Cr(10nm) with $t_{\mathrm{Gd}}$ from 0 to $5\,\mathrm{nm}$ by combining electrical harmonic Hall measurements with magnetometry. A detailed understanding of the magnetometric data is obtained by cross-sectional chemical composition mapping. The data show temperature-dependent magnetic compensation points, while elemental analysis provides evidence of pronounced intermixing, in particular of Gd and Co layers. From the harmonic Hall dataset we extract the damping-like (DL) and field-like (FL) torque efficiencies normalized to the applied electric field, $\xi_{\mathrm{DL}}^{E}$ and $\xi_{\mathrm{FL}}^{E}$, and interpret their dependence on the Gd interlayer thickness using two different descriptions: (i) a naive-layer model and (ii) an alloy model that accounts for interfacial mixing. Notably, upon reversing the stack order, the FL contribution changes sign, whereas the DL contribution does not change sign within the harmonic Hall measurements.

We investigate the Self-Healing Diffusion Monte Carlo (SHDMC) method using a one-dimensional model with periodic boundary conditions. An inversion symmetry is introduced to mimic the antisymmetry property of fermionic wave functions, with the bosonic and fermionic sectors being modeled by the even and odd eigenstates, respectively. As in realistic fermionic systems, the nodal structure is only partially constrained by symmetry, making this model a non-trivial testbed for nodal optimization algorithms such as SHDMC. We show that the nodal evolution under SHDMC iterations can be cast into a dynamical system exhibiting both attractive and repulsive fixed points. When applying SHDMC to this model in the absence of statistical noise, the fixed-node energy is found to increase during iterations and the node converges to an incorrect value. This occurs for any finite basis, even when the exact node is representable in it; the attractive fixed point approaches the exact node only as the basis becomes complete, while the convergence toward it becomes increasingly slow. We further show that this problem can be largely cured by modifying the nodal update criterion to give more importance to the nodal region. Our results suggest that, in the general case, an efficient nodal optimization may require both an improved nodal update criterion and a localized basis set allowing local distortions of the trial wave function, as is the case for this model.

Optimal transport describes the most efficient way to move mass between two distributions, given a cost matrix for moving mass between each pair of locations. Entropic optimal transport, solved via the Sinkhorn algorithm, is a widely used regularized version of this problem. Its inverse problem asks the opposite question: given an observed transport plan, what cost matrix produced it? This is difficult because the cost is identifiable only up to an additive gauge freedom. Here we show that this freedom can be fixed exactly by a single double-centering operation applied to the observed plan, yielding the true cost matrix in closed form, with no iterative optimization required. When a modest number of true cost entries are known, the same approach lets us jointly estimate the temperature parameter controlling the entropic regularization, together with a diagnostic for the reliability of this estimate. We further show that the method is not specific to the entropic optimal transport, but extends to a broader class of transport models defined by an invertible relation between cost and plan.

We show that a superselction sector describing a single nonabelian anyon violates Haag duality, which is equivalent to the fundamental quantum-information theoretic principle of uniqueness of purifications. We provide a simple physics argument as well as a rigorous proof using sector theory, and instantiate our result concretely in Levin-Wen models. We also show that the associated ground state does not allow for quantum steering despite being a pure state. Finally, we show that this ground state violates approximate Haag duality, disproving the conjecture that all gapped ground states satisfy this condition. Our result implies that there are gapped phases of matter where Haag duality fails at every point in the phase.

We experimentally investigate the dynamics of a spherical intruder driven horizontally at a constant force in a granular medium subjected to a localized surface overload. While intruder motion beneath a free surface exhibits constant acceleration in the quasistatic regime, the presence of a surface load induces a pronounced transient deceleration when the intruder passes below the loaded region. The magnitude of this deceleration increases with the applied overload and saturates at large overloads, while it decreases with intruder depth. Introducing a characteristic timescale and an overload-based Froude number, we show that the deceleration dynamics collapse onto master curves. We further develop a model incorporating stress transmission from the surface, which partially captures the intruder deceleration. In this approach, this deceleration is shown to depend on two parameters: the overload and the area on which this overload is applied. These results provide a framework to quantify how localized surface stresses influence subsurface intruder dynamics, with implications for locomotion, root growth, and underground transport in granular media.

Electron tunneling between sheets of bilayer Bernal graphene twisted at different small angles was studied experimentally and theoretically. The current-voltage characteristics exhibit resonant peaks, steps, and regions of negative differential resistance, the origin of which is explained by the intersections of energy- and momentum-shifted electron dispersions of adjacent layers. A theoretical analysis of tunneling transport demonstrated that the key to understanding this phenomenon lies in the competition between two contributions: between like (conductivity-conductivity or valence-valence) and unlike (conductivity-valence) bands of parallel bilayer graphene sheets. A systematic evolution of the tunneling current patterns with increase of the twist angle is investigated. Polarization of electron wave function across graphene sublayers caused by displacement field within bilayer graphene is shown to strongly affect the tunneling probability, thus enhancing negative differential resistance due to Van Hove singularities at the band edges.