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We establish a rigorous non-perturbative closure framework for the three-dimensional (3D) $ϕ^4$ scalar field theory near criticality, bypassing the long-standing limitations of perturbative Feynman diagrammatic expansions. By slicing the 3D Euclidean space along a spatial axis, the exact dressed theory is mapped onto a matrix operator evolution governed by the infinite-dimensional symplectic Lie algebra $\mathfrak{sp}(\infty)$. We generalize the classical Stroh formalism and Barnett-Lothe integral invariants from anisotropic elasticity to the quantum field Hilbert space. Crucially, we prove that the dressed operator-valued Barnett-Lothe tensors satisfy the algebraic identity $\hat{\mathbf{S}}^2 + \hat{\mathbf{H}}\hat{\mathbf{L}} = -\hat{\mathbf{I}}$ exactly and non-perturbatively, regardless of the coupling strength. By coupling this symplectic invariance with the Källén-Lehmann spectral representation and the Schwinger-Dyson equations, a novel "Symplectic Bootstrap" master spectral integral equation is formulated. The framework exhibits exact dimensional reduction, naturally degenerating to the Onsager exact solution ($η= 1/4$) in 2D and the Gaussian triviality limit ($η= 0$) in 4D. Solving the transcendental bootstrap equation under the strong-coupling conformal fixed point yields the non-perturbative anomalous dimension $η\approx 0.0363$, matching the state-of-the-art conformal bootstrap numerical limits. Finally, a profound holographic duality between the statistical state equations and the post-buckling bifurcation of fluctuating soft matters is discussed.

We construct exact, positive-energy, normalizable wave-packet solutions of the Dirac equation in the axisymmetric potential $V=-\,v_0/ρ$ -- to our knowledge, the first such solutions in any external potential. Remarkably, one family comprises only elementary functions whose longitudinal profiles reproduce the free-Schrödinger Hermite--Gauss wave packets in the nonrelativistic limit. All packets share two striking features: (i) a probability density that is pointwise decoupled from spin orientation -- despite the inherent spin-orbit coupling of the Dirac equation -- and (ii) a complete freezing of their time evolution at the critical coupling $v_0\to\hbar c/2$. We also present a simple scheme that maps solutions of the 2D Helmholtz equation to further exact Dirac wave packets.

We prove a `nonlinear graviton theorem' for higher-spin self-dual gravity. We consider small deformations of the complex structure of the non-projective twistor space that are bounded in a specified region near the origin and investigate the space $M_{HS}$ of holomorphically embedded complex planes $\mathbb{C}^2$ that intersect the origin. We show that this space is an infinite dimensional complex manifold with a canonical projection onto a four-dimensional holomorphic self-dual spacetime $\mathcal{M}$, and discuss the geometry induced on this new higher-spin space. Solutions of higher-spin self-dual gravity are then obtained by choosing an embedding of spacetime $\mathcal{M}$ into higher-spin space $M_{HS}$, with higher-spin symmetries arising from the different choices of embedding. Integrability of the theory is manifested in the form of a Lax pair for the system that we present. We conjecture that chiral higher-spin gravity can similarly be realized by considering deformations that are unconstrained at the origin.

By incorporating leading $c\,$-dependent corrections to the Carroll transformations, we introduce the ``post-Carroll transformations''. We demonstrate that these transformations are consistent with post-Carrollian mechanics \cite{Najafizadeh:2025ksm}; furthermore, they give rise to the so-called ``post-Carroll algebra''. We show that, unlike the Carroll algebra, this new structure allows for a central charge in higher dimensions; we refer to it as the ``Carroll-Bargmann algebra''. To construct conformal extensions, we first build the conformal extension of the post-Carroll algebra and study field theories invariant under this symmetry. We then construct the conformal extension of the Carroll-Bargmann algebra, referred to as the ``Carroll-Schrödinger algebra'', and demonstrate that it precisely matches the symmetry algebra of the higher-dimensional Carroll-Schrödinger theory \cite{Najafizadeh:2024imn}. Finally, we derive the general form of two-point functions in a post-Carrollian CFT, which in $1+1$ dimensions exhibits both electric and magnetic sectors, while in higher dimensions only the magnetic sector survives.

We study the semiclassical limit of SL_2-opers on the four-punctured sphere in Nekrasov-Rosly-Shatashvili Darboux coordinates. Using exact Wentzel-Kramers-Brillouin (WKB) connection formulae, we express the trace coordinates of the corresponding SL_2(C) character variety as finite Laurent sums of Voros exponentials. Tropicalizing these formulae and the NRS relations gives a chamberwise integer affine linear system for the leading logarithms of the NRS coordinates. In chambers where this system is unimodular and the selected cycles form a primitive symplectic pair, the leading asymptotics agree, up to flavor-period shifts, with Seiberg-Witten periods of the N=2 SU(2) theory with N_f=4 fundamental hypermultiplets. We verify this mechanism in a sample chamber and in the weak-coupling degeneration. No global coordinate-independent recovery theorem is claimed; non-unimodular or degenerate chambers are treated as limitations of the chosen NRS chart. In the weak-coupling degeneration, we show that the NRS chart can be chosen compatibly with the plumbing limit so that the resulting chamber is unimodular and non-degenerate away from tropical walls.

A long-standing conjecture claims that Virasoro conformal blocks exponentiate in the semiclassical limit $c \to \infty$ with $h/c$ finite. However, this has been proven only for four-point blocks on the sphere and one-point blocks on the torus. Here we extend the proof to general conformal blocks for higher-point functions and higher-genus backgrounds in arbitrary channels. The statement is to be understood at the level of a formal power series. Our proof builds upon a novel extension of the oscillator method for the computation of conformal blocks to cases where three internal lines meet at a vertex. This extension also gives a new constructive method to compute global conformal blocks in 2d CFTs at general genus.

We establish a new connection between supersymmetric theories and scattering amplitudes. We show that the Coon amplitude coincides with the 3d $\mathcal{N}=2$ half-index of the XYZ model with nontrivial boundary conditions. Our 3d theory, intrinsically defined in the UV, flows to a sigma model in the IR whose partition function is the Veneziano amplitude. Crossing symmetry is realized as a consequence of 3d $\mathcal{N}=2$ mirror symmetry between XYZ and SQED. We use this correspondence to construct a meromorphic modification of the Coon amplitude by promoting the long-standing dressing factor $\mathfrak{q}^{ST}$ responsible for a branch cut to an elliptic completion thereof. This illustrates that one does not have to give up single-valuedness to achieve positivity at the physical poles.

The Ashtekar-Lewandowski (AL) volume operator of loop quantum gravity is central to the Hamiltonian constraint, but its vertex action is usually obtained from dense spectral decompositions of finite recoupling matrices, obstructing numerical analysis on large kinematical Hilbert spaces or high-valence vertices. We formulate a matrix free action of the $SU(2)$ AL vertex volume operator in standard recoupling basis, making use of the Brunnemann-Thiemann expression for the oriented AL volume density $Q_{v}$ whose matrix elements can be generated locally from recoupling theory without forming the full matrix. Based on the Balakrishnan-Stieltjes representation of $(Q_{v}^{2})^{1/4}$ we approximate the volume by shifted-resolvent quadrature (SRQ). The resulting action uses only repeated applications of $Q_{v}$ and shifted positive linear solves, making it compatible with multi-shift Krylov methods. We prove exact preservation of the volume kernel, provide operator-norm and residual error estimates, discuss sector-wise scaling bounds, and validate the method on an embedded $K_{5}$ graph at small spin cutoffs against exact dense local-block operators. Numerical simulations show rapid convergence of vertex expectation values, controlled dependence on bound parameters, and exact preservation of zero-volume modes. We further demonstrate matrix free Monte Carlo estimates at doubled-spin cutoff $2j=250000$ beyond dense materialisation, and show that SRQ can be combined with stochastic Lanczos quadrature to estimate fixed-sector volume spectral measures without dense volume matrices.

Superconducting qubits are artificial atoms whose spectra and interactions can be engineered through appropriate circuit design, a versatility that can be exploited for quantum simulation. We theoretically investigate a linear array of capacitively coupled transmons, effectively described by a Bose-Hubbard Hamiltonian with attractive interaction. We revisit the discrete-soliton nature of the lowest-energy band of the spectrum, and identify spatially localized quantum solitons. The solitonic character of these states is revealed through their time evolution, which displays a quantum interference pattern, or quantum walk, highlighting their composite nature. We discuss protocols for preparing spatially localized quantum solitons that are compatible with current state-of-the-art tunable-transmon circuits. Our results demonstrate that superconducting circuits provide a promising and experimentally accessible platform for the investigation of quantum soliton physics.

Electronic Fabry-Pérot interferometers (FPIs) operating in the fractional quantum Hall regime are a key platform for probing anyonic braiding statistics, yet interpreting their interference signals is complicated by Coulomb charging effects, which are commonly treated as parasitic, static properties governed by the cavity's geometry and electrostatics. Here, using a gate-defined quantum Hall cavity tuned to the Coulomb-dominated regime, we demonstrate that the charging energy is in fact strongly and non-monotonically modulated by the magnetic field, varying by up to 60% over a range of only 100 mT. The effect appears exclusively when the quantum point contacts (QPCs) forming the cavity are weakly pinched off, i.e., in the strong cavity-to-lead coupling regime. By correlating the charging energy modulation with the QPC magneto-conductance, we attribute this behavior to field-dependent changes in local compressibility and electrostatic screening between the cavity and the leads, driven by the formation of incompressible fractional quantum Hall states within the constrictions. This result establishes QPC constrictions of quantum Hall cavities as active electrostatic elements rather than passive boundaries, revealing a dynamic screening mechanism, with direct consequences for the interpretation of interference measurements and the extraction of anyonic statistics.

Vacuum electromagnetic fluctuations have recently emerged as a promising means of controlling collective quantum phases. Although cavity-induced modifications of superconductivity have been widely predicted, experimental studies have so far reported only suppression of superconducting properties. Here, by carefully tuning a terahertz cavity to resonate with key phononic modes in few-layer niobium diselenide (NbSe2), we demonstrate cavity-enhanced superconductivity in few-layer NbSe2 coupled to a complementary split-ring resonator. In trilayer NbSe2, the superconducting transition temperature increases by ~10%, from 3.02 K to 3.41 K, when coupled to a cavity resonant at 2.04 THz. The enhancement exhibits a clear spatial dependence following the cavity field profile and a non-monotonic frequency dependence, with maximal enhancement near 2 THz. These results provide experimental evidence that vacuum electromagnetic fields can enhance superconductivity and establish cavity engineering as a powerful platform for tailoring quantum materials.

The nature of superconductivity in 2H-NbSe2 has generated sustained debate in the recent past. While angle resolved photoemission spectroscopy data have been interpreted as evidence for multiband superconductivity, the data from scanning tunneling microscope experiments relate to strongly anisotropic single-band superconductivity. In the later case, the charge density wave (CDW) order mimics the multigap character. Because the CDW reconstructs the Fermi surface and modifies the superconducting gap distribution, disentangling intrinsic multiband pairing from CDW-related effects is challenging. To address this issue, we investigate single-crystalline 2H-NbSeS, a mixed-chalcogen analogue of 2H-NbSe2 in which random Se/S substitution suppresses long-range CDW order while preserving the layered crystal structure P63/mmc. The material becomes superconducting below 6.0 K with moderate magnetic anisotropy. The upper critical field exhibits a pronounced upward curvature that cannot be described within a single-band framework but is well captured by a dirty-limit two-band model with a large diffusivity ratio. This indicates strong band-dependent scattering. The in-plane upper critical field exceeds the weak-coupling Pauli limit. Measurements of the lower critical field, superfluid density, and electronic specific heat are consistent with an interpretation of a fully gapped superconducting state with two nodeless gaps of different magnitudes.

The structure of a porous material, and in particular its spatial variability, is known to control the intrinsic permeability of the system. We investigate how dead-end pores influence the intrinsic permeability of a porous medium beyond their contribution to total pore volume. Dead-end pores are ubiquitous in porous media, yet they are often treated as hydraulically inactive regions whose influence is assumed to be negligible or absorbed into effective-porosity descriptions. We perform pore-scale flow simulations across different dead-end pore structures, including heterogeneous arrangements, controlled granular assemblies, and a minimal single-channel model to study their impact on the system macroscopic permeability. This strategy allows us to isolate the effects of dead-end pore density, depth, and orientation while preserving the transmitting network. We find that dead-end pores can influence intrinsic permeability: increasing the density of dead-end pores along percolating flow paths enhances permeability, whereas pore depth and junction orientation have negligible effects. The observed permeability enhancement originates from localized hydrodynamic interactions at junctions between transmitting and dead-end pores. Based on these results, we propose an effective formulation that relates the density and spatial organization of dead-end pores relative to the transmitting network to macroscopic permeability. Our findings show that dead-end pore architecture provides an additional geometric control on intrinsic permeability beyond porosity and pore-size statistics.

Sphere packings in circular cylinders have attracted substantial research interest, among which the discovery of chiral helical structures is the most iconic. However, recent experimental results on zebrafish do not match the known packing structures in circular cylinders. To account for the inherent imperfections of biological tubes, we take elliptic cylinders as the canonical deformation of circular cylinders and investigate the densest packings of hard spheres in them using simulation, theory, and experiments. Starting from the chiral structures in circular cylinders, we demonstrate that even a weak cross-sectional deformation can trigger entirely new phases, including ones that either eliminate global chirality or significantly complicate the chiral structures. This reveals the significant effect of cylindrical anisotropy. The new helical phases under anisotropic confinement remain chiral and develop hierarchical periodic structures, which are difficult to obtain by simulations but are predicted by our newly developed theory for helical phases in elliptic cylinders. The theory also predicts double oscillated-chain phases without chirality, which perfectly match the simulations. Our work offers fresh insights into understanding packings in anisotropic cylinders, which will help researchers to design new materials and to understand many living systems.

Establishing a versatile, fast and reliable magnetic memory technology is a giant bottleneck for cryogenic computing since present-day room-temperature solutions either cease to work or consume too much power. The long-term goal of superconducting spintronics has been to overcome this bottleneck by generating magnetic memories with equal-spin triplet supercurrent driven through them to control their magnetization direction. This path has been hampered by the short spin relaxation length and strong anisotropy in ferromagnets. Here we show how the supercurrent driven generation of spin accumulation in a superconductor/magnetic insulator bilayer, together with Gilbert damping of magnetization lead to a motion of magnetic domain walls. This manifests as a local voltage across the wall, which allows its position to be identified. Associated with this voltage and the current, there is Joule power which is dissipated via the Gilbert damping. The power required to maintain domain wall motion is orders of magnitude smaller than in the normal state, where most of the power is wasted in producing the current.

Red blood cells (RBCs) are essential for oxygen transport, and their remarkable ability to undergo significant deformations during flow is a crucial feature for their physiological function. At intermediate shear rates typical of the microcirculation, RBCs can adopt complex, multi-lobed shapes, signifying a dynamic instability. Here we adopt a perturbative theoretical framework of a quasi-spherical RBC under external shear flow to study such shape instabilities. To better capture RBC maturation and enucleation, we first extend the framework to explicitly account for different excess areas between the stress-free and current membrane shapes. We revisit the reduced equations of motion obtained for an ellipsoidally-shaped RBC, and demonstrate the effect of different excess areas and initial orientation on the dynamical trajectories. Then, we introduce additional spatial modes and show that an emerging instability critically depends on the RBC's shear and bending moduli, the internal to external viscosity ratio, and the excess area, mainly through the RBC's membrane tension. We also study the instability-induced saturation of the membrane tension, and the resulting excess area redistribution at long times. The theoretical framework and the emerging picture of the different instabilities provide insights into the emergence of stomatocyte and trilobe shapes exhibited by RBCs under external flow.

Large-deviation tails of critical probability distributions provide a sensitive probe of universality beyond standard finite-size scaling. We study these tails for critical percolation and Fortuin--Kasteleyn Ising models on two-dimensional lattices, three-dimensional lattices, and complete graphs. We consider two rescaled order parameters: the magnetization-like variable $x_m=|M|/\langle |M|\rangle$, including a signed cluster-mass analogue for percolation, and the largest-cluster variable $x_C=C_1/\langle C_1\rangle$. For $x_m$, we test the expected stretched-exponential large-deviation tail and show that the same form applies to the percolation analogue. For $x_C$, guided by the exact complete-graph result and scaling arguments, we propose universal scaling forms for both tails of the cumulative distribution and test them by extensive Monte Carlo simulations. In the complete-graph FK-Ising model, the left tail is governed by rare configurations with percolation-like scaling rather than by the typical Ising scaling. Our results show that the tails of order-parameter distributions reveal universal features of critical fluctuations that are not captured by averaged observables alone.

Quantum transport in mesoscopic systems is conventionally formulated within the Landauer--Büttiker scattering framework, where steady-state currents emerge from the transmission of plane waves representing propagating carriers. While highly successful, this description obscures the explicit time-domain dynamics of individual fermionic excitations and their role in establishing macroscopic transport. Here, we present an exact and self-contained time-domain construction of Landauer transport based on a discrete basis of orthogonal fermionic wave packets. Starting from a second-quantized formulation, we define packet creation operators via a continuous Fourier transform over a finite transport energy window. By encoding the Pauli exclusion principle, which enforces a fundamental temporal spacing $Δt = h/eV$, the current is reproduced in terms of orthogonal wave packets that are used for the rigorous construction of the many-body fermionic state. In this representation, a noiseless current emerges as a deterministic sequence of charge-carrying events, yielding the Landauer conductance $G_0 = e^2/h$ without invoking momentum-space kinematics. We further demonstrate that this construction remains exact for arbitrary energy dispersion. Additionally, the underlying Fock space decomposition into finite disjoint energy sub-bands renders the numerical approach highly scalable for high performance computing platforms. Our results establish a direct and rigorous bridge between the continuous scattering description of quantum transport and a discrete, time-resolved picture based on fermionic wave packets.

Anyons are quasiparticles with quantum statistics interpolating between those of bosons and fermions. Two distinct manifestations of anyonic behaviour have been theoretically established: fractional exchange statistics where particle exchange can produce any phase, and generalized exclusion statistics which extends the Pauli exclusion principle. While anyons exhibiting fractional exchange statistics have been observed in diverse platforms, experimental realizations of generalized exclusion statistics and direct measurements of its thermodynamic signatures have remained elusive. Here, we realize an anyonic thermodynamic ensemble obeying generalized exclusion statistics and detect its anyonic thermodynamics in a one-dimensional strongly interacting quantum gas. To achieve this, we exploit the bijective mapping between dynamical and statistical interactions in one dimension. By tuning interaction strength and temperature over a wide range, we measure the equation of state and identify clear departures from Bose-Einstein and Fermi-Dirac statistics. These deviations are quantitatively captured by generalized exclusion statistics, providing direct evidence for the generalized Pauli principle. Independent probes of other thermodynamic quantities including pressure and the Tan contact further validate this framework. Our results establish a versatile platform for engineering anyonic exclusion statistics and open the door to thermodynamic applications of anyons in quantum technologies.

Electronic correlations in graphene are generally considered weak due to the large bandwidth of its $π$ electrons. Here we show that tensile expansion of the honeycomb lattice provides a direct route to enhancing correlation effects. Using variational and diffusion quantum Monte Carlo, we compare a conventional Jastrow-Slater determinant wave function with a resonating-valence-bond (RVB) Jastrow-antisymmetrized geminal product ansatz for a series of stretched graphene lattices. We find that the energy gain of the RVB state relative to the single-determinant description increases with bond expansion up to a critical strain $δ_{\mathrm{cr}}$, and decreases beyond it, revealing a nonmonotonic evolution of electronic correlations. The crossover is found to occur in the range $15\% < δ_{\mathrm{cr}} < 20\%$, in agreement with mechanical stability limits. This behavior indicates a transition from a weakly correlated Dirac semimetal to a regime with enhanced non-dynamic correlation and short-range singlet pairing. Our results provide direct many-body evidence that lattice expansion drives graphene into a regime where RVB-like correlations become energetically favorable, offering a simple route to tuning correlation effects in Dirac materials.

We present an analytical investigation of the extrinsic contributions to the anomalous Hall conductivity in the context of the half-quantized Hall effect observed in disordered parity anomalous semimetal emerged from semi-magnetic topological insulator thin films. The gapless Dirac cone surface state, which embodies the quintessence of the half-quantized Hall effect, exhibits remarkable robustness against disorder scattering. Two primary extrinsic mechanisms, the side-jump and skew-scattering, are deemed irrelevant and make no contributions. These results establish the parity anomalous semimetal as a disorder-resilient quantum phase, thereby providing insights into Dirac fermion physics.

The coexistence of superconductivity and finite electric fields may enable access to intriguing forms of electronic states. We demonstrate the emergence of an intermediate state in which electric fields penetrate the system while superconductivity still persists. Our measurements reveal a nonclassical regime characterized by the simultaneous presence of supercurrent and dissipative charge transport. This state, realized in a pristine unpatterned three-dimensional system, arises from electric-field-driven order parameter fluctuations. It provides a platform to explore dissipative states of charged quantum fluids far from equilibrium.

Classical nucleation theory (CNT) describes the formation of a stable phase from a metastable one. In equilibrium systems, it quantifies the free-energy competition between a favorable bulk gain and an unfavorable interfacial cost. For systems without detailed balance, the corresponding nonequilibrium nucleation theory (NNT) was so far developed only for cases with a conserved order parameter, such as active fluid-fluid phase separation. Here we construct the NNT for systems with a (single, scalar) nonconserved order parameter. Unlike in the conserved case, the nucleation barrier controlling (noise-driven) droplet growth is profoundly altered by deviations in the interfacial density profile from the one arising during (deterministic) droplet relaxation. The barrier can nonetheless be analysed by carefully defining the reaction coordinate (droplet radius) to project out those deviations. We give explicit NNT predictions for models drawn from population dynamics and active matter, finding excellent agreement with numerical studies.

We investigate equilibrium and non-equilibrium thermodynamics of one-dimensional photonic diamond lattices with Kerr nonlinearity. The equilibrium phase diagram is obtained as a function of the synthetic magnetic flux acting on each plaquette. In the linear regime, the magnetic flux can induce Aharonov-Bohm caging, flattening all Bloch bands and suppressing particle and energy currents. In this caging regime, non-vanishing currents are enabled by nonlinearity. By imposing stationary temperature- and chemical potential- imbalances at the system boundaries, we show that at weak nonlinearity fine tuning the flux at the Aharonov-Bohm caging transforms the system from a conductor to an insulator. For intermediate nonlinear strength, the system remains conducting for all magnetic fluxes; however, the caging condition significantly enhances the Seebeck coefficient and thermoelectric figure of merit, improving the thermoelectric features of the system. Our results give evidence of a novel route towards optimization of coupled transport devices, based on the control of linear versus nonlinear conduction channels via a synthetic magnetic flux.

The modern theory of orbital magnetization successfully describes the response of Bloch electrons to magnetic fields in fully periodic crystals, but it does not directly address the distinct regime of an in-plane field in multilayer systems with layer hybridization. Coherent interlayer tunneling allows electrons to form circulating current loops, producing an in-plane orbital response that is absent in a strictly two-dimensional limit and qualitatively different from the conventional three-dimensional one. Here we develop a theory of in-plane orbital magnetization for this {\it transdimensional} regime, where the layer thickness is comparable to the vertical mean free path. Starting from the current-loop picture, we construct the in-plane orbital angular momentum operator and derive exact expressions for the orbital magnetic moment and the in-plane orbital magnetic susceptibility. As an application, we predict a gate-tunable in-plane orbital magnetoelectric effect in layered materials. Our framework establishes a general foundation for in-plane orbital responses and suggests new opportunities for orbitronics in layer-hybridized quantum materials.

We propose a physical realization of the unstructured database search that works via classical, dissipative model of spherical spins. The database is implemented via spin-spin couplings, where the selected coupling refers to a larger ferromagnetic interaction between two selected spins. The low-temperature equilibrium of this model leads to magnetization strongly concentrated on the selected spins, which means that the search is complete. The search time refers to the relaxation time to equilibrium from a homogeneous initial state, and is described via Langevin equations. This time scales as ${\cal O}(M^a)$ with $a<1/2$, where $M$ is the database volume. This is faster than Grover's search, showing how a dissipative, classical analog computer can overcome the quantum unitary computer.

Out-of-time-order correlators (OTOCs) provide a fundamental metric for quantum chaos, but capturing the fine structure of information scrambling requires exploring their higher-order generalizations. Here, we systematically investigate the sequence of higher-order OTOCs in a Luttinger liquid and its lattice realization, the XXZ Heisenberg chain. Using bosonization and numerics, we extract the full temporal dynamics of the first three OTOCs, revealing that they rapidly erase memory of the initial state, and quickly saturate to their steady state values. Strikingly, we show that calculating the late time saturation values for the entire sequence of higher-order OTOCs maps exactly onto determining the partition function of a non-Hermitian Harper model. Through this mapping, we demonstrate that for moderately strong interactions, the steady-state OTOCs become parametrically small up to the seventh order, mimicking higher $k$-design. Our results reveal that Luttinger liquids exhibit an unexpectedly profound degree of apparent scrambling when viewed through the lens of higher-order OTOCs.

We study the $I^G(J^{PC})=0^+(1^{++})$ $K\bar Kπ$ system in an infinite-volume three-body unitary framework, focusing on the pole content of the region of the $f_1(1285)$ and $f_1(1420)$ resonances. The coupled $πa_0$-$K\bar K^*$ amplitude is constructed in the spectator-isobar representation, where the one-particle-exchange interaction required by three-body unitarity automatically incorporates the triangle-singularity mechanism. The short-range three-body interaction is constrained by fitting the $0^+(1^{++})$ component of the BESIII $K^0_SK^0_Sπ^0$ invariant-mass distribution in the $J/ψ\toγ(K^0_SK^0_Sπ^0)$ decay. Analytically continuing the fitted amplitude to the relevant unphysical Riemann sheets, we find two robust poles: \begin{align} \sqrt{s_{f_1(1285)}}&= \left(1277\pm2\pm1\right) -i\left(12\pm1\pm0\right)\text{MeV}\,,\notag\\ \sqrt{s_{f_1(1420)}}&= \left(1435\pm2\pm7\right) -i\left(40\pm2\pm1\right)\text{MeV}\,.\notag \end{align} The pole trajectories indicate that the $f_1(1285)$ originates from dressing a bare state introduced in the potential. In contrast, the $f_1(1420)$ is predominantly dynamically generated, and a single-channel analysis traces it to an $S$-wave $K\bar K^*$ quasi-bound state mixed with the nearby bare state, supporting its hadronic-molecule interpretation. We also find an additional pole deeper in the complex plane in the best-fit amplitude on the same Riemann sheet as the $f_1(1285)$. This additional pole is generated by the $P$-wave $πa_0$ contact interaction alone. It has a sizable cutoff and two-body-input dependence, and leaves little visible imprint on the physical lineshape. Finally, we provide a detailed and pedagogical appendix on how three-body cuts affect the solution of the integral equation.

Advances in novel materials science enable structures to function as intelligent machines by embedding memory and learning capabilities directly into materials. Our work introduces a physical adaptive material motor unit neural network,leveraging a new generation of controllable actuators composed of wood- and carbon black-based composites, sensitive to temperature and relative humidity. These material actuators are assembled into a motor unit-like structure inspired by muscle contraction trigger, forming an intelligent machine capable of dynamic shading control that can be used, for example, in buildings. The machine is governed by a neural network trained on over 350 experimental data points collected under diverse environmental conditions. By establishing a new data-aware backpropagation training, we show that the machine predicts shading responses and learns to predict appropriate behaviour incrementally as the database expands. We also demonstrate the ability of the machine to optimise configurations to achieve similar shading outputs under two distinct conditions.

We show that the broad X-ray photoelectron lines of silicon oxide on silicon arise from a continuous statistical distribution of core-level binding energies. Statistical simulations spanning compositions from Si to SiO$_2$ reproduce the full extent of this broadening, reaching 5 eV for SiO$_{1.0}$ , in quantitative agreement with 0.23 nm layer-resolved spectra reconstructed from Ar$^+$ sputtering data. This continuous distribution blurs distinct spectral fingerprints of local structural motifs, thereby challenging conventional chemical state assignment in oxide X-ray photoelectron spectra.