We report the ground-state entropy of a two-dimensional Ising model on the Shastry-Sutherland lattice. We also study a generalization of this model, where a constraint on the zero-temperature-allowed configurations is removed continuously.

A higher-order interaction is irreducible when the vector field of one unit depends jointly on two or more other units, in a way that no sum of pairwise terms reproduces. Inferring such couplings from time series of coupled oscillators faces two separate obstructions. The first is identifiability. We measure it with an order-resolved indicator, the smallest singular value of the three-body block of the design matrix after projection onto the complement of all other blocks. We prove that this indicator vanishes on every phase-locked trajectory, that an intervention restores it for almost every system, and that a small kick restores it only in proportion to the square of its amplitude. With ensembles of independently prepared states, every irreducible coupling of a four-oscillator network is detected at phase noise up to 0.03, whereas single passive trajectories detect about half of them. In mean-field networks of up to 50 units the number of prepared states needed grows in proportion to the number of three-body coefficients per unit, each preparation resolving about seven of them. The second obstruction is attribution. Phase reduction of pairwise Stuart-Landau networks generates effective three-body terms, whose coefficients we derive and recover quantitatively with the same ensemble design. A short-time intervention separates physical from effective three-body terms: The nonadditive response to paired kicks grows linearly with the response time for an irreducible coupling, and quadratically when the three-body term is mediated by a hidden node or by eliminated amplitudes.

Single-particle finite-size errors remain a central obstacle in quantum Monte Carlo simulations of periodic systems, conventionally reduced via twist averaging. Here, we introduce good-$\mathrm{\Gamma }$ (GG) particle numbers as system sizes $N$ at which the $\mathrm{\Gamma }$-point Hartree-Fock energy of the high-density two-dimensional uniform electron gas (2D UEG) lies anomalously close to its thermodynamic-limit (TL) value. All results in this work concern the 2D UEG in its high-density Fermi-liquid regime, $r_s=1–4$. We systematically investigate the kinetic- and exchange-energy errors, $\mathrm{\Delta }\text{KE}\left(N\right)$ and $\mathrm{\Delta }\text{EX}\left(N\right)$, that underlie this one-body finite-size-error cancellation across four densities and both spin polarizations. We then compare diffusion Monte Carlo energies extrapolated to the TL from GG-$N$ sequences against twist-averaged extrapolations at the same densities and polarizations, finding agreement to within a fraction of a millihartree in every case, independent of whether a $1/N$ or an $N^{-5/4}$ extrapolation form is used.

We theoretically investigate the shape dependence and microscopic mechanism of the magnetoelectric (ME) effect, including both nonmagnetic (Edelstein-type) and magnetic origins, in a V-shaped one-dimensional chain model. Numerical calculations based on the Kubo formula reveal that the nonmagnetic-driven ME response is maximized at an apex angle of $\theta \approx 0.6\pi$. To clarify its origin, we derive a low-energy effective Hamiltonian in the $s$-orbital subspace and demonstrate that the polarity induced by the V-shaped geometry manifests as an effective spin-orbit interaction. An analytical derivation of the Green’s function shows that the geometric effect can be described as a $T$-matrix contribution associated with local symmetry breaking. This scattering-theoretical representation enables us to identify the contributions of local geometric symmetry breaking to the ME response. Using a multipole-basis representation, we identify symmetry-based selection rules for the ME tensor and show that the coupling between the effective spin-orbit interaction and the orbital angular momentum generated across the apex plays an essential role. The resulting angular dependence, $sin\theta sin\theta /2$, peaks at $\theta =2{tan}^{-1}\sqrt{2}\approx 0.608\pi$, in good agreement with the numerical results. We also analyze a ferromagnetic V-shaped model including the Zeeman interaction and show that the magnetic-driven ME response originates from the spin magnetization induced by the coupling between the electric-field-driven charge-potential gradient and the Zeeman term. These results reveal distinct ME mechanisms depending on the presence or absence of time-reversal symmetry and clarify the microscopic origin of shape-dependent ME responses in V-shaped chains.

Understanding how the physical properties of a fluid influence bacterial behavior is essential for explaining how microorganisms interact with their environment and with animal hosts. Here, we examine how changes in fluid viscosity and rheological properties affect the locomotion of the marine bacterium Vibrio fischeri and its ability to produce luminescence through cell-cell communication. We track the three-dimensional motion of single cells in well-defined fluids with different physical properties and measure the luminescence emitted by cell populations. We find that fluids with higher viscosity cause V. fischeri to spend more time in a slower, turning-focused swimming mode, which reduces how effectively cells spread out and encounter the chemical signals required to activate luminescence. As a result, luminescence first increases and then decreases in Newtonian fluids, but decreases monotonically in fluids that exhibit non-Newtonian rheological behavior. Computer simulations based on our measurements confirm that the ability of cells to explore their surroundings plays a central role in determining when and how strongly they communicate. These findings reveal a direct link between the physical environment, bacterial movement, and collective behavior, and offer insight into how microorganisms adapt to complex fluid habitats, including those found inside animal hosts.

The interplay of chirality, self-propulsion, and confinement generates pronounced nonequilibrium fluctuations, with higher-order moments encoding the shape of the position distribution. We present an exact analytical framework, based on the Laplace transform of the Fokker-Planck equation, for the transient dynamics of a chiral active Brownian particle in a harmonic trap in two and three dimensions. Closed-form expressions for time-dependent moments up to fourth order allow a full characterization of the excess kurtosis across transient and steady-state regimes. In two dimensions, the excess kurtosis exhibits damped oscillations with multiple reentrant crossovers, evolving from negative values, indicative of off-centered ringlike distributions, to small positive values characteristic of near-Gaussian distributions with a weak tail enhancement; increasing trap stiffness progressively suppresses this oscillatory response. In three dimensions, the excess kurtosis of a torque-driven active Brownian particle stays negative, reflecting robust non-Gaussian fluctuations with half-ring-like to bandlike position distributions in the plane defined by the torque axis. These results reveal how chirality, propulsion, confinement, and dimensionality jointly shape transient dynamics and provide experimentally accessible signatures of confined chiral active motion.

As quantum computing scales up, circuits relying on sequential two-qubit gates face severe challenges from excessive depth and decoherence. In trapped-ion systems, global entangling gates offer a highly parallel alternative but are hindered by complex numerical optimization. We propose an efficient numerical framework for piecewise-constant amplitude-modulated global gates. Based on the Mølmer-Sørensen protocol, we utilize null-space projection for linear constraints of spin-motion coupling and tangent-space gradient descent to minimize laser power, while achieving high-order robustness against frequency drifts. At the application level, we identify a structural correspondence between hardware-native global interactions and Pauli strings in Hamiltonian simulation and propose an efficient compilation scheme. By reducing common physical models to fundamental $XX$ interactions and formulating interaction graph partitioning as a Set Cover problem, we leverage global gates to significantly optimize the compilation process. Explicit pulse-level benchmarks further show that, for the tested weighted interaction graphs, the reduction in entangling-gate count can translate into a substantial reduction in total entangling duration. These results demonstrate that integrating hardware-native operations with tailored compilation strategies can substantially reduce circuit overhead, providing a practical roadmap for the codesign of near-term quantum simulators.

The local metal-$\pi$ bond is the microscopic unit from which metal-organic quantum materials are built. We benchmark this bond with both density-functional theory (DFT) and fixed-node diffusion quantum Monte Carlo (DMC), using Slater-Jastrow (SJ) and Slater-Jastrow-backflow (SJB) trial wave functions, to compute binding-energy curves for the first-row metallocenes $M{\left({\mathrm{C}}_5{\mathrm{H}}_5\right)}_2$ with $M=$ Ti, V, Fe, and Co as the metal-carbon distance $d$ is varied. Both DFT and DMC exhibit a distance-controlled crossover in which Fe and Co are favored under compression, while V and Ti form deeper wells near equilibrium and remain more strongly bound at larger separation. Similar $V>\mathrm{Ti}>\mathrm{Fe}>\mathrm{Co}$ ordering at the binding minima persists from DFT through SJ and SJB DMC. DFT-PBE (Perdew-Burke-Ernzerhof), however, overbinds all four metallocenes relative to the correlated DMC benchmark by a large amount that is close to uniform across the series but grows mildly from early to late transition metals showing that semilocal mean-field DFT captures the qualitative topology of the crossover but is quantitatively inaccurate. $\mathrm{DFT}+U$ with standard literature $U$ values does not reliably correct this overbinding and can substantially reorder the binding-strength ranking across the series, showing that $U$ must be determined self-consistently for this bonding environment rather than adopted from unrelated chemistry.

We investigate multiple-$Q$ magnetic states in centrosymmetric itinerant magnets, focusing on the competition between two inequivalent groups of ordering wave vectors on a triangular lattice. Using an effective spin model with bilinear and biquadratic interactions, we systematically study the effects of momentum-space frustration, the biquadratic interaction, and an external magnetic field by simulated annealing and classical Monte Carlo simulations. For weak momentum-space frustration, the system stabilizes conventional triple-$Q$ skyrmion crystals with skyrmion numbers of one and two. In contrast, strong momentum-space frustration destabilizes these topological states and instead stabilizes mixed multiple-$Q$ states composed of inequivalent ordering-wave-vector sectors, including noncoplanar but topologically trivial triple-$Q$ and quadruple-$Q$ states. We further show that increasing the biquadratic interaction promotes higher-order multiple-$Q$ superpositions and leads to the emergence of unconventional sextuple-$Q$ states. Most notably, near zero magnetic field, the competition between the two symmetry-inequivalent wave-vector sectors stabilizes an isotropic sextuple-$Q$ state with finite uniform scalar spin chirality, in sharp contrast to the chirality-compensated sextuple-$Q$ state formed from a single symmetry-related wave-vector star. Our results demonstrate that the interplay between momentum-space frustration and biquadratic interactions provides a route toward exotic higher-order multiple-$Q$ states beyond conventional skyrmion crystals in centrosymmetric frustrated magnets.

We evaluate the electrostatic self-energy of a uniformly charged regular polygon, treated as a planar charge distribution embedded in three-dimensional space and interacting through the Coulomb potential. By exploiting the piecewise-linear nature of the boundary, the four-dimensional Coulomb integral can be reduced exactly to a finite sum of elementary sector contributions that is valid for any number of sides. This construction leads to closed-form expressions for the uniformly charged triangle, square, pentagon, and hexagon. The pentagon result, although involving a quartic number field, is remarkably compact. As the number of sides increases, the energy decreases monotonically toward the corresponding value for a uniformly charged disk. A boundary-perturbation analysis gives the leading relative correction, which decreases as the inverse square of the number of sides. The second variation of the energy produces a nonanalytic correction proportional to the inverse fourth power of the number of sides multiplied by its logarithm. This term provides a direct signature of the polygonal corners. The arithmetic structure of the exact results also explains why compact closed forms cease to be available beyond the uniformly charged hexagon. All results are validated by high-precision numerical calculations and provide useful benchmarks for studies of confined two-dimensional Coulomb systems.

Finite-temperature topological diagnostics in quasiperiodic systems are subtle because quasiperiodicity removes the Bloch momentum torus on which mixed-state band indices are usually formulated. We study a quasiperiodic Qi-Wu-Zhang Chern insulator on finite Fibonacci approximants and use twisted boundary phases as an operational two-torus. A gap scan over $L=21,34,55$ shows that the fixed-boundary spectral gap can remain finite while extended low-gap regions appear elsewhere on the twist torus. Projected-Uhlmann diagnostics reveal a sharper finite-size result: The stability of the projected winding is not determined by the scalar minimum twist gap alone. A high-resolution $L=34$, $25\times 41$ audit gives operational stability scales $5\times {10}^{-4}$, ${10}^{-2}$, and $3\times {10}^{-2}$ for three cases whose minimum twist gaps are all of order ${10}^{-3}$. The same ranking is obtained with projection bases on the ${\theta }_x=0$ and exact ${\theta }_x=\pi$ slices. Direct phase-curve diagnostics show that collapse is associated with the loss or singularization of a $2\pi$ projected-Uhlmann phase winding, whereas stable cases preserve the winding despite small spectral gaps. Within the finite approximants studied here, these results identify phason-resolved boundary-phase geometry and projected-holonomy sensitivity, rather than the fixed-boundary gap or scalar minimum gap alone, as the mechanism controlling this finite-size projected diagnostic.

Spontaneous pattern formation at unstable fluid-fluid interfaces is a popular feature of nonequilibrium systems, often arising from the interplay between interfacial tension and hydrodynamic instabilities. One of the most prominent examples is viscous fingering in quasi-two-dimensional Hele-Shaw geometries, where the displacement of a more viscous fluid by a less viscous one produces highly branched, dendritic morphologies. In this work, we report the formation of nearly dendritic patterns in Langmuir Reverse Schaefer ($\mathcal{L}$-RSh) films of the nematic liquid crystal $N$-(4-methoxybenzylidene)-4-butylaniline (MBBA) upon incubation with silver nanocolloids (AgNcs) of average diameter $\sim 30$ nm, whereas linear stripelike structures are observed for larger nanoparticles ($\sim 64$ nm) on the same $\mathcal{L}$-RSh film of MBBA molecules. The origin of this size-dependent morphological transition is interpreted in terms of topological defects generated due to the incorporation of metal nanoparticles within the continuum $\mathcal{L}$-RSh liquid crystal matrix. A comprehensive statistical characterization of the patterned substrate has been carried out through parameters such as lateral correlation length (ξ), fractal dimension ($D$), Hurst exponent (β), and interface width (ω). Further insights into the complexity of the patterns reveal their multifractal nature, evaluated using two-dimensional multifractal detrended fluctuation analysis. To the best of our knowledge, this study appears to be the first report where thorough investigations on the surface properties of the as-prepared patterned substrate have been discussed in detail. Finally, the patterned substrate demonstrates the good performance as surface-enhanced Raman scattering platforms, enabling detection of rhodamine 6G and 1,10-phenanthroline molecules at extremely low concentrations.

For classical field theories with probabilistic initial conditions, the classical field observables are an idealization. Their arbitrarily precise values poorly reflect the characteristic uncertainty in the presence of substantial fluctuations. We propose to employ observables based on fluctuating fields. In terms of these “statistical observables,” the probabilistic classical field theory becomes a quantum field theory. Noncommuting operators are associated with observables. The quantum rules follow from the laws for classical probabilities. The “quantum” is part of the “classical.” A regularized functional integral guarantees the unitarity of the quantum field theory. We discuss in detail the classical relativistic Klein-Gordon equation with interactions.

Physics-informed neural networks and neural quantum states have consolidated a new paradigm to analyze and discover physical phenomena through constrained neural parametrizations. In this context, we investigate whether the semiclassical structure of the eigenfunctions of a quantum chaotic system can be unveiled through unsupervised learning. To this end, we train a “quantum dictionary,” formulated as an overcomplete autoencoder, that sparsely represents the eigenstates of the system, using as an illustration the quantum baker map. The only explicit physical information imposed on the dictionary atoms is their localization in phase space, without providing any kind of information about the periodic orbits of the corresponding classical system. The model achieves high fidelity in reconstructing held-out validation eigenstates not used in the gradient optimization of the dictionary. By comparing the learned atoms with an independently constructed “semiclassical dictionary,” we find that many of them develop scarlike Husimi-density concentrations around short periodic orbits. This result is interesting in two ways: Phase-space localization, combined with sparse reconstruction and dictionary diversity, can recover nontrivial semiclassical organization from spectral data and at the same time periodic orbits confirm their fundamental role in the structure of eigenfunctions of quantum systems with chaotic classical dynamics. More generally, our proposed architecture opens a route to learning representations whose atoms optimize other chosen physical properties.

IceCube observes a break near 30 TeV in the diffuse astrophysical neutrino spectrum. We interpret it as the photomeson ($p\gamma$) threshold. Accelerated protons interact with the soft x rays of accreting black holes through the $\mathrm{\Delta }\left(1232\right)$ resonance. One kinematic relation sets the break energy from the target field’s lowest photon energy, the seed scale ${\varepsilon }_0$. The measured break fixes ${\varepsilon }_0\simeq 0.13\mathrm{keV}$ and supplies the low-energy suppression no sum of falling power laws can produce. Building on the $\mathrm{\Delta }\left(1232\right)$ identification of Khatee Zathul, Fang, Halzen, and Hooper and the single-source-class photo-pion fit of Winter, Fiorillo, and Buson, we give closed-form relations that invert the four broken-power-law fit parameters to the source physics with no remaining freedom, namely, ${\gamma }_2=s$ and ${\gamma }_1=s-({\alpha }_x-1)$ ($s, {\alpha }_x$ the proton and target photon indices), and $E_{\mathrm{br}}\propto {\left[(1+\overline{z}){\varepsilon }_0\right]}^{-1}$. The break width then measures the population’s uniformity. The total smearing is bounded to ${\sigma }_s\le 0.235\mathrm{dex}$ (68% confidence level), no broader than redshift alone must make it, and the seed scale is the same across the sources to within a factor $\lesssim 1.5$, a constraint mean-spectrum fits do not provide. The model also predicts that below-break neutrinos come on average from higher redshifts than those above. The threshold also fixes the flavor and neutrino-antineutrino composition, including the energy-dependent ${\overline{\nu }}_e$ fraction and the Glashow-resonance discriminator computed in detail by Winter et al., matching current flavor data. Inverted source by source, the relation gives each resolved IceCube source its target photon scale, from the keV coronae of NGC 1068 and PKS $1424+240$ to the $\sim 20\mathrm{eV}$ jet of TXS $0506+056$. That two-decade spread means they cannot supply the homogeneous break. It requires a separate, fainter population. KM3-230213A points to a warm-dust target, ${\varepsilon }_0\simeq 0.02\mathrm{eV}$, unless cosmogenic.

We analyze a class of one-dimensional quantum systems characterized by a position-dependent kinetic term arising as the continuum limit of an inhomogeneous tight-binding model with spatially varying hopping amplitudes. In this limit, the Schrödinger equation takes the so-called BenDaniel-Duke form with an effective mass, scaling as $m_{\mathrm{eff}}\left(x\right)=m_{\mathrm{eff}}{\left|x\right|}^{\alpha }$, with $\alpha >0$, leading to a framework we term “sluggish quantum mechanics,” where particle motion is progressively suppressed at larger distances. For the case with no external confinement, we obtain the eigenfunctions and the quantum propagator exactly. In the presence of a confining potential $V_{\mathrm{ext}}\left(x\right)=\frac{1}{2}{m}_{\mathrm{eff}}\left(x\right){\omega }^2{x}^2=\frac{1}{2}{m}_{\mathrm{eff}}{\omega }^2{\left|x\right|}^{\alpha +2}$, we show that the model remains exactly solvable and obtain the spectral properties and the propagator analytically. We then investigate the problem of $N$ noninteracting spinless fermions in the trap, determining the many-body ground-state wavefunction and the joint probability density function of the positions of the $N$ fermions. We show that the many-body quantum probability density in the ground state forms a determinantal point process whose correlation kernel can be computed for any $N$, giving access to the average density as well as higher-order correlation functions for any finite $N$. Moreover, we analyze the scaling form of this kernel in the large-$N$ limit in the bulk, near the edge, and close to the origin. Our results show that the scaled average density profile for large $N$ has a finite support symmetric with respect to the origin, but has a nonmonotonic shape with a vanishing minimum at the origin for any $\alpha >0$. One of the key findings of our work is that the scaled kernel near the origin $x=0$ for $\alpha >0$ is neither the Bessel nor the Airy kernel (that are standard for trapped fermions), but is new, and is given by a sum of two Bessel kernels with different indices. Our results thus provide a framework relevant to engineered optical lattices with position-dependent tunneling.

We study a model system consisting of a tunneling barrier driven by an external harmonic field and coupled to two leads with finite bandwidth. Avoiding Floquet expansions, we derive simple expressions for the time-dependent tunneling current in the adiabatic regime. Our approach relates the barrier modulation to a measurable time delay in the steady-state periodic current. It provides a physically consistent definition of the tunneling time inside the barrier by subtracting the time delay associated with the leads from the total time delay. We find that the tunneling time always vanishes for wide/high barriers. Remarkably, the time delay persists even when the barrier becomes static, i.e., in the limit where the modulation frequency vanishes. This indicates that the time delay obtained through the introduction of an external periodic perturbation actually reflects an intrinsic property of the tunneling dynamics, rather than an effect of the external drive or of a particular system. We apply our results to the analysis of tunneling times in optical experiments and find good agreement with the experimental data.