Papers

A theoretical framework is proposed to engineer both first and second-order topological superconducting phases in a two-dimensional (2D) heterostructure, consisting of a quantum spin Hall insulator (QSHI) and an unconventional $p$-wave magnet in presence of proximity-induced $s$-wave superconducting pairing. Our analysis establishes that the transitions between the trivial and topological superconducting (TSC) phases can be regulated though the parameters of $p$-wave magnet. Presence of chiral symmetry leads to the characterization of both types of TSC phases by the respective invariants, one-dimensional winding number and quadrupolar winding number. These results are supplemented by an analytical effective low-energy edge theory that yields a deeper insight into the emergence of the different topological phases of the system. Bulk pairing analysis reveals the competition between the effective $(p_x+p_y)$ and $(p_x+ip_y)$ type pairings that are governed by the intrinsic spin-orbit coupling inherited to the QSHI and spin-split bands of the $p$-wave magnet, respectively.

Background: The quasiparticle random-phase approximation (QRPA) within nuclear density functional theory provides a powerful framework for describing collective excitations. Although the finite-amplitude method (FAM) efficiently solves the QRPA problem, repeated calculations for different external-field parameters remain computationally demanding. Purpose: We construct a reduced basis method (RBM)-based emulator for the FAM that treats the complex energy of the external field as a model parameter to efficiently reproduce FAM amplitudes and QRPA eigenmodes. Methods: High-fidelity FAM calculations are performed at a small set of training points in the complex-energy plane. The resulting FAM amplitudes form a non-orthogonal reduced basis. A variational equation yields an emulator that can predict the response at arbitrary complex energies and QRPA eigensolutions without additional full FAM calculations. Results: The RBM emulator accurately reproduces FAM strength distributions in both giant-resonance and low-energy regions when the relevant energy domain is covered by the training set. It also reproduces imaginary QRPA modes associated with shape instabilities of the HFB state. Applied to the $K^\pi=0^+$ mode of rare-earth Dy isotopes in a realistic model space, the emulator reproduces strength distributions and the lowest $0^+$ collective states with precision comparable to full FAM calculations, reducing the computational cost by more than an order of magnitude. Conclusions: The RBM provides an efficient and accurate FAM emulator. Its ability to reproduce giant-resonance, low-energy, and imaginary-energy modes at drastically reduced computational cost makes it promising for density-functional optimization, calculations of collective inertia, and large-scale surveys of nuclear collective excitations.

Recently, Sobhani and Luo \cite{sobhani2025unified} proposed a new empirical formula for $\alpha$ decay based on the $Q_\alpha^{-1/4}$ energy dependence, incorporating the proton number $Z$, neutron number $N$, and relative neutron excess $I = (N - Z)/(N + Z)$ as primary parameters. In this work, we extend this model by explicitly including the angular momentum of the emitted $\alpha$ particle and the quadrupole deformation of the daughter nucleus. Using this improved formula to evaluate the $\alpha$-decay half-lives of 400 nuclei yields a root-mean-square (RMS) deviation of 0.97 relative to experimental data. Furthermore, we employ support vector regression (SVR)-taking $Q_\alpha^{-1/4}$, $N$, $Z$, angular momentum, and daughter-nucleus deformation as input features-which further reduces the RMS deviation to 0.56. Finally, we apply both the extended formula and the SVR model to predict the $\alpha$-decay half-lives of even-even nuclei with $Z = 120$ and $Z = 122$. The predicted half-lives show good consistency with those from the Sobhani and Poenaru formulas, and both approaches strongly support $N = 184$ as the next neutron magic number.

The way numbers are represented strongly influences which arithmetic structures are easy to see. The prime clockwork is a recursively growing discrete dynamical system: a list of autonomous two-hand clocks driven by one common $+1$ signal. No primes or primality labels are supplied. Starting empty, the process appends a clock of period $n$ whenever none already present rings; the primes are generated internally as its growth times. For each installed prime $p$, the seconds reading $R_p$ advances through $0,\ldots,p-1$, and each return to zero increments the minutes reading $M_p$, which counts completed $p$-cycles. The hands use only increment, comparison, reset, and carry, without explicit mod or div operations. At time $n$, $n=pM_p(n)+R_p(n)$. The valuation readout $V_p(n)=\nu_p(n)$ is generated locally: it is zero when the seconds counter is non-zero (silent state) and otherwise (when the p-clock rings) one plus the earlier valuation addressed by the current minutes reading. The valuation vector gives the integer in unique prime-factorized form. Its coordinates add and subtract under multiplication and division, representing every positive rational uniquely; divisibility becomes weak componentwise order, and unique factorization is natural in this representation. Finite seconds arrays form Cartesian-product state spaces whose common orbit visits every joint state once before repeating; this grand cycle is the order-sensitive dynamical counterpart of the Chinese remainder theorem. The same coordinates expose gcd, lcm, perfect powers, Bézout's identity, and Euler's totient. Rational valuation levels reach certain positive algebraic irrationalities, but not algebraic numbers in general.

The soft-mode of electro-optic (EO) metal-oxide perovskites plays a critical role in determining their Pockels responses. This is the case of potassium tantalate niobate (KTN), which exhibits an intrinsic Pockels response 2.5 times larger than that of state-of-the-art barium titanate (BTO), highlighting its potential for high-performance EO applications. By combining ab initio calculations at the density-functional theory level and far-IR measurements, we reveal that the harmonic approximation combined with semi-local exchange-correlation functionals fails to accurately capture the soft transverse optical (TO) Slater mode of both potassium niobate and KTN, which dominates the technologically relevant r51 Pockels coefficient. Replacing the calculated mode frequency with its measured value provides an experimentally constrained approach that substantially improves the predicted Pockels response. For that purpose, the previously unreported TO Slater-mode frequency of KTN is extracted from far-IR reflectivity measurements. The results emphasize the potential of KTN-based EO modulators as an alternative to standard lithium niobate and BTO technologies, with a potentially lower energy consumption and device footprint.

With the capabilities of the new visible CHARA/SPICA instrument and the multiple spectral band operation of CHARA, our goal is to resolve orbits of short-period binaries and develop a robust framework for combining interferometric, spectroscopic, and photometric observations into a single consistent model. For our target sample, we selected suitable binaries based on brightness, angular separation, and orbital properties based on the expected performance of the CHARA/SPICA instrument. As a case study, we analysed the bright eclipsing binary $\beta$ Aurigae, composed of two slightly evolved A1 stars. We combined new interferometric observations of $\beta$ Aur obtained with CHARA/SPICA, MIRC-X, and MYSTIC with archival MIRC data, radial velocities, and light curves. We first derived astrometric positions from interferometric observables and computed an orbital solution. Afterwards, we implemented a unified model, capable of tying interferometric modelling with the ellc code to simultaneously fit all observables using MCMC sampling. We performed a detailed analysis of the noise statistics of each data set and in the end we adopted a profile likelihood approach to account for underestimated noise and systematics. We derived a consistent orbital and physical solution for $\beta$ Aur through joint modelling. The inclusion of interferometric data tightly constrains the angular semi-major axis and inclination. Using profile likelihood to account for the different intrinsic levels of uncertainty of the fundamentally different observables, we derived the masses of the two stars, $M_1 = 2.359 \pm 0.005$ M$_S$ and $M_2 = 2.293 \pm 0.004$ M$_S$, their radii $R_1 = 2.752 \pm 0.002$ R$_S$ and $R_2 = 2.622 \pm 0.002$ R$_S$, and the distance to the binary, $d = 24.30\pm0.05$ pc.

Martian gullies are geologically recent landforms that may form either through liquid-water activity and/or through processes involving CO2 ice. We investigated the mechanisms responsible for the formation or modification of these features by focusing on the active site of Sisyphi Cavi (68{\deg}S, 1{\deg}E), located outside the typical latitude range of gully presence. Using CRISM and OMEGA infrared data, we characterized the composition and physical state of seasonal surface ices to test the relevance of H2O and CO2 ice driven mechanisms. Our analysis shows that H2O ice is not detected as an independent surface deposit, although it may be present as minor inclusions within the CO2 ice layer. In particular, during the final phase of CO2 ice sublimation in late spring, no H2O ice signature is observed. In the area, faint spectral signatures of sulfate salts are observed, but their distribution and amount do not suggest any direct link with gully activity. Available observations during early and mid-spring reveal that CO2 ice is translucent during these times, suggesting that it likely remains in this state through most of the ice season. However, a temporal mismatch between dark spot formation - indicative of CO2 geysers through translucent ice - and gully modification (respectively occurring late winter to early spring, and mid to late spring) exists. This does not suggest a systematic link between both processes. Overall, the available observations provide no evidence that liquid water contributes to present-day gully activity at Sisyphi Cavi, while offering no support either for the hypothesis that gully modifications are mainly driven by the formation of CO2 geysers. Gully modifications at Sisyphi Cavi, observed during the late sublimation stages of CO2 ice, may be rather more appropriately explained by CO2-ice-based fluidization or avalanche processes.

Axion haloscopes use radio-frequency cavities immersed in a magnetic field to search for dark-matter axions, which could resolve two central puzzles in fundamental physics: the strong charge-parity problem in quantum chromodynamics and the nature of dark matter. Multi-tesla fields trigger axion-to-photon conversion but induce severe vortex dissipation in standard superconductors, whereas copper cavities are limited by the anomalous skin effect ($Q \lesssim 10^5$). Here, we overcome these barriers by introducing a pole-to-pole 3-dimensional cavity architecture constructed from strain-controlled, mechanically delaminated rare-earth barium copper oxide (REBCO) tapes. By selectively stripping the lossy metallic substrate while utilizing the copper stabilizer as a "conductive backing" we convert the longitudinal assembly gaps into waveguides below cutoff, effectively suppressing cross-seam RF leakage. Employing a two-track strategy, we first unveiled the intrinsic high-field potential of the material with a 5.4 GHz resonant cavity, achieving an unloaded quality-factor ($Q_0$) of $1.4 \times 10^7$ in an 8 T magnetic field, exceeding conventional copper baselines by two orders of magnitude. Second, prioritizing practical haloscope integration, we engineered a tunable, volume-maximized 2.3 GHz pathfinder cavity. Deployed in the Pilot Axion Cavity Experiment at the Center for Axion and Precision Physics Research (CAPP-PACE), this system achieved a 180 mK noise temperature and a 5-fold $Q$ enhancement over copper, cumulatively delivering a $\sim$8.4-fold scan-rate acceleration.

Metallic nanoring networks can serve as promising flexible transparent electrodes. These materials are crucial components in a wide range of applications, including solar cells, touchscreens and displays. In this work, a computational investigation considers in detail (i) the electrical conductance and optical performance of nanoring networks and (ii) the breakdown of these networks due to electrical damage. The electrical resistance of both the nanorings and the contacts between the rings (junctions) is taken into account. In part (i), the effects of 5 parameters on the electrical sheet resistance and optical transparency are presented. It is shown that several parameter combinations achieve better performance in comparison to indium tin oxide, currently the most widely used transparent electrode. In part (ii), due to electrical damage, the nanoring systems display the formation of a crack, running parallel to the vertical terminals, where a voltage difference is applied. The network degradation is measured by its sheet resistance, and a universal effect is observed: networks with varying filling factors exhibit the same degradation profile.

Recent experiments indicate that PtBi$_2$ is a Weyl semimetal whose surfaces become topological superconductors with i-wave gap symmetry at low temperature. The bulk hosts 12 Weyl cones while in the superconducting state each of the two surfaces hosts in addition 6 Majorana cones. We study a simplified model in a slab geometry, where the finite thickness gaps out the bulk Weyl cones and leaves the surface Majorana cones as the low-energy degrees of freedom. We identify two competing mechanisms that gap these cones: inter-cone hybridization opens a trivial gap, whereas a Zeeman field opens a nontrivial one. In the nontrivial regime, chiral Majorana edge modes connect the gapped cones. We determine their wavefunction profile and relate it to the momentum-space distribution of the cones. Mapping out the phase diagram, we find both trivial and nontrivial regions in the quasi-two-dimensional limit.

Estimating the auto-correlation function (ACF) and cross-correlation function (CCF) of sampled series is a standard task in many physics fields, including astronomy and environmental sciences. We present nufftcf, an ACF/CCF estimator designed primarily for irregularly sampled series, numerically consistent with established kernel-weighted definitions and scaling as O(nK) for K requested lags, rather than O(n^2). nufftcf was initially developed to evaluate the Wiener-Khinchin theorem for irregularly sampled data using the Non-Uniform Fast Fourier Transform (NUFFT), through the Flatiron Institute FINUFFT library, with Gaussian and rectangle kernels. An O(n)-per-lag two-pointer scan replaces the naive O(n^2) computation of the effective pair count used to normalize each lag bin. This enabled real-space estimators using the same kernels, providing exact reference implementations with the same O(nK) complexity and, in some cases, lower cost than the NUFFT path. The library also provides dedicated classical-FFT estimators for regularly sampled data. All estimators share a common calling convention. Using synthetic time series, we validate nufftcf for ACF against pastas, a library used in groundwater time-series analysis, and for CCF against pyZDCF, used in astronomical time-series analysis. Benchmarks confirm O(nK) scaling for the NUFFT and real-space nufftcf estimators, compared with O(n^2) for the pastas slotting technique. nufftcf is already advantageous at moderate series lengths because of its low millisecond-scale overhead. For regularly sampled data, the FFT path further reduces computational cost. We also demonstrate nufftcf on a simulated ground-based stellar light curve combining quasi-periodic rotation, correlated flicker noise, seasonal sampling gaps, and heteroscedastic measurement errors. Notebooks and scripts are provided to reproduce the examples and explore other use cases.

Deng et al. discovered that Drt3b synthesizes protein-primed poly(AC) DNA without a nucleic-acid template. The structures reveal a finite protein architecture and product-associated contacts, but not the renewable dynamical rule that converts a bounded pocket into a long period-2 sequence. We propose that Drt3b is a regenerating protein-substrate free-energy register. The framework specifies a sampled quantum mechanics/molecular mechanics (QM/MM) potential of mean force and a preregistered, within-domain first-order electronic-descriptor map for edge-specific activation barriers; physical curvature is admitted only through a training-frozen Taylor-remainder bound that widens uncertainty but never corrects a held-out mean. Conditional hazards derived from those barriers are averaged over unresolved conformational, hydration, protonation, and metal-coordination trajectories to yield a semi-Markov event kernel. Pointwise ratios of competing hazards are therefore fixed by the same barrier differences and preregistered prefactor rules that govern exit timing, so nucleotide choice and dwell statistics are co-generated rather than separately fitted. A regime gate separates stationary or slowly driven experiments, analyzed by a joint sequence-time cycle determinant, from genuinely nonstationary protocols, analyzed by the full age-structured tilted propagator. The decisive test is one locked parameterization: without condition-specific refitting, it must jointly predict nucleotide choice, waiting-time laws, product-length tails, and the rank, minors, null spaces, and rescue structure of perturbation responses. An independent 2026 DRT3 study supplies a stringent cross-construct transport test after sequence and structural alignment are frozen. The proposal requires neither coherent quantum computation nor coupling to an external field.

We investigates the joint compatibility problem of the three pairwise concurrences, the three-tangle, and the Kempe invariant in arbitrary pure three-qubit states, and gives necessary and sufficient conditions for these five quantities to be simultaneously realizable by the same pure state. This five-dimensional compatibility region can be viewed as a fiber structure over the previously derived four-dimensional reachable region. We further find that the residual continuous local-unitary freedom depends on the position of the state within this region. In the generic interior, one continuous degree of freedom remains. It is fixed if the three-tangle vanishes or a pairwise concurrence becomes zero, and also at the boundary of the four-dimensional tangle region. The Kempe invariant gives the simplest algebraic parametrization of the fifth coordinate, but the same degree of freedom may be described by a known pure-state entanglement monotone. The compatibility conditions can also be expressed in terms of concurrence-based bipartite measures and multipartite quantities fixed by the pairwise concurrences and the three-tangle.

We classify a class of abstract Bose field models in quantum field theory up to unitary equivalence. The class includes abstract free Bose field models, abstract van Hove–Miyatake models, and infrared-renormalized van Hove–Miyatake models. Moreover, as an application of our classification, we classify quadratic interaction models. In particular, our results answer a question of A. Arai concerning the classification of infrared-renormalized van Hove–Miyatake models.

We present a theory for the optimal control of stochastic systems in structured environments, represented by penalty terms in the cost functional. We show that such control problems generically feature sharp finite-time transitions associated with a qualitative change in the control strategy at a critical time. Starting from an overdamped Langevin equation and a quadratic cost functional, we show that all resulting problems fall into three canonical equivalence classes (parabolic, hyperbolic, and elliptic), distinguished by the sign of the determinant of the control Hamiltonian. For each class, we obtain the optimal protocol, the cost function, and the critical time in closed form, and show that the transition exhibits features of a continuous phase transition at mean-field level. We then establish a mapping between the optimal control cost and the large-deviation rate function governing non-equilibrium relaxation after a potential quench. The mapping covers the parabolic and hyperbolic classes, while the elliptic class has no simple relaxation counterpart. This correspondence implies that recently discovered finite-time dynamical phase transitions, which are exponentially costly to sample directly, are accessible through ordinary averages over optimally controlled trajectories. To validate our theoretical findings, we report three experiments with optically trapped colloidal particles: a control transition for the mean stochastic work, and the finite-time dynamical phase transitions in free diffusion and in harmonic relaxation.

Over the last decade, gravitational-wave science has developed from an era where a single detection was a Nobel-winning achievement to an (almost) everyday occurrence. The LIGO-Virgo-KAGRA (LVK) Collaboration's flagship scientific results are now their catalogues of detections, which include a comprehensive set of analysis results characterising the astrophysical properties of sources, and their implications for fundamental physics and cosmology. We review discoveries from the fourth observing run (O4) of the LVK network. The most recent catalogues each include $\sim100$ new detections. Among these new detections are remarkable single discoveries: the loudest signals detected so far, and sources unlike those seen before. However, significant advances in the field are coming from population-level analyses, leveraging the increasing sample size to infer constraints on the astrophysical distribution of merging compact binaries, potential deviations to general relativity, and the expansion rate of the Universe. Analyses of the latest data have revealed evidence for multiple subpopulations of sources. These observations provide a unique probe into the evolution of massive stars and the formation of coalescing binaries. Our understanding of gravitational-wave signals and their sources will continue to deepen with more observations. The final catalogue from O4}is due for release in December 2026, and future observing runs with even greater detector sensitivity are planned. These will bring even larger catalogues, and additional loud signals, continuing to advance gravitational-wave science.

The Kibble-Zurek mechanism (KZM) and finite-time scaling (FTS) provide a foundational framework for driven critical dynamics, yet their predictive power has been largely confined to local observables. Here, we establish a universal finite-time scaling theory for the nonequilibrium dynamics of quantum entanglement. Using unbiased quantum Monte Carlo simulations, we investigate the corner entanglement entropy of (2+1)-dimensional interacting Dirac fermions driven from ordered phases toward a quantum critical point. We find that the corner entanglement accurately obeys a universal driven scaling governed by the driving rate and system size, persisting whether the initial ordered state is fully gapped or hosts gapless Goldstone modes. Crucially, this dynamical entanglement exhibits a logarithmic dependence on the driving rate, from which the universal corner coefficient of the underlying conformal field theory can be robustly extracted far from equilibrium. These results generalize the KZM from local observables to the intrinsic nonlocal quantum information measures, offering a practical blueprint for characterizing quantum criticality and entanglement on programmable quantum simulators.

From protein complexes to electronic circuits, many natural and engineered systems function only if assembled in an exact, reproducible fashion. The structure of each of these systems can be understood as a network, yet network science lacks the mechanisms to consistently reproduce exact topologies, focusing instead on generating network ensembles. We introduce the framework of network design where we encode the local constraints obeyed by a system's building blocks in a design set, and derive the Unigraphical Design Theorem, which determines when these constraints guarantee reproducible assembly into a unique structure, a process we call unigraphical assembly. For systems whose design sets do not specify a unique outcome, we identify guided assembly as a second route to reproducibility, in which temporal ordering decomposes construction into unigraphical steps. Applying these results to 3,618 reproducible systems, including protein complexes, molecules, and robots, we classify those that undergo unigraphical assembly and those that require guided assembly. We further identify a diversity-redundancy boundary that explains how systems trade component variety for structurally interchangeable parts while retaining unique assembly. Finally, we experimentally test the theory using 3D-printed components to re-engineer generative construction sets into systems that assemble unigraphically into prescribed topologies. Network design thus reframes reproducibility as a mathematically testable property of real networks, opening a route to the rational engineering of complex systems.

We investigate whether a perfectly ordered periodic nanolaminate is intrinsically less mechanically dissipative than an isotropic co-sputtered mixture designed to provide the exact same optical function. Focusing on a room-temperature SiO2/TiO2 system, we compare coating Brownian dissipation under strict parity of optical thickness and effective refractive index. Amorphous phases are modeled using complex Young's moduli and real Poisson's ratios. The comparison is highly non-trivial: while the nanolaminate is optically optimal, its structural anisotropy forces in-plane shear to operate at the highly dissipative Voigt upper bound, mechanically penalizing it against an isotropic medium. The nanolaminate is treated via exact optical (Wiener) and mechanical (Backus) relations. The isotropic mixture is described by optical closures (Lorentz–Lorenz, Bruggeman) coupled to a complex mechanical self-consistent scheme. To assess uncertainty from the unknown co-sputtered morphology, we explore rigorous optical and mechanical admissible regions in the complex plane. Owing to the small intrinsic losses of SiO2/TiO2, these regions collapse into extremely narrow lenses, strictly limiting microstructural uncertainty. Across all realistic isotropic closures, the nanolaminate systematically exhibits lower mechanical dissipation than the co-sputtered mixture. Even against the thermodynamic lower bound of the isotropic state, this topological advantage remains valid for high effective refractive indices. We prove the ordered architecture exploits the optical upper bound to minimize the required volume fraction of the highly dissipative high-index phase, overwhelmingly overcompensating for its intrinsic mechanical anisotropy penalty.

The Schrödinger-Lohe (SL) model is a coupled system of nonlinear Schrödinger equations describing the temporal-spatial evolution of the component wave functions, and it corresponds to the infinite-dimensional counterpart of the Lohe matrix model for quantum synchronization. In this paper, we study a rigorous mean-field limit of the SL model and provide a quantitative estimate on the fluctuations between one-marginal distribution and one particle distribution in 2-Wasserstein distance. For the derived kinetic SL equation, we present sufficient conditions leading to the complete and practical synchronizations.

Using the Lifshitz theory of the van der Waals and Casimir forces, we calculate the Casimir free energy of thin peptide films deposited on silicon substrates. The Casimir free energy is found as a function of film thickness for different fractions of water in the film, in the presence of either nonmagnetic or magnetic nanoparticles, and under the impact of irradiation of a silicon substrate with laser pulses or dopants resulting in the dielectric-to-metal phase transition. It is shown that for a dielectric silicon there is the borderline value of the film thickness, such that the Casimir free energy is negative and contributes to the film stability for thicker films, but is positive and makes the film less stable for thinner ones. According to our results, the borderline value of peptide film thickness decreases with increasing volume fractions of water and in the film. This decrease is more pronounced for the magnetic nanoparticles and becomes stronger with increasing their radius. The borderline value of peptide film thickness is found as a function of the fraction of water in the film. If the silicon substrate is in metallic state, the Casimir free energy of peptide coating is always positive, which makes it less stable. Possible applications of the obtained results in organic electronics and biomedicine are discussed.

Couplants are indispensable for ultrasound-based applications to ensure seamless propagation of the acoustic waves between the transducer and targets. Existing hydro/oil-based gel couplants provide excellent acoustic coupling but are single-use and therefore not suitable for emerging applications such as wearable health monitoring, ultrasound-based biometric devices, and prolonged sonodynamic therapy. Alternatively, polymer-based solid couplants have been explored as reusable solutions but generally fail to simultaneously provide effective mechanical conformability and efficient acoustic transmission. Here, we propose an innovative composite material design based on a silicone elastomer matrix, in which mechanical and acoustic properties are tailored independently through the microencapsulation of diols and triols. An emulsion-based material formulation strategy is employed to produce a family of high-liquid droplet content elastomeric composites containing up to 75 volume fraction (%) of liquid. A robust material formulation strategy is established that enables independent parametric control over the resulting mechanical and acoustic properties. A specific composition containing 70 % glycerol has been identified and explored for biomedical applications, exhibiting mechanical softness comparable to that of skin and acoustic properties matching those of soft tissues. The material has been integrated into a functional ultrasound characterization device, demonstrating structural homogeneity and applicability of the proposed couplant. Furthermore, the composites exhibit mechanical conformability to stiff substrates with surface irregularities, making them also promising candidates for industrial applications.

The entanglement spectra of fractional quantum Hall states contain universal fingerprints of their underlying topological order, as posited by the Li-Haldane conjecture. In this work, we uncover a finer universal structure within the entanglement spectra unravelled by projective measurements. Concretely, we study the projected ensemble of fractional quantum Hall states, defined as the collection of quantum states on a subsystem conditioned on measurement outcomes of its complement. We find that this ensemble exhibits a hidden hierarchy inside the Li-Haldane edge manifold: by conditioning on measurement outcomes, the entanglement spectrum's support is split into measurement-dependent sectors whose ranks we demonstrate are fixed by conformal field theory counting, an observation we dub the measurement-resolved Li-Haldane conjecture. For the non-Abelian Moore-Read state, this hierarchy is particularly rich: each parity-resolved edge manifold contains internal subspaces whose dimensions reproduce the conformal field theory counting of the opposite-parity sector. This structure persists even in realistic Coulomb-interacting ground states, establishing the projected ensemble as a sharp new probe of topological order beyond what the entanglement spectrum alone can detect.

For a general class of two-dimensional non-interacting semi-metallic electron systems on a lattice, we derive an explicit formula for the whole conductivity matrix, by using Euclidean many-body formalism. The semi-metallic phase takes place whenever two Bloch bands touch at the Fermi energy with conical intersections and generally occurs at the transition between distinct integer quantum Hall phases. Unlike the longitudinal conductivity (which depends solely on the shape of the cones at the Fermi level), the transverse conductivity is remarkably determined both by the conical structures of the bands and by the nature of the two nearby topological phases. Generically, in the semi-metallic state, neither the longitudinal nor the transverse conductivities are quantized in integer multiples of a universal conductivity quantum; however, universality of the conductivity matrix is restored under the assumption of emergent rotational symmetry of the linearized Hamiltonian at the Fermi points. Using our formula, we compute the conductivity matrix for several physically relevant models of quantum Hall fluids at the topological phase transition, exhibiting cases where the transverse conductivity is quantized in half-integer multiples of $e^2/h$ and cases where it depends continuously on an external strain parameter, thus shedding light on its universality or non-universality features.

Quantum error correction acts as an entropy pump, transferring noise-induced uncertainty from a protected quantum system into syndrome information stored in an auxiliary memory. Repeated operation requires this memory to be cleared which unavoidably contributes to the energetic cost of error correction. Here, we characterise this contribution for subspace quantum error-correcting codes and identify how it depends on the joint structure of the code, the noise, and the representation of the retained syndrome information. Starting from the Knill–Laflamme conditions, we construct an effective syndrome state whose von Neumann entropy sets a lower bound on the ideal work required to maintain a reusable syndrome register. Projective syndrome readout generally generates additional entropy, and we quantify the resulting gap through measurement inefficiency. We then specialise to stabiliser codes under independent local Pauli noise and analyse two classical levels of syndrome representation. At the level of abstract error labels, degeneracies among single-qubit errors reduce the leading-order entropy of processed recovery labels. At the parity-check level, lower-weight checks reduce the marginal entropy generated by individual measurement outcomes in the low-noise regime. We identify the additional burden associated with retaining and separately erasing these outcomes as a bit-level inefficiency, and illustrate both costs for the five-qubit, Steane, generalised Shor, and rotated surface codes. Our results establish a hierarchy of syndrome-memory energetic costs and identify the code, noise, and measurement structures that control the ideal thermodynamic burden of subspace quantum error correction.

Rare-event search experiments demand ever-lower backgrounds, and the resulting radio-pure materials and suppressive shielding make related background simulations computationally expensive without event biasing. We present a method for optimising the widely used importance splitting and Russian roulette technique for rare-event searches, in which a whole number of equal-width importance layers fill the shielding geometry. Balancing relative uncertainty against execution time, we optimise the layer thickness for both $\gamma$-rays and neutrons, and across different shielding materials and thicknesses. Expressed as a multiple of the primary particle's mean free path, the optimal thickness generalises across energies for a given particle type and yields a physics-based prediction applicable to any shielding design. The same trend reveals that over-biasing is possible, with relative uncertainty worsening at high layer counts for fixed execution time. The optimal configuration gives an $\mathcal{O}$(20) gain in computational efficiency over the unbiased case.

In this article, we investigate the two-species zero-range process, a multi-species generalization of the classical zero-range process. First, we analyze its condensation regime, which directly parallels its single-species counterpart. As our main result, we establish the dynamical metastable behavior of the location of the single condensate, showing that its motion is governed by a simple Markov chain on the accelerated time scale $N^{1+\alpha}$, where $N$ denotes the total number of particles in the system and the parameter $\alpha>1$ governs the attractivity of the system. Another novelty of this work lies in the proof technique, which integrates the recently developed resolvent approach with the $H^{1}$-approximation method to rigorously characterize metastability.

We investigate the geometry of viable Froggatt–Nielsen-like flavor textures in a controlled toy landscape. In this first texture-level analysis, each point is represented by the eighteen integer exponents entering the up- and down-type Yukawa matrices, without imposing the additional charge-factorization constraints of specific Froggatt–Nielsen models. Viability is imposed through cuts on quark mass ratios and selected CKM observables. We construct four benchmark ensembles, ranging from masses-only constraints to the inclusion of the full set of CKM observables considered in this work, and study the resulting point clouds in the raw exponent space. Principal-component analysis shows no evidence for strong linear compression: in all benchmarks, fifteen principal components are required to account for 90% of the variance. Nearest-neighbour intrinsic-dimensionality diagnostics, including TwoNN and Levina–Bickel estimators, support the same qualitative conclusion, yielding high effective dimensions of order 10-12. These results do not rule out hidden flavor-theory geometry in other coordinates; rather, they suggest that raw Froggatt–Nielsen exponents may not provide natural coordinates for revealing such a geometry.

The Knaster-Tarski fixed-point theorem states that every monotone function over a complete lattice has a fixed point. Beyond its fundamental role in order theory, the theorem and its algorithmic variants have found broad applications in areas such as economics, game theory, and programming languages. While the query complexity of finding a Tarski fixed point has been extensively studied in classical models, comparatively little is known in the quantum setting. We prove an $\Omega(k\log n)$ quantum query lower bound for finding a fixed point of a monotone function on $[n]^k$, using the nonnegative spectral adversary method. In the two extremal regimes $n = 2$ and $k = 1$, our quantum lower bound matches the previous classical lower bounds $\Omega(k)$ and $\Omega(\log n)$, respectively. For $n, k\geq 2$, our bound improves the best previous classical lower bound when $n < k$ and is within a factor of $\log n / \log k$ compared to the known classical lower bound when $n \geq k$. To construct the adversary matrix, we develop the Tree–Filtration Adversary Method. Besides yielding our lower bound, the method offers a more transparent combinatorial interpretation of the nonnegative spectral adversary method. When the hard instances of a problem admit a tree-like organization and suggest an intuition analogous to classical decision-tree lower bounds, our method provide a promising approach to establishing quantum complexity lower bounds.

Fluid shear can induce detachment of a thin elastic sheet adhered to a flat substrate. This peeling process is important in a variety of environmental and technological systems. The condition for peeling depends on: the shear rate $\dot{\gamma}$, the fluid viscosity $\eta$, the length of the detached portion of the sheet $L$, the bending rigidity $B$ and the adhesion energy $\Gamma$. What are the laws governing the detachment? We address this question experimentally in the regime of intermediate adhesion, using macroscopic sheets bonded to a substrate and immersed in a shear cell containing a viscous fluid. The experiments indicate a critical shear rate for peeling of the order of $\dot{\gamma} \sim B/(\eta L^3)$. This threshold is, unexpectedly, independent of adhesion. We rationalise this result by applying Griffith's fracture theory to optical measurement data of the shape of the sheet, under conditions of freely moving peeling front or clamped boundary. The results indicate that the large curvature of the sheet for $\dot{\gamma} \sim B/(\eta L^3)$ yields a nearly diverging strain energy release rate at this threshold. This approximate divergence in turn yields a peeling threshold that depends at most weakly on $\Gamma$, confirming a theory that was proposed recently (Salussolia et al., J. Mech. Phys. Solids, 2020, 134). Among other applications, our work provides a quantitative formula that can aid the production at scale of 2D materials such as graphene.