Papers

Parameterised graph theory studies how the complexity of graph-theoretic problems depends on structural parameters of the input graph. This perspective has proved useful in analysing tensor-network simulation (Markov and Shi, 2008). Its implications for tensor-network representations and tomography are less well understood. In particular, which graph parameters determine whether a tensor-network state (TNS) admits a tractable matrix product state (MPS) or tree tensor network (TTN) representation, and which control the complexity of learning the state? We address these questions using parameterised graph theory. First, we show that cutwidth and tree-cutwidth bound the bond dimension overhead required to represent a TNS as an MPS or TTN. In the TTN case, tree-cutwidth also bounds the local dimension of the grouped subsystems. The proofs are based on entanglement rerouting, a tensor-network analogue of rerouting information in a classical network. Second, we derive graph-dependent upper bounds on the sample and computational complexity of realisable TNS tomography, with exponents that depend on cutwidth, tree-cutwidth, and a new graph parameter, learning complexity, which we bound in terms of degree and treewidth. We obtain these results by extending the disentangling MPS learner of (Cramer et al., 2010), as analysed further in (Bakshi et al., 2025; Lin et al., 2025), to TTNs and to tensor networks on arbitrary known graphs. Finally, we extend the framework beyond the realisable setting. For an arbitrary input state, our agnostic learner outputs a pure state whose fidelity is within additive error $\epsilon$ of the optimum over tensor-network states on the given graph with a given bond dimension, with explicit graph-dependent bounds on sample and computational complexity.

The Peierls instability is a foundational mechanism in condensed matter physics, showing how the electron–phonon interaction can transform a simple metal into an insulating state with a new lattice periodicity. In a one-dimensional (1D) metal the Peierls instability follows from the enhanced electronic response at wavevector $Q=2k_F$ (connecting the Fermi points) producing a Kohn anomaly: a softening of the phonon mode at the same wavevector. Condensation of this mode then generates the tell-tale Peierls periodic lattice distortion and charge-density wave (CDW) that gaps the electronic spectrum. Here we show an analogous instability at the edge of a two-dimensional (2D) superconductor, where a dispersing Andreev bound state (ABS) hosts Bogoliubov Fermi points at $\pm k_c$. The enhanced quasiparticle response at the connecting wavevector $Q=2k_c$ couples directly to pairing-fluctuations and produces a superconducting Kohn anomaly: a softening of a pairing mode at the same wavevector. Condensation of this mode then generates an edge pair-density wave (PDW) that gaps the ABS. We refer to this as a superconducting Peierls instability and identify the boundary quasiparticle structure that enables it. As a concrete realization, we consider a square-lattice extended Hubbard model whose mixed-symmetry $s+d+ip$ state hosts a dispersing ABS with zero-energy crossings at finite edge momenta. Using self-consistent Bogoliubov–de Gennes (BdG) calculations we show that the order parameter develops an edge PDW, with the wavevector set by the superconducting Kohn anomaly, that gaps the ABS crossings. Our results identify a novel mechanism for spontaneous translation-symmetry breaking in a superconductor. As this superconducting Peierls mechanism does not require an extensive zero-energy flat band or topologically protected edge states, it may apply broadly to unconventional superconductors.

The high-recoil event reported by LUX–ZEPLIN motivates a TeV Higgsino with a sub-MeV neutral-state splitting. Away from cancellations, such a small gap in the MSSM points to electroweak-gaugino masses of order $10^7\,\mathrm{GeV}$, far above the Higgsino mass. We show that the non-universal boundary condition $M_1^G/M_2^G=-3/5$ at the $\mathrm{SU}(5)$ GUT scale cancels the leading bino and wino contributions and is preserved by homogeneous one-loop evolution down to the Higgsino scale. The remaining finite-gaugino terms admit a controlled tree-level solution with a wino mass near $120\TeV$ for a $350\keV$ gap, a $1.091\TeV$ Higgsino and $\tan\beta=10$. We identify mixed $\mathrm{SU}(5)$ representations that realize the required gaugino ratio and examine the radiative sensitivity and spectrum consistency of this construction. Because the inelastic $Z$ coupling remains essentially unsuppressed, a full-density thermal Higgsino is still subject to the published solar-capture bounds under their astrophysical and transport assumptions.

We derive nonasymptotic upper bounds on the probability that a generalized current of a geometrically ergodic diffusion observed for any amount of time, or its sample mean over any arbitrary sample size, deviates from the stationary mean by more than any given amount. The concentration-of-measure behavior of generalized currents is universally governed by the relaxation time of the underlying dynamics, the locally observed dissipation rate, and the intrinsic local fluctuations of the observable. We uncover stark qualitative and quantitative differences in fluctuations in and out of thermodynamic equilibrium. We further obtain refined inverse thermodynamic uncertainty relations, bounding the variance of generalized currents from above. We construct nonasymptotic confidence intervals for controlling uncertainty in thermodynamic inference from small data, i.e., from short trajectories and small samples, and provide the first quantitative answer to when a trajectory is sufficiently long and a sample is sufficiently large. As an illustration, we apply our results to currents observed on a two-dimensional Ornstein-Uhlenbeck process in and out of equilibrium and show how they can be used to rigorously detect broken detailed balance.

Exact CNOT synthesis seeks a minimum-size circuit implementing a given invertible binary linear transformation. We study its vanilla formulation: synthesis from the identity on fixed labeled qubits, without ancillas and with all-to-all connectivity. We prove that this problem is NP-hard and that its bounded decision version is NP-complete. Hardness persists even for unitriangular targets that are low-rank perturbations of the identity and under near-linear gate budgets. Our proof gives a polynomial-time reduction from the NP-complete Hamiltonian path problem on grid graphs. A unary hypercube embedding translates graph vertices into circuit parities and edge traversals into CNOT updates. The central challenge is that Hamiltonian paths require intermediate vertex visits, whereas exact synthesis constrains only the final transformation. We bridge this gap with a replicated recorder qubits construction that encodes the required parities in the final outputs, together with a tight gate budget that forces every sufficiently short implementation to trace a Hamiltonian path. Crucially, this path structure is enforced by the construction rather than imposed as a restriction on the circuit. The result directly implies NP-hardness for shortest word problem and Cayley-graph distance computation over $\mathrm{GL}(n,2)$ with elementary transvections as generators, as well as fixed-width sequential XOR program minimization. For CNOT-minimal exact phase polynomial synthesis, it yields NP-hardness with a zero phase polynomial; extending the reduction to grid-graph Hamiltonian cycle problem establishes hardness even when the final linear transformation is the identity. These complementary results show that the linear and phase components each independently suffice for NP-hardness of exact phase polynomial synthesis.

In his seminal paper, Bell [Physics Physique Fizika 1, 195 (1964)] considers the correlations that result from space-like separated measurements on a pair of entangled particles. He uses relativity theory to motivate the Bell causal structure, then shows the existence of quantum correlations that cannot be explained classically within this causal structure. Classical explanations of such quantum correlations are possible in alternative causal structures, for instance, those that allow superluminal causal influences, but, as shown in [New Journal of Physics 17 033002 (2015)], all such alternative explanations require fine tuning (causation without correlation). Here we discuss the existence of spurious quantum correlations — correlations that look quantum in one causal structure, but have a natural classical explanation in another. More precisely, there are causal structures that admit non-classical quantum correlations, but for which the same correlations have a classical explanation in another causal structure without fine tuning. The realisation in the other causal structure can also be achieved without breaking any natural constraints on the causal structure that follow from relativity theory. However, similarly to non-classical quantum correlations in the Bell causal structure, we find other causal structures with non-classical quantum correlations that do not have a classical causal explanation in any alternative causal structure without fine tuning.

Electric quadrupole transition probabilities $B(E2)$ serve as key probe of nuclear shell evolution, yet anomalous $B(E2)$ values in exotic nuclei complicate the identification of new magic numbers. In this letter, employing the configuration-interaction relativistic Hartree-Fock model, we demonstrate that effective charges are sensitive to orbital radii, and this orbital dependence is significantly amplified by the halo structure of valence nucleons. This mechanism is critical for reliably describing $E2$ transitions and understanding the unusual behavior of $B(E2)$ in exotic nuclei. Our calculations predict reduced $B(E2; 2^+_1 \rightarrow 0^+_1)$ values in $^{52,54}\text{Ca}$, signaling the emergence of subshell closures at $N=32$ and 34. Furthermore, the suppressed $B(E2; 7/2^{-}_{1} \rightarrow 11/2^{-}_{1})$ transition in $^{53}\text{Sc}$ underscores the robustness of the $N=32$ new magic number, whereas the enhanced transition strength in $^{55}\text{Sc}$ indicates the rapid erosion of the $N=34$ shell gap with the occupancy of the proton orbital $\pi1f_{7/2}$.

We study the spectral and eigenvector properties of random mixed graphs, combining undirected and directed interactions, using random matrix theory (RMT). The network is represented by a Hermitian adjacency matrix, with undirected links as real entries and directed links as purely imaginary conjugate pairs, ensuring a real spectrum. Network density is controlled by the connection probability, while directionality sets the fraction of directed edges. We focus on the GOE-to-GUE crossover: at fixed connectivity, increasing directionality breaks time-reversal symmetry and drives spectral statistics from GOE to GUE. We show that this transition requires sufficient connectivity. In sparse networks, weak level repulsion produces Poisson statistics regardless of directionality. At fixed directionality, increasing connectivity drives a Poisson-to-GUE crossover; only above a sparsity threshold does the directionality-induced GOE-to-GUE transition emerge. In the dense regime, where the spectral density follows the Wigner semicircle law, the crossover is characterized using spacing distributions, spacing ratios, and spectral rigidity. In sparse networks, where unfolding is unreliable, spacing-ratio statistics provide an unfolding-free characterization. Eigenvector structure is examined through multifractal dimensions and component distributions, while Kullback–Leibler divergence confirms the robustness of the transitions. Applied to S&P 500 mixed graphs, the framework reveals a GOE-to-GUE crossover across four major market crashes. Denser crisis periods show sharper crossovers than sparser recovery periods. The results provide a unified picture of how connectivity and symmetry breaking govern spectral and eigenvector universality, while providing a transparent probe of changing financial-market organization.

Coherent interfaces between optical photons and mechanical excitations provide a promising route towards phonon-state engineering and hybrid quantum information processing. Cavity optomechanical systems enable such interfaces via optomechanically induced transparency (OMIT), allowing coherent mapping between traveling optical fields and localized mechanical modes. However, previous implementations of OMIT conversion protocols were limited to classical input signals with large coherent state photon numbers due to room temperature operation and corresponding thermal mechanical noise. Here, we demonstrate efficient low-noise photon-phonon state transfer close to the single-quantum regime in an optomechanical crystal operated at Millikelvin temperatures. Using weak coherent optical input pulses at the few-photon level, we achieve a record-level photon-phonon conversion efficiency of $\eta=0.76$, a mechanical storage lifetime of $T_\mathrm{1}=7.3~\mu s$, and a tunable conversion bandwidth exceeding 4.5 MHz. Hanbury Brown-Twiss measurements of the retrieved signal demonstrate the coherent nature of the converted phononic state, evidencing low added thermal noise in the conversion process ($n_\mathrm{th}=9.0$). These results establish optomechanical crystals as efficient optical interfaces to GHz mechanical modes and provide a pathway toward deterministic single-quantum-level mechanical state preparation.

Moiré materials host fractional Chern insulators and electron crystals in close proximity, but the mechanism selecting between them remains an open question. We address this competition in Chern bands with ideal but momentum-dependent quantum geometry – Aharonov-Casher bands. We present an ansatz wave function for generalized Wigner crystals and, by comparing its energy to that of the competing Laughlin-like state, map out the phase diagram at filling fraction $\nu=1/m$ as a function of the degree of geometric non-uniformity. Our work identifies quantum geometry-controlled zero point fluctuations of the charge density of the generalized Wigner crystal as the mechanism controlling its relative stability, implying a kind of quantum Lindemann criterion for the crystal-liquid phase boundary.

Competing phases of strongly correlated systems are often described by trial wavefunctions built on phase-specific assumptions. We propose the hyperdeterminant (HyperDet) wavefunction as a phase-agnostic ansatz for both bosonic and fermionic quantum many-body systems exhibiting spontaneous symmetry-breaking, fractionalization, and/or topological order. The HyperDet structure emerges by fusing auxiliary fermionic parton Slater determinants into physical orbitals through a learnable \emph{fusion tensor $\mathcal F$}. Optimized using variational Monte Carlo, a single HyperDet architecture achieves overlaps exceeding $99.9\%$ with exact-diagonalization ground states for nearly all sampled parameters across fractional Chern insulator (FCI) phases and their neighboring competing phases in both bosonic and fermionic models. Beyond its variational expressiveness, the optimized fusion tensor also provides rich interpretability. We show that, (i) the singular-value spectra of the bipartite fusion matrix can be used to track phase transitions; (ii) the reconstructed Bott indices reproduce the parton Chern numbers expected for the FCI states without parton-Hamiltonian input; and (iii) faithful lifts of physical translations to the parton degrees of freedom recover the expected translation fractionalization in the bosonic FCI without projective symmetry class assignment. These results establish HyperDet wavefunction as a promising framework for both variational ground-state searches and phase-diagram explorations across strongly correlated phases, and for providing theoretical insights by connecting the optimized wavefunction with parton microscopics and field-theory descriptions.

X-ray flares from Sgr~A* span broad ranges in duration, fluence, and luminosity, but their origin remains unsettled. We test whether standing shocks in low-angular-momentum magnetized accretion flows can provide a viable energy reservoir to account for these events. Using semi-analytic trans-magnetosonic shock solutions, we estimate the kinetic energy available in the downstream post-shock flow and compare it with the 25-year Chandra X-ray flare catalog. For each theoretical solution, we compute the required efficiency $\epsilon=E_{\rm data}/E_{\rm sh}$, where $E_{\rm data}$ is the observed radiated energy for each flare and $E_{\rm sh}$ is the available energy in the shocked flow. Notably, the weak flares require $\epsilon\sim10^{-3}$–$10^{-2}$, while moderate flares require a few percent. We perform the analyses for weakly and highly spinning cases, and the resulting weak-to-moderate flare energy budget remains unchanged. For the fiducial accretion rate and bolometric correction, the kinetic energy reservoir in standing shock is sufficient for the observed weak-to-moderate flare population, whereas the strongest events likely require higher efficiency which can be mediated via additional magnetic energy dissipation channel.

Minimal dark matter extended to include a Majorana and a Dirac multiplet coupled through the Higgs — the HC-MDM model — provides a compelling and predictive framework. We show that in certain limits of this model, the mass splitting and the inelastic interaction are representation-independent, while the thermal-relic masses are representation-dependent. We then show that this model can account for the high-energy recoil event recently reported by LUX-ZEPLIN (LZ) while also respecting thermal-relic, elastic-scattering, and solar-capture constraints. Generic inelastic DM models do not connect all these tests and generic Higgsino models do not survive them.

We present the first QCD determination of an energy-dependent form factor for a two-hadron scattering state. In particular, we calculate the QCD contribution to the forward electromagnetic $\pi^+\pi^+ + \gamma\to\pi^+\pi^+$ amplitude at $m_\pi\approx 400$~MeV using lattice QCD. Because lattice calculations are performed in a finite Euclidean spacetime, where asymptotic scattering states are absent, this amplitude cannot be accessed directly from correlation functions. Instead, we can constrain this and related amplitudes nonperturbatively using a finite-volume formalism that requires two ingredients: the discrete finite-volume spectrum and finite-volume matrix elements of the electromagnetic current. We calculate three-point correlation functions coupling $\pi^+\pi^+$ finite-volume states and extract the corresponding electromagnetic matrix elements. Combining these results with the previously determined spectrum, we constrain the infinite-volume $\pi^+\pi^+ + \gamma\to\pi^+\pi^+$ amplitude in the forward limit. Using constraints from Lorentz symmetry, unitarity, and analyticity, we describe this amplitude in terms of a single real-valued energy-dependent two-hadron form factor. The resulting amplitude and form factor agree with the Ward-Takahashi identity across all energies and moving frames considered, providing the first QCD validation of this finite-volume approach and a pathway toward first-principles studies of the electromagnetic structure and electroweak responses of resonances and multi-hadron bound states.

This paper is the third and final article in a series of papers constructing the canonical conformally invariant metric on the set of loops of the conformal loop ensemble (CLE) with critical parameter $\kappa=4$. The previous two articles construct, as a subsequential limit of the renormalized graph metric on the loops of CLE$_\kappa$ as $\kappa \downarrow 4$, a conformally invariant, local metric on the loops of a CLE$_4$ whose metric ball growth from the domain boundary coincides with the uniform exploration of Werner and Wu. In this paper, we establish that this metric is uniquely characterized by its properties, as are its geodesics, and that it is a measurable function of the CLE$_4$. In particular, we show that the renormalized CLE$_\kappa$ graph metric converges as $\kappa \downarrow 4$ without passing to a subsequence. A key step in the proof is to show that the metric is determined by the geodesics from each loop to the domain boundary, which are in turn determined by the uniform exploration; this representation will have important applications in future work.

We continue our study of the conformal loop ensemble (CLE) with parameter $\kappa=4$, the critical threshold at or below which the loops are simple and disjoint, touching neither each other nor the domain boundary. This paper is the second in a series of three establishing that the loops of a CLE$_4$ uniquely determine a conformally invariant, local, and geodesic metric such that the metric ball growth from the domain boundary coincides with the uniform exploration of Werner and Wu. In this second paper, we prove the existence of geodesics, showing that any geodesic between two loops is supported on the CLE$_4$ loops (off a set of Hausdorff dimension zero) and does not intersect the domain boundary. Along the way, we establish sharp quantitative estimates for the CLE$_4$ metric geometry, including exponential tail bounds for rectangle distances and multi-scale four-arm SLE$_4$ non-intersection bounds for metric balls.

We consider the conformal loop ensemble (CLE) with the parameter $\kappa=4$, the critical value at or below which the loops are simple and do not intersect each other or the domain boundary. We show that the loops of a CLE$_4$ uniquely determine a conformally invariant, local, and geodesic metric so that the metric ball growth from the domain boundary coincides with the uniform exploration of Werner and Wu. This metric was previously constructed in unpublished work of Sheffield, Watson, and Wu. Our approach differs in that we show that the metric arises as the renormalized limit of the graph metric on CLE$_\kappa$ loops as $\kappa \downarrow 4$. In this first paper in a series of three, we prove that the subsequential limits exist and define a non-trivial conformally invariant metric on CLE$_4$ which is local and such that the metric ball growth from the boundary is given by the uniform exploration of Werner and Wu. In subsequent work, we will show that the subsequential limit exists as a true limit.

We study four-dimensional axion wormholes in the Lorentzian mini-superspace path integral using dual scalar and three-form flux formulations. We analyze this duality for generic metric boundary conditions and real lapse integration contour, and show that it holds on any background, including complex ones. With the Dirichlet condition on the metric, the fixed-flux path integral is evaluated exactly. In the Euclidean regime, saddle geometries organize into same-side and cross-throat segments of the Giddings-Strominger (GS) wormhole, depending on whether the two boundaries lie on the same or opposite sides of the throat. A Picard-Lefschetz analysis in the covering plane of lapse reveals that the cross-throat saddle has vanishing intersection number, and therefore does not contribute. In the asymptotically flat limit, it corresponds to the imaginary wormhole that saturates the imaginary distance bound (IDB). The same conclusion follows independently on the scalar side of the duality, and is confirmed by the exact amplitude. Replacing the Dirichlet condition with a one-parameter Neumann condition, the cross-throat saddle that leads to the imaginary wormholes remains irrelevant for the physical lift of the contour. This purely imaginary parameter characterizing the Neumann condition interpolates continuously between the half- and complete-wormhole geometries. Convergence of the sum over fixed-charge sectors imposes a corresponding interpolating bound not only on the imaginary part of the boundary axion but also on the parameter characterizing the Neumann boundary condition. An independent analysis based on the KSW criterion reproduces exactly the same bound, emphasizing its compatibility with the IDB.

The moving lens (ML) effect is a secondary anisotropy of the cosmic microwave background (CMB) generated by the transverse motion of gravitational potentials, providing a direct probe of the large-scale cosmic velocity field. Its detection relies on cross-correlating a CMB map with the transverse galaxy momentum field, constructed from the galaxy overdensity and a velocity field reconstructed from it. Restricting the reconstruction to large-scale modes strongly suppresses contamination from small-scale astrophysical foregrounds while preserving the ML signal. In this work, we develop a theoretical framework for the ML estimator and its foreground contamination. We show that the signal and foregrounds have a distinct dependence on the direction of the long-wavelength mode represented by the reconstructed galaxy velocity. In the squeezed limit enforced by the velocity reconstruction filter, the bispectrum sourcing the foreground correlation becomes independent of this direction, causing its leading contribution to vanish after angular averaging. In turn, the ML signal survives by matching this directional dependence, with its amplitude reduced only by the filtered velocity variance. Using the halo model, we derive the leading corrections beyond the squeezed limit and show that the residual contamination remains parametrically suppressed. Finally, we model the cross-correlation exactly in the curved sky, and show that it is sourced solely by the longitudinal component of the galaxy momentum field, in the form of a spin-1 $E$-mode, with all other contributions either strongly suppressed on small scales or exactly zero.

Quantum benchmarks provide compact measures of performance that are important for evaluating and comparing quantum systems. Circuit-level benchmarks are particularly valuable because they capture the accumulated effects of noise across interacting operations, but existing approaches may require structured gate sets and costly compilation, classical simulation of reference outputs, or subsystem decompositions that do not capture full-register behavior. We introduce Error Per Circuit Layer (EPCL), an overlap-based circuit-level benchmark that estimates an effective layer polarization by applying identical random circuits to two disjoint quantum registers and measuring the overlap between their output states as a function of circuit depth. EPCL avoids classical simulation of ideal output distributions and recovery to a known reference state, and is compatible with arbitrary gate sets, including non-Clifford gates. We derive the expected overlap decay under an ensemble-averaged depolarizing model and identify the assumptions under which the fitted decay parameter represents an effective layer polarization. Numerical simulations show that EPCL recovers the predicted polarization under weak local stochastic noise and remains well described by a single-exponential decay at stronger stochastic noise levels. The simulations further show that coherent errors associated with fixed entangling layers may require Pauli twirling or randomized compiling to produce the expected decay, while inter-register correlations contribute an additional covariance term to the measured overlap. Finally, experiments on IBM quantum hardware demonstrate clear EPCL decay in 8- and 16-qubit implementations. These results support EPCL as a method for measuring aggregate register performance without requiring classical simulation of ideal circuit outputs or restriction to structured gate sets.

We characterise the accretion rate properties of radio-detected AGN by combining deep radio and X-ray observations of the Boötes field. We used deep international LOFAR telescope observations to identify 2840 radio-AGN across $0.3 < z \leq 2$, divided into samples that are complete in radio luminosity. We further split this sample into four different classes: radio-quiet AGN (RQ-AGN), high-excitation radio galaxies (HERGs), and low-excitation radio galaxies (LERGs) hosted by star-forming (SF-LERGs) and quiescent galaxies (Q-LERGs). Through performing X-ray stacking, we determined the average X-ray luminosities, $L_{\rm{X, 2-10\,keV}}$ and average specific X-ray luminosities, $\lambda_{sL_{X}}$ (X-ray luminosity scaled by the stellar mass; a proxy for the accretion rate). We studied how these X-ray properties depend on radio luminosity, stellar mass, and redshift for each of the four AGN classes. We found that the LERGs, regardless of their star-formation activity, show significantly lower $L_{\rm{X, 2-10\,keV}}$ and $\lambda_{sL_{X}}$ than both HERGs and RQ-AGN across all redshifts. The average X-ray luminosities for the HERGs, RQ-AGN, and SF-LERGs typically increase with redshift, which may be associated with the increased cold gas fractions at earlier times, resulting in more enhanced black hole accretion. The average X-ray luminosities show weak-to-no correlation with radio luminosity at a given redshift, suggesting that the physical processes producing the X-ray and radio emission may not be coupled on spatial and/or temporal scales.

We present lattice QCD results for the CP violating pion-nucleon coupling $\bar{g}_0$ induced by the QCD $\overline\Theta$ term from the analysis of three 2+1+1-flavor ensembles generated with highly improved staggered quarks (HISQ) by the MILC collaboration. These ensembles are at lattice spacing $a\approx 0.09~\text{fm}$ and pion masses of 313, 226 and 138 MeV, respectively. The coupling $\bar{g}_0$ is extracted in two ways. First, from the matrix element of the correlation between the pesudoscalar current and the topological charge evaluated between the nucleon ground state. The data for correlation functions with both the pseudoscalar and axial vector exhibit large contamination from the $N\pi$ excited state. We show that these can be controlled at the leading order using chiral perturbation theory ($\chi$PT) and the axial Ward identity (AWI, also called the partially conserved axial current (PCAC) relation). The result after removing the $N\pi$ contamination and extrapolating to the physical pion mass is, however, noisy: $\bar{g}_0/(2F_\pi)=-7(63)\times 10^{-3} \,{\overline{\Theta}}$. The more precise result $\bar{g}_0/(2F_\pi)=17.4(1.9)\times 10^{-3} \,{\overline{\Theta}}$ is obtained using low energy effective field theory methods or equivalently the AWI. Since contamination from the $N\pi$ excited states arises in the calculation of many nucleon matrix elements, we give an extended discussion on them and the use of the AWI for controlling them in the calculation of $\bar g_0$.

Quantum thermalization explains how an isolated many-body system naturally evolves towards a thermal state, rendering information about the initial conditions inaccessible to local measurements. This is precisely the mechanism utilized in quantum error correction, where information is protected by design through a nonlocal encoding. In this work, we leverage this connection to port the rigorous framework of (approximate) quantum error correction to the study of quantum thermalization. Treating typical late-time states as codewords, we characterize the error-correcting properties of generic thermalizing dynamics. We numerically uncover a universal relationship between the encoding rate, distance, and thermal entropy density of the emergent code. At infinite temperature, this universal curve saturates the quantum Singleton bound, achieving the same optimal limit as Haar-random codes. At finite temperature, we introduce a code family based on the Scrooge ensemble, the natural thermal analogue of the Haar ensemble, and prove it saturates the entropic quantum Singleton bound, establishing this family as optimal within entropic constraints. Our extracted universal curve independently saturates this same bound, revealing that finite-temperature thermalization is itself optimal. Finally, we show how conserved quantities limit the error-correcting behavior of thermalization: codewords with differing energies, or other conserved charges, leak only classical information, and correctability persists until the difference reaches the scale of thermal fluctuations. Our results reveal a universal optimal coding structure in thermalizing dynamics, while introducing new optimal codes that achieve fundamental limits of approximate quantum error correction.

Non-local magic quantifies the non-stabilizerness beyond the local choice of basis. Its evaluation is a hard problem requiring optimization over local unitaries. Here, we show that for the log-stabilizer fidelity this optimization admits an exact closed-form analytic solution depending only on the Schmidt spectrum. We then address the open problem of non-stabilizerness of mixed states by introducing the magic of purification and show that it naturally induces a resource theory whose free states are the states with zero stabilizer entropy. For the log-stabilizer fidelity, the magic of purification admits a distance-based formulation in terms of the Uhlmann fidelity. We prove that non-local magic coincides with the minimum magic of purification along the unitary orbit of the reduced density operator. This framework introduces non-local magic as the relevant resource for non-trivial steering and the characterization of entangling and non-stabilizer resources in measurements. These results provide both an efficient analytical characterization and a mixed-state resource-theoretic interpretation of non-local magic.

Motivated by predictions that globular clusters associated with nearby giant elliptical galaxies are prime environments for detecting fast radio bursts (FRBs) from magnetars, we report on a targeted high-sensitivity search across five local massive elliptical galaxies. We utilized the GREENBURST single-pulse search pipeline and the VEGAS backend on the Green Bank Telescope (GBT) to conduct an L-band (1.4 GHz) survey for FRBs in each target environment. We discovered FRB 20240817A in the direction of M49 (NGC 4472) which has a pulse width of 15 ms, a signal-to-noise ratio of 13, and a dispersion measure (DM) of $983~\rm{cm}^{-3}$ pc. Although a Bayesian spatial association framework initially flags M49 as the host, carefully accounting for the foreground electron column contributions from the Milky Way and both the Virgo intracluster medium and M49's hot gaseous halo ($\sim300-400~\rm{cm}^{-3}$ pc combined) strongly disfavours a physical connection. We conclude that FRB 20240817A is a background event. We also identified a repeating cluster of three low-significance pulses from the direction of M49 at a physically plausible DM of $150-160~\rm{cm}^{-3}$ pc. Accounting for the fraction of each target's extended globular cluster distribution observed, the absence of unambiguous, host-localized bursts allows us to place a joint upper limit on the intrinsic burst rate of a single active source within these systems of $R_0 < 0.028~\rm{hr}^{-1}$ (and an integrated rate limit of $<1.0$~hr$^{-1}$ for M49), lowering previous upper limits and suggesting that magnetar formation within dynamical clusters is less efficient than previously assumed.

Open-system lattice gauge theory (LGT) has so far been developed predominantly in Abelian settings, leaving open how genuinely non-Abelian gauge structure reshapes dissipative real-time dynamics. Here, we study a $1+1$D SU(2) Yang–Mills LGT with dynamical matter coupled to a thermal scalar environment through a gauge-preserving Lindblad evolution, which we solve using tensor networks. Starting from a quark–antiquark pair connected by a chromoelectric flux string, we find that the thermal medium melts the string by delocalizing the color charges and screening the flux; on resonance, this dissipative melting competes with and delays coherent string breaking. The thermalization time is non-monotonic in the environment coupling, decreasing through environment-assisted transport at weak dissipation before increasing in a quantum-Zeno regime. In the strong-dephasing limit, a Schrieffer–Wolff expansion maps the dynamics to a classical exclusion process and yields the Liouvillian thermalization time analytically. Beyond these generic open-system effects, the non-Abelian matter structure produces a systematic mesonic bias in the steady state, while the thermalization time decreases with temperature, in contrast to the Abelian Schwinger model trend and in qualitative agreement with pNRQCD studies of the quark–gluon plasma. These results establish a gauge-preserving framework for thermalization and string dynamics in open non-Abelian lattice gauge theories.

Understanding real-time string dynamics in three spatial dimensions is essential for connecting quantum simulations of lattice gauge theories (LGTs) to the physical dimensionality of QED and QCD, where transverse fluctuations and competing local processes proliferate. We present the first real-time simulations of string breaking in $3+1$D lattice quantum electrodynamics. Using tree tensor networks, we simulate the quench dynamics of electric flux strings in a $3\!+\!1$D U(1) LGT with dynamical matter. At strong coupling, the string breaks resonantly at a sharp resonance condition of mass and gauge couplings, converting electric energy into matter–antimatter pairs that screen the static charges. Off resonance, we classify all competing channels—pair production, string deformations and extensions, and flux loops—whose multiplicity, extensive for pair production and flux loops, depletes the string sector even far from resonance. A channel-resolved perturbation theory quantitatively reproduces these dynamics and their Fourier spectrum. Our results establish diagnostics and benchmarks for upcoming quantum simulators of higher-dimensional LGTs.

A scalar field non-minimally coupled to gravity can be the driver of cosmic acceleration. Such a non-minimal coupling (NMC) can produce a non-zero gravitational-wave (GW) friction function $\alpha_M(z)$, which modifies the luminosity distance inferred from GW sources relative to its electromagnetic counterpart. We use a particular NMC scalar-tensor model, that explains time-varying dark energy in good alignment with DESI, to predict $\alpha_M(z)$ and the expected GW/EM luminosity-distance ratio $D_L^{\rm GW}/D_L^{\rm EM}$, and map it onto two common parametrizations—the $c_M$ and the $(\Xi_0,n)$ models. We find $c_M = -0.5\pm 0.2$ and $\Xi_0 = 0.88\pm 0.05$, $n=3.2\pm 0.3$, both consistent with GWTC-5 constraints at the $\lesssim 1\sigma$ level. This consistency is mostly driven by current large uncertainties in GW data, which lead to measurements consistent with both $\Lambda$CDM and the NMC model. By contrast, the dark energy constraints derived from analyzing cosmological data, under the common parametric scalar-tensor model using $\alpha_M(z)=c_M\Omega_\Lambda(z)/\Omega_{\Lambda 0}$ and the CPL parametrized equation of state $w_0w_a$, are in $2.2\sigma$ ($3.6\sigma$) tension with the NMC predictions for the $c_M$ ($w_0w_a$) parameter. We confirm that, in order to avoid cosmological instabilities, this parametrized model imposes strong implicit priors that are incompatible with physically-motivated scalar-tensor models when dark energy is dynamical.

In this work, we constructed a new metric describing a rotating cosmological black hole with electric and magnetic charges in the presence of quintessence dark energy, where the cosmological constant and quintessence are associated with external matter. Starting from a Schwarzschild-type metric and considering all energy contributions in the function $f(r)$, we introduced rotation through the Newman–Janis algorithm using a unique and general complexification rule, avoiding possible ambiguities. Assuming that the metric satisfies the Einstein field equations with matter, we calculate the event horizon condition, the total stress–energy tensor $T_{\mu\nu}$, and the Kretschmann and Ricci scalars. We also analyze the influence of the cosmological constant $\Lambda$ and quintessence parameter $\alpha$ on the event horizon and ergosphere. In the limit $\alpha \rightarrow 0$, the scalar curvature differs from the vacuum result, $R \neq -4\Lambda$, while the singularity region remains unchanged. Finally, we investigate the angular and rotational velocities of a test particle, as well as the energy conditions, through the energy density and pressures required for the existence of this black hole solution.

The application of silicate glasses in severe service environments requires a precise evaluation of structural strength under mechanical loads and surface tribological conditions. Because glass strength is governed by surface flaws and microcracks rather than being an intrinsic material property, residual surface compression fields, balanced by interior tensile zones, are widely implemented to inhibit flaw opening. Rather than relying on conventional allowable stress criteria to establish product acceptance, this study adopts a fracture mechanics framework based on the stress intensity factor KI and fundamental material limits: the critical stress intensity factor KIC for rapid fracture and the threshold stress intensity factor KIth for time-delayed static fatigue failure. Using the Weight Function Method (WFM), KI is evaluated across generic surface flaw depths for two-dimensional continuous (2D-Continuous) surface cracks subjected to non-uniform internal residual stress fields and external loads. Flaw stability criteria are established for both zero-risk and moderate-risk design methodologies. Finally, the interaction and superposition of externally applied mechanical and thermal stresses with internal residual stress fields are evaluated.