Papers

To explore the pathways toward establishing a global quantum network, we investigate several link architectures for transatlantic quantum entanglement distribution over a 6,500 km ground distance. We define free-space link configurations involving satellites and stratospheric high altitude platforms (HAPs), using today's technology and without relying on quantum memories and repeaters. Considering link budgets, space radiation, orbital characteristics, and system complexity we find that a hybrid architecture consisting of an entangled photon source located on a low Earth orbit (LEO) satellite supported by two passive optical relays located on HAPs provides the overall highest entanglement distribution rate. In addition, the satellite HAP architecture offers practical advantages in payload design and launch requirements, and the ability to lower the weather-related link interruptions assuming some maneuverability of HAPs. Overall, this hybrid configuration yields on the order of 5X10^6 secure key bits per year using 30 cm aperture ground receivers, nearly two orders of magnitude higher than achievable with a single MEO satellite and 1 m aperture ground receivers. Our results highlight the major benefits of hybrid satellite HAP architectures by reducing system complexity while enabling scalable and more accessible long-range quantum communication networks.

Evaporating black holes can leave distinct imprints on gravitational wave (GW) backgrounds. We show that black hole populations with finite width mass distributions exhibit a universal late time evolution governed by the evaporation dynamics rather than the details of the initial mass distribution, leading to a characteristic power law suppression of the induced GWs. We demonstrate this for a broad class of mass functions in primordial black hole (PBH) scenarios featuring an early Universe matter-dominated era, and identify the suppression of PBH-induced GWs found for critical collapse distributions as a manifestation of this general phenomenon. Our results establish a direct connection between the asymptotic GW spectrum and the underlying law of black hole evaporation.

Immersed boundary methods (IBMs) are widely used to simulate flows around complex geometries and moving bodies, but they often involve a trade-off between precision and computational efficiency. Eulerian formulations require special treatments for moving walls and may generate spurious force oscillations, whereas Lagrangian formulations can suffer from slip errors at the immersed surfaces. We propose a novel sharp-interface IBM for incompressible flows involving moving, deformable, and arbitrary-thickness bodies. The method combines a fast tagging algorithm, a two-sided Eulerian forcing strategy, and a consistent mass correction that reduces the splitting error of fractional-step schemes, while preserving the structure of the discrete Laplacian operator. This formulation retains the efficiency of direct Poisson solvers, thus avoiding the overhead of cut-cell, multigrid, and projection-based approaches. The method naturally handles moving boundaries, and yields small transpiration errors with second-order accuracy in the enforcement of the no-slip condition. Numerical tests using rigid, deformable, turbulent, and biologically inspired flows demonstrate the accuracy, robustness, and efficiency of the method, without compromising computational cost.

We predict a fundamentally new superconducting state in superconductor/antiferromagnet heterostructures with Ising spin–orbit coupling: proximity-induced orbital antiferromagnetism. In this state, the order parameter acquires a periodic phase modulation locked to the magnetic lattice, generating atomic-scale loop currents with opposite orbital moments on neighboring unit cells. Its emergence requires at least three nonequivalent magnetic sublattices per unit cell and finite spin–orbit coupling. Using NbSe$_2$/MnPS$_3$ as a concrete example, we combine first-principles and Bogoliubov–de Gennes calculations to demonstrate that the proximity-induced exchange field leads to robust phase modulation. Unlike FFLO and helical states, the phase gradient is atomic-scale, the state is current-carrying, and it remains uniquely stable over the full parameter range. The state manifests as characteristic finite-energy dips in the local density of states, accessible by STM.

Dedekind's problem counts monotone Boolean functions, equivalently downsets of a Boolean lattice. We recast this enumeration as a finite layer-ratio reconstruction problem for the Whitney numbers of the ranked ideal lattice. An exact adjacent-layer double count expresses each layer ratio through local averages of the number of addable elements and the number of removable elements. Reversible fixed-layer Markov chains estimate these averages and hence estimate the Dedekind number $M(n)$. Backtests at $M(8)$ and $M(9)$ calibrate seed-level variability under the fixed protocol and measure the observed Monte Carlo budget scaling. The resulting estimate probes the Whitney-number sequence of the ideal lattice. Although these rows have previously been described empirically as unimodal, the high-precision $n=9$ estimate has a shallow two-shoulder feature around the central rank, contrary to that empirical description; $n=11$ and $n=13$ center-window estimates show a larger-contrast analogous pattern. The protocol estimate for $M(10)$ is \[ \widehat M(10)=(8.9360\pm0.0010)\times 10^{78}, \] where the displayed uncertainty is the budget-based forecast scale from the cross-$n$ scaling law under the production budget.

Tropospheric ozone (O3) is a key greenhouse gas and atmospheric oxidant, yet its sources in the remote troposphere remain strongly debated. Observation-based tracer analyses suggest that O3 attributed to biomass burning is much greater than that from fossil fuel sources (by a factor of ~2-10), contradicting state-of-the-art global models. Here we show that this discrepancy primarily arises from the strong sensitivity of tracer methods to differences in tracer lifetimes, especially after extended transport to the remote regions. To resolve this discrepancy, we develop a deep learning (DL) framework that synthesizes global observations and chemical transport model simulations. The DL approach accurately infers source contributions and reveals that fossil fuel emissions contribute over three times more O3 to the remote troposphere than biomass burning. Our findings underscore that phasing out fossil fuels remains the most powerful lever for mitigating remote tropospheric ozone.

The Monte Carlo method, applied to lattice quantum field theory, gives access to Euclidean correlation functions with well-understood error bars. Recovering the observables one cares about, such as the spectral density, requires solving an ill-posed inverse problem, usually tackled with heuristics that lose rigorous control of the error. Instead of trying to find the “best” spectral density $\rho(\omega)$, we ask how small or large linear functionals $\int_{\mathbb{R}^+} G(\omega) \rho(\omega) \mathrm{d} \omega$ of it can be, given the Monte Carlo data and the reflection positivity of the lattice action. This is a convex but infinite-dimensional problem. We show how its dual can be rigorously relaxed into a hierarchy of finite semidefinite programs, solvable with standard solvers and enjoying strong convergence guarantees. The resulting bounds are rigorous even when the relaxation is not tight, and converge quickly to the regime where the error is entirely dominated by Monte Carlo statistics. The method also flags implausible Monte Carlo data, for instance underestimated error bars, through an infeasibility certificate. We demonstrate it on lattice $\phi^4$ theory in two dimensions.

The Mpemba effect refers to faster relaxation of states that are initially farther from equilibrium, yet its characterization is often tied to a chosen distance or resource measure. We introduce resource-Markovianity, an extended concept of quantum Markovianity to quantum resource theories, and formulate the resource Mpemba effect operationally as the breaking of resource-Markovianity by a relaxation operation. This yields a measure-independent operational characterization of resource Mpemba effects in general resource theories, together with quantitative characterizations based on resource-non-Markovianity measures. We illustrate the framework with the Mpemba effect for distinguishability of states, due to its relation to quantum Markovianity, and with the thermomajorization Mpemba effect from an operational perspective. These results reveal a deep interplay between quantum resources, non-Markovianity, and the Mpemba effect.

We study static neutron stars in an algebraic sector of Poincaré gauge gravity with parity-even and parity-odd quadratic torsion invariants. Since torsion is non-propagating, the contorsion equation is algebraic and can be solved in terms of the spin current. For a Weyssenhoff fluid satisfying the Frenkel condition, the metric field equations reduce to ordinary Riemannian Einstein equations sourced by an effective fluid containing spin-squared corrections. We derive the effective energy density, radial pressure, and tangential pressure, allowing both isotropic and anisotropic spin correlations. In contrast with Einstein–Cartan theory, the coefficient of the effective spin-spin interaction is not fixed, but depends on the dimensionless quadratic-torsion couplings. In the Einstein–Cartan limit, using the metric definition of the stress-energy tensor, the unpolarized spin contribution gives $w_{\mathrm{spin}}=-1/3$. We then derive the corresponding modified Tolman–Oppenheimer–Volkoff equations and solve them numerically using the DD2 equation of state. For the positive effective spin-spin coupling branch considered here, the torsion correction makes the stellar configurations more compact, lowers the maximum mass, and reduces the binding energy relative to the general-relativistic sequence. For the smooth weak-polarization profiles considered, spin-correlation anisotropy has only a negligible effect on the mass–radius relation.

We develop a general framework for investigating the influence of topological defects on the local characteristics of a quantum scalar field in a warped geometry background. The Ricci tensor and curvature scalar are decomposed into contributions from the warp factor, the radial geometry and the angular defect structure. For an arbitrary curvature coupling parameter, the field equation is separated into independent radial, angular and warp-coordinate parts. A complete set of normalized mode functions is obtained for general values of the angular deficit parameters. The general formalism is applied to several specific cases, such as conformally flat warped spacetimes, generalized cosmic strings, global monopoles and anti-de Sitter (AdS)-type warped geometries. The Hadamard two-point function is then evaluated for a global monopole in AdS spacetime using the obtained mode functions.

Using the finite-temperature heat kernel method, we compute the gauge-invariant effective Lagrangian up to dimension-six for massive hot scalar QED. We propose two complementary methods: integrating out heavy modes at finite temperature, and deriving the finite-temperature heat kernel coefficients from the zero-temperature ones. We show that in the static limit, both lead to the same three-dimensional effective operators. We also compute the gauge-invariant Coleman-Weinberg effective potential for a constant background at finite temperature. We further examine how the Polyakov loop modifies the matching coefficients and assess its impact together with the higher-dimensional operators on the thermodynamics of cosmological first-order phase transitions, which in turn can affect an associated gravitational-wave spectrum.

Hard safety filters are increasingly placed downstream of learned controllers to guarantee constraint satisfaction at run time. Yet a filtered controller that never violates a constraint may still have learned nothing about safety: the filter can silently repair an incompetent upstream policy, so that post-filter success measures the filter, not the policy. We argue that safe policy learning should ask who earns the safety - the policy or its protective layers - and we make this question measurable. We introduce Intervention-Aware Variational Quantum Differentiable Predictive Control (IA-VQC-DPC), which (i) trains a compact variational quantum circuit (VQC) policy under a primal-dual intervention budget that penalizes reliance on a differentiable Control-Barrier-Function (CBF) projection, and (ii) is evaluated with a safety-attribution protocol that decomposes the executed-trajectory correction into a CBF term and a deployment runtime-guard term, and stress-tests the policy with guard-off evaluation. On closed-loop, high-fidelity BOPTEST building-control emulators (5 seeds, 60 episodes per method), intervention-aware training significantly lowers the quantum policy's raw pre-filter violation and total safety-layer reliance (both p < 10^-4) with no significant energy regression; at an equal approximately 400-parameter budget the quantum policy is significantly safer and more comfortable than a matched classical policy. Guard-off evaluation confirms the improvement is policy-level and exposes a valuable negative result: a learned differentiable energy head is only safe when paired with a distribution-aware runtime guard. The attribution protocol is general beyond quantum policies and buildings.

We present a detailed study of the spatial distribution and chemical composition of interstellar ices toward six Class 0 protostars (HOPS-56, HOPS-60, HOPS-73, HOPS-91, HOPS-96, and HOPS-108) in the Orion A molecular cloud. Using high-resolution spectroscopic data from the JWST NIRspec and MIRI MRS instruments (4.3 - 8.1 $\mu$m), we have constructed the first pixel by pixel absorption maps with a resolution of $\sim$100~AU for key ice species, including $^{13}$CO$_2$, OCN$^-$, CO, H$_2$O, NH$_4^+$, and H$_2$CO. CH$_4$ and OCS were analyzed toward the continuum peaks. The column densities were derived by fitting the observed spectra with laboratory ice analogs. We employed radiative transfer modeling, which confirmed the reliability of our column density estimates within the protostellar envelopes. Our analysis reveals significant variations in ice abundances and distributions, reflecting the physical structure and energetic processes within the envelopes. Specifically, we observe the influence of protostellar heating and outflows on the ice mantles, most notably in HOPS-60. The total ice composition is consistent with astrochemical models and covers $\sim$90% of observed ice inventory suggesting that ice is primarily formed during the prestellar stage and subsequently inherited by the protostellar envelope. Based on the abundance relative to water, the sources can be categorized into two distinct groups, possibly indicating evolutionary differences or variations in envelope density and temperature profiles.

Understanding the dynamical properties of quantum systems is an essential task in quantum computing, quantum control, and many-body physics. Tools such as representation theory and Lie theory provide crucial information on reachability and computational power. However, this information can be difficult to access exactly or compute efficiently for arbitrary generating sets. Here we focus on the setting of Pauli strings, which satisfy numerous exceptional properties that simplify the problem. We find deep connections between Pauli Lie algebras and certain subgroups of the Clifford group generated by transvections, through the symplectic properties of the Pauli strings. This allows us to give an invariant-based perspective on these objects and their reachability, in the language of Pauli orbits, symmetries, and invariant subspaces. The invariant-based approach provides efficient algorithms for identifying Lie algebras and orbits, as well as a simple framework for analyzing structured Pauli generating sets. We also show in an elementary way that Clifford subgroups generated by transvections provide 3-designs for the corresponding Pauli Lie groups. We illustrate the framework through structured examples from variational quantum algorithms, restricted quantum computation, many-body systems, and random circuits.

A fraction of the electromagnetic power used to generate and heat the plasma in helicon sources and electrodeless plasma thrusters can leak into the outer expansion region, interacting with the plasma in the magnetic nozzle and affecting the performance of the device. This work analyzes the properties of the plasma in a convergent-divergent magnetic nozzle when right-hand polarized waves of varying amplitude propagate into it. This is accomplished with a 1D3V fully-implicit, Vlasov-Darwin particle-in-cell model of the collisionless ion and electron plasma in a magnetic tube. The code exactly conserves charge locally and energy globally. It features a nonuniform grid and an enhanced substepping routine for the macroparticle trajectories. The requirement that the expansion be current-free is satisfied thanks to linear closed-loop controllers on the injection and downstream boundary conditions. Wave heating increases the electron perpendicular temperature, especially in the vicinity of an electron cyclotron resonance surface, always present inside the magnetic nozzle of a helicon device. The energized electrons become anisotropic, and drive a more pronounced potential drop and a higher ion acceleration than in the absence of waves, at the expense of the wave power. The computed moments of the ion and electron distributions reveal the dominant balance of the electron thermal terms, electrostatic terms, and ion inertial terms in the momentum and energy equations. Wave heating helps populate otherwise-inaccessible regions of the electron phase space and modifies the doubly-trapped electron population found in the purely electrostatic case. The overall efficiency of the magnetic nozzle increases mildly at low wave power, but drops quickly as it is increased beyond a threshold, as part of the energy is wasted...

We propose and study all-multiplicity building blocks for tree-level string amplitudes in AdS. These are worldsheet integrals obtained by dressing the corresponding flat-space disc and sphere integrals with multivariable multiple polylogarithms and their single-valued analogues, respectively. We derive monodromy relations for the open-string building blocks and a KLT factorisation for their closed-string counterparts. This extends the non-commutative AdS uplift of lower-point flat-space structures to general $n$-point kinematics.

We present a dispersive amplitude analysis of the low-energy $\pi^0\pi^0$ system in the radiative decay $J/\psi\to\gamma\pi^0\pi^0$, using the mass-independent BESIII $0^{++}$ and $2^{++}$ intensities, the total spectrum, and the measured $0^{++}-2^{++}$ $E1$ phase difference. The isoscalar $S$-wave is described by a coupled-channel $\pi\pi/K\bar K$ Muskhelishvili-Omnès representation, which implements the strong final-state interactions associated with the $f_0(500)$ and $f_0(980)$. The $D$-wave is treated with a single-channel $\pi\pi$ Muskhelishvili-Omnès representation, where we identify all kinematic constraints of helicity amplitudes before transforming them to the experimental $E1$, $M2$, and $E3$ multipoles. Smooth short-distance production of a pseudoscalar-meson pair is encoded in subtraction polynomials, while left-hand-cut effects are estimated and found to be numerically subleading. We identify the negative solution of the BESIII $0^{++}-2^{++}$ $E1$ phase ambiguity, after using the modulo-$\pi$ freedom of production amplitudes, as the phase solution compatible with unitarity constraints, showing that the measured phase information can be accommodated with the Omnès phase motion without requiring large additional phases. By normalizing the BESIII intensities with the extracted branching fraction, we fix the absolute scale of the fitted amplitudes, making them suitable as input for future dispersive studies of two-pion contributions to gravitational form factors.

In this work, we study a model problem involving a point particle spiraling into a non-rotating black hole in higher-derivative theories of gravity. In such theories, both the background spacetime and the generation and propagation of gravitational waves differ from those in General Relativity. We develop a modified Teukolsky formalism to describe gravitational waves sourced by the point particle and, as an illustrative example, compute the resulting fluxes to the black hole horizon and null infinity for a cubic gravity theory. The formalism is constructed in a way that can be naturally extended to rotating black holes. These results represent essential steps to build extreme mass-ratio-inspiral waveforms in modified gravity theories, which may also be rescaled to approximate waveforms from comparable-mass binary black hole systems, analogous to existing approaches in General Relativity.

Observing the physical world is a foundational pursuit in science. In the quantum realm, however, observation necessitates a fundamental quantum-to-classical conversion: destructive measurements irreversibly project quantum states into classical data, inevitably incurring a loss of information. What physical principles govern this information loss, and how can we construct optimal measurements to maximize the readout? Here, we address these questions by establishing an intrinsic relationship between readout capability–quantified by the ratio of accessible classical Fisher information to the total quantum Fisher information (QFI), and measurement complexity–defined as the quantum circuit depth required prior to projection. Remarkably, we uncover a sudden emergence of observability: a sharp hidden-to-visible transition driven entirely by measurement complexity. We rigorously prove that below critical depth thresholds–$\Theta((\log n)^{1/\delta})$ for $\delta$-dimensional architectures and $\Theta(\log\log n)$ for all-to-all connectivity–readout capability decays exponentially with system size $n$, rendering the quantum information fundamentally inaccessible. Surprisingly, immediately above this threshold, the system enters a visible regime: we demonstrate that randomized measurements universally recover a constant fraction of the QFI using approximate unitary 3-designs, for which we explicitly develop optimal-depth circuit constructions tailored to finite-dimensional architectures. By unveiling the fundamental scaling laws and transitions that govern quantum observation, our results delineate definitive resource boundaries for quantum learning, state certification, and quantum metrology.

We present a variational formulation of the random phase approximation (RPA) that places density functional theory (DFT), linear-response time-dependent density functional theory (LR-TDDFT), one-body reduced density matrix functional theory (1RDMFT), and Green's function many-body perturbation theory (MBPT) into a common source-variable hierarchy. The central claim is that a broad class of RPA constructions can be organized, independently of any one problem-specific formula, diagrammatic resummation, or small-amplitude equation of motion, as closure approximations to the exact Hessian of an effective functional. In this language, exact linear response is governed by the Hessian of the corresponding effective functional, while RPA is obtained by retaining a reference contribution together with an explicit interaction kernel and discarding the irreducible remainder. The hierarchy has two independent enrichments of the density-level description. One may enlarge the static local density to a time-dependent density, giving the dynamical density channel of LR-TDDFT, or enlarge it to an equal-time bilocal one-body reduced density matrix, giving the static bilocal channel of 1RDMFT. The Green's function level combines both enrichments, since the one-particle Green's function is bilocal in both space and time. This picture clarifies the relation between DFT, LR-TDDFT, 1RDMFT, and MBPT through exact forward reductions and source restrictions, while emphasizing that the corresponding RPA closures need not commute under projection. The hierarchy also distinguishes the local branch-wise Legendre geometry common to all four levels from the stronger global convex duality that may emerge only in source sectors possessing additional positivity and global regularity.

The Einstein-de Haas (EdH) effect describes the emergence of collective rotation driven by spin alignment under an external magnetic field. We investigate this effect in a dynamically expanding quark-gluon plasma (QGP) using a quasiparticle model (QPM). We compute the EdH-induced angular velocity $\omega_{\mathrm{EdH}}$ as a function of temperature, proper time, and fireball radius. Our results show that $\omega_{\mathrm{EdH}}$ grows with proper time and is consequently suppressed at higher temperatures. Near the QGP crossover temperature, $\omega_{\mathrm{EdH}}$ attains a substantial, non-negligible magnitude. We identify a nontrivial crossing between the strong and weak magnetic field regimes that reflects the competition between spin alignment and the energy required to sustain orbital motion. This nontrivial crossing temperature separates a spin-dominated regime from an inertia-dominated regime of magnetic field-induced rotation. These findings establish the EdH effect as a manifestation of angular momentum conservation in magnetized QCD matter.

Rydberg atoms possess strong electric dipole transitions and tunable energy levels, making them promising candidates for microwave to optical conversion on integrated superconducting atom chips. Achieving strong coupling of the atoms to e.g. the microwave field of an on-chip resonator requires placing the atoms within tens of micrometers from the chip surface. However, inhomogeneous stray electric fields originating from the surface can induce position-dependent Stark forces, resulting in atomic motion and leading to time-dependent shifts of the Rydberg energy levels. We experimentally investigate these effects using time-of-flight and spectroscopic techniques, observing substantial level shifts and signal loss attributable to field-induced atomic motion. A theoretical model incorporating an exponentially decaying surface field with a superimposed bias accurately reproduces the observed dynamics. To mitigate the level shift, we introduce a Stark echo sequence that dynamically reverses the force. This approach suppresses the atomic motion and maintains the atomic resonance. The method relies solely on global field control and is compatible with atom-resonator coupling architectures, providing a robust strategy for preserving coherence of Rydberg atoms in inhomogeneous electric fields near surfaces.

Lattice simulations provide the thermodynamics of quantum chromodynamics (QCD) as a function of the temperature, at zero-to-moderate values of the baryonic chemical potential. However, the contribution of single hadronic species cannot be directly isolated from lattice calculations. In this work, we find linear combinations of up to fourth order susceptibilities which isolate the contribution of hadrons to the QCD pressure according to their baryon number $B$, electric charge $Q$ and strangeness $S$ content. These combinations are valid, provided that the thermodynamics of a strongly-interacting gas in the low-temperature regime can be modeled as a gas of non-interacting hadrons and their resonances. Finally, we test the validity of these linear combinations in the Hadron Resonance Gas (HRG) model and compare them to available lattice QCD results, using continuum-estimated susceptibilities.

Responses to perturbations are key to understanding physical systems. The ability to contrast such responses by comparing how a system reacts under slightly different conditions provides a mechanism for learning. Here, we introduce Perturbative Contrastive Physical Learning (PCPL), a general framework in which learning emerges from measurable contrasts between physical states produced by controlled changes to inputs, boundary conditions, parameters, or interpreter functions. PCPL unifies and extends prior approaches: Equilibrium Propagation is rooted in contrasts between free and nudged equilibria in energy-based systems, while Frequency Propagation corresponds to contrasts extracted from sinusoidally driven, frequency-demodulated responses. We show that contrast-driven updates can reflect either local sensitivities or global inverse-problem structure, yet do not require centralized gradient computation. Instead, effective learning geometry emerges implicitly from the system's own physical response, allowing learning behavior to arise without an external processor or explicit backpropagation. We demonstrate PCPL in two platforms: (i) spring networks that update bond stiffness using measured displacements and forces, and (ii) continuous-variable photonic circuits trained via x quadrature measurements and finite-difference estimates of the Jacobian. Both platforms successfully learn classification tasks. We further show that a continuous-variable photonic circuit can be trained to implement analog multiplication, illustrating a step toward more autonomous physical learning systems.

Microwave-induced resistance oscillations (MIROs) occur when a 2D electron gas is subjected to radiation of frequency $\omega = 2 \pi f$ and varying magnetic field $B$. MIROs are periodic in $1/B$, with the period determined by the radiation frequency $\omega$, and their amplitude scales with the radiation power. Stepping from single-photon transitions between Landau levels, MIROs are found on the low-field side of the cyclotron resonance, $\omega_c \lesssim \omega$, where $\omega_c$ is the cyclotron frequency. Here, we report on another class of magneto resistance oscillations, which are induced by high-intensity radiation in the radio frequency range and occur at $\omega_c \gg \omega$. These oscillations are independent of frequency $\omega$, can be either $1/B$ or $1/B^2$-periodic, and their period is controlled by the radiation electric field. We further show that using a displacement model in the limit of short-range (“sharp”) disorder we can extract the radiation field and the width of the cyclotron resonance.

We construct the double-current deformations of two-dimensional quantum field theories whose partition functions have background gauge-field anomalies. Extending the path integral construction of [1], we couple the seed theory to dynamical gauge fields and compact Stueckelberg fields and insert parallel transport in the anomaly line bundle. The deformed partition function then has the same anomaly as the undeformed one. For flat background gauge fields, the Stueckelberg non-zero modes localize the dynamical gauge fields to flat connections, reducing the deformation to a finite-dimensional holonomy integral. We derive the integral kernel on the torus and its higher-genus generalization. For the compact boson, or equivalently the Abelian $U(1)$ WZW model, the kernel gives a Gaussian transform of the torus partition function: at zero background the spectrum is obtained by $k\to K_\lambda$, while contact terms and spectral-flow data remain controlled by the original anomaly. As anomaly-free massive examples, we apply the kernel to massive complex bosons and massive Dirac fermions, for which the finite-volume spectra are obtained from the undeformed twisted spectra by charge-dependent shifts of the twists. We also formulate the anomaly-compatible non-Abelian and homogeneous Yang-Baxter generalization.

Many works have attempted to estimate the correlation and integral timescales associated with turbulent fluctuations in the solar wind, which are interpreted as length scales based on Taylor's~Hypothesis. However, accurate estimates of these timescales from spacecraft observations heavily rely on the accurate estimation of autocorrelation functions (ACF), which have been recently shown to depend strongly on the interval length used to estimate them. In this Letter, we show that this dependence on interval length may be artificial because common ACF estimators do not correctly capture the long-lag behavior of the true ACF of the underlying turbulence. We introduce a new ergodicity-based methodology to unambiguously estimate the integral timescale, and a new ACF estimator with better ergodic convergence than current ones. Due to its ergodic properties, the new ACF estimator properly captures the long-lag behavior, and is independent of the interval length. We use this approach to estimate the integral and correlation scales of magnetic fluctuations in the solar wind near $1~{\rm au}$.

Using the open source MPI-AMRVAC framework, we study oscillatory reconnection in a laboratory plasma, which occurs when a magnetic null is perturbed by incoming fast magnetoacoustic waves driven by an alternating current. The magnetic null region collapses to first form a $y$-directed current sheet that later changes its orientation to the $x$-direction. The $x$-directed current sheet has smaller enhanced thermal pressure and out-of-plane current than the $y$-directed current sheet. The Hall effect produces an out-of-plane plasma flow that evolves with a time lag with respect to the enhanced thermal pressure and out-of-plane current density. Increasing the amplitude of the alternating current produces higher thermal pressure, out-of-plane current density, and out-of-plane plasma flow, while the first peaks of thermal pressure and out-of-plane current density occur earlier.

We study feed-forward ReLU networks with fixed readout and quadratic loss, and rewrite gradient descent as a collective dynamics of activation fields and conjugate fields on the training set. Working to first order in the learning rate inside a fixed activation chamber, we derive explicitly the one-, two- and three-hidden-layer cases, and then give the arbitrary-depth recursion. For one hidden layer the activation dynamics closes directly and the residual update is governed by the product of an input Gram matrix and a co-activation/backpropagation Gram matrix. For two hidden layers a conjugate field is required, but no nontrivial pullback Gram metric has yet appeared. For three hidden layers the first weight-induced pullback Gram metric enters the conjugate-field dynamics. At arbitrary depth, activation variations propagate forward through a recursive response operator \(\cU_\ell^{\alpha\beta}\), while conjugate-field variations propagate backward through an effective transport operator \(\cM_\ell^{\alpha\beta}\). Their contractions reconstruct a layerwise residual kernel \[ K_{\alpha\beta}^{(L)}=\sum_{\ell=1}^{L}Q_{\alpha\beta}^{(\ell-1)}S_{\alpha\beta}^{(\ell)}. \] The resulting description exposes a duality between push-forward and pullback transport across every layer cut, and identifies the first Gram metrics as the lowest nontrivial terms in a broader hierarchy of activation-conditioned transport operators. We deliberately stop at the level of collective fields, conjugate fields, residual kernels and cut-wise transport metrics, leaving the later tensorial geometric formulation outside the scope of this paper.

Training parameterised quantum circuits (PQCs) on quantum hardware is bottlenecked by the measurement cost of gradient estimation, which under the parameter-shift rule scales linearly in the number of trainable parameters and dominates the total shot budget of training at scale. In this work, we propose a framework of forward gradient estimators for PQCs, based on the forward mode of automatic differentiation, that yields an unbiased estimator of the gradient by averaging a freely tunable number of random directional derivatives and recovers SPSA, random coordinate descent, and the parameter-shift rule as limiting cases, with no ancilla qubits or controlled-gate overhead. We prove that stochastic quantum forward gradient descent converges under standard assumptions, with an explicit second-moment expansion that interpolates between the single-direction extreme of SPSA and the full-gradient extreme of parameter-shift. Within this framework we derive QUIVER (Quantum Iterative V-adaptive Estimator Rule), an adaptive optimiser for parameterised circuits whose update rule follows from a closed-form minimum measurement-cost allocation. We show numerically that forward gradients train Hamming-weight-preserving orthogonal quantum neural networks with up to 60 qubits and 1770 parameters on the ECG5000 and MNIST datasets orders of magnitude more efficiently than the parameter-shift rule. We also demonstrate that our proposed QUIVER optimiser can outperform iCANS and gCANS measurement-frugal optimisers on optimisation problems using the quantum approximate optimisation algorithm and quantum simulation with the variational quantum eigensolver.