Papers

The geometry of quantum states has emerged as a key ingredient in understanding the linear and nonlinear responses of quantum materials. To date, however, the connection between geometry and nonlinear response is best understood for clean, noninteracting systems at zero temperature. In this work, we develop a theory of multi-state geometry for density matrices and use it to derive sum rules for second-order rectification, making no assumptions about the strength of disorder or interactions. We first show that perturbation theory for thermal density matrices gives rise to two dual information-theoretic connections and an almost complex structure. We introduce a complex, quantum generalization of the Amari-Chentsov tensor of classical information theory, the cQAC tensor, which captures the multi-state geometry of the perturbed density matrix. We derive a zero-temperature sum rule for the frequency-integrated DC rectification response of an insulator as a difference between a ground state third cumulant and the complex distortion tensor, a multi-state geometric quantity built from the cQAC tensor. This generalizes known single-particle sum rules for the shift and nonlinear Hall currents to many-body systems and general perturbations. Specializing to the shift current, we resolve the geometric contribution for multiband insulators into particle-like and hole-like terms. We verify the sum rule numerically in a generalized Kane-Mele model, finding that the geometric contribution can dominate the integrated response. Finally, we show that although the splitting of the sum rule into cumulant and geometric contributions does not survive at nonzero temperature, the measured sum rule for insulators differs from its zero-temperature form by corrections exponentially small in the gap, allowing low-temperature rectification measurements to probe the multi-state geometry of insulators.

We present a framework for decomposing solar-wind velocity distribution functions (VDFs) using orthogonal polynomial bases. We aim to establish a practical procedure for applying polynomial decompositions to in-situ spacecraft VDFs and to clarify how the resulting spectra of expansion-coefficient power can be used for noise reduction, VDF reconstruction, and diagnostics of velocity-space structure. The method represents measured VDF structure with Hermite-Hermite and Hermite-Laguerre expansions, providing a nonparametric description of departures from Maxwellians, such as anisotropy, skewness, beams, and suprathermal tails. Expansion coefficients are estimated by Gaussian-weighted quadrature after interpolation of measured distributions onto polynomial nodes. We demonstrate several applications of polynomial decomposition to Solar Orbiter, Parker Solar Probe, and Magnetospheric Multiscale 1 measurements, including noise identification through high-order spectral flattening, noise-reduced VDF reconstruction, and characterization of VDF-structure variations under different plasma conditions, e.g., turbulent solar-wind streams and shocks. For instance, noise-reduced reconstructed VDFs can provide smoother estimates of distinct ion populations and VDF gradients. Examples from solar-wind streams and collisionless-shock crossings further show that the resulting spectra respond to changes in parallel and perpendicular VDF structure, illustrating their potential for comparing kinetic modifications under different plasma conditions. Overall, orthogonal-polynomial decomposition provides a bridge between measured particle distributions and kinetic plasma physics by converting complex VDF morphology into quantitative velocity-space spectra.

Transcranial focused ultrasound is a non-invasive neuromodulation modality with millimetre-scale resolution, but its biophysical mechanism of action remains unresolved. Exposure is conventionally specified by transducer surface or derated focal pressure, quantities only indirectly related to what matters for therapy: which neurons fire and through which pathway. We address this gap with an end-to-end computational framework that maps a transcranial acoustic field to per-voxel neural firing maps registered to anatomy. The pipeline couples heterogeneous nonlinear full-wave acoustic propagation, viscoelastic shear-wave propagation, Pennes bioheat diffusion, a bilayer-mechanics conversion from tissue strain to membrane tension, and a multi-compartment Hodgkin-Huxley neuron carrying mechanosensitive, cavitation-coupled, calcium-coupled, thermosensitive, astrocytic-gliotransmitter, and mechanosensitive-synaptic pathways. Six candidate mechanisms are implemented as interchangeable components on a shared neuron model, so their firing predictions can be compared directly on the same field, and every numerical parameter is classified by source and bracketed by sensitivity analysis. We demonstrate the framework on a theta-burst sonication delivered through a micro-CT human-skull specimen targeting the left dorsal anterior cingulate cortex, predicting a focal firing zone of approximately 8,500 mm^3 at a focal thermal rise well within ITRUSST consensus safety envelopes. The principal output is a per-voxel firing-volume map resolved jointly with the acoustic, elastic, and thermal field histories that drive it, giving spatially resolved, falsifiable predictions that are testable against high-density extracellular recordings and support parameter estimation, cell-type-resolved mechanism identification, and quantitative safety assessment for ultrasound neuromodulation.

Rare fluctuations in physical systems depend on the detailed microphysics responsible for the fluctuations. In classical statistical systems, the large deviation principle has elucidated the role of semi-classics in describing this regime, and has simultaneously provided a the mathematical foundation of statistical mechanics. Large deviation theory for quantum system is considerably less developed. As all physical systems are fundamentally quantum mechanical, this leaves a major gap in our understanding of rare fluctuations relevant to statistical physics, cosmology, and more. In this paper, we develop the practical aspects of the theory of large deviations relevant for calculating rare events in physical systems from quantum walks to cosmology. We first analyze the case of the anharmonic oscillator coupled to a bath, showing explicitly how the system evolves from dominantly statistical (e.g. thermal) to quantum fluctuations. We then generalize these results, showing that the dominant rare fluctuations minimize the measurement-induced relative entropy. This perspective provides a thermodynamic description of a wide range of open quantum systems. We apply these results to random walks that arise in cosmology through stochastic inflation. We show that the evolution of the density matrix of long wavelength fields on a fixed de Sitter background breaks the KMS symmetry, giving rise to a stationary density matrix that does not respect detailed balance.

As quantum computing matures, there is an increasing need for deeper and longer experiments to characterize quantum devices precisely and higher circuit throughput to validate more domain applications. However, this need is hindered by a memory bottleneck at the quantum control system layer, arising from the limited capacity of on-chip block random-access memory (BRAM) and the non-deterministic latency of dynamic random-access memory (DRAM). To break this bottleneck, we present Ant-Q, a memory hierarchy design for the QubiC 2.0 control system that integrates DRAM with BRAM to support pipelined quantum circuit execution while keeping inter-circuit timing deterministic whenever each circuit outlasts the refill of the next. A switch between command buffers then takes a constant 134 ns and, inside a circuit, acts on the qubit as a 144 ns idle. On the bench, Ant-Q runs deep one- and two-qubit randomized benchmarking beyond the command capacity of the baseline. For circuits with at least 1000 shots, it reduces the time the board spends beyond the circuit execution from 18.91%-104.54% to at most 0.53% of the execution time, and it improves the board-level throughput of 30-circuit batches by 51.06% against a baseline with the same shared tables (59.90% against the stock baseline). On a transmon qubit, Ant-Q executes a 5101-Clifford sequence and acquires uninterrupted 100 s Ramsey records with 0.01 Hz frequency spacing. In simulations, these records detect 1/f frequency noise of 1.37 and 1.62 times lower spectral density than the same records split into the 2.048 s runs of the baseline. The measured spectra resolve no 1/f component and match the measurement floor from 0.1 to 100 Hz. Ant-Q has been merged into the open-source QubiC gateware and software.

The Fe I 5434.5 Å line is widely used as a non-magnetic reference due to its small effective Landé factor of $-0.014$. Nevertheless, this line can show significant non-zero Stokes $V$ polarization in active regions on the Sun. In this work, we study the distribution of magnetic fields in the sunspot observed on August 17, 2024 using the high-fidelity Stokes $I+V$ and $I-V$ spectra of three photospheric spectral lines of different magnetic sensitivity: Fe I 5434.5 Å, Ni I 5435.9 Å and Mn I 5432.5 Å. The observed splitting of the Stokes $I\pm V$ bisectors in the Fe I 5434.5 Å line follows the variation of the corresponding splitting in the two other spectral lines, indicating the presence of a spatial component with an extraordinarily strong magnetic field reaching 22 kG.

The object of investigation in this paper are the nonlinear equations of motion for two-dimensional inviscid water flows with piecewise constant density stratification in a three-layer fluid with a flat bottom, a free surface and two interfaces. We establish a Hamiltonian formulation for the nonlinear governing equations in this setup. The Hamiltonian of the system and the equations of motion of the surface and of the interfaces are expressed with the help of the Dirichlet-Neumann (DN) operators, which are introduced for each of the layers. Then, the linear equations for small amplitudes of the elevation of the surface and of the interfaces in the leading order are derived from which a bi-cubic equation for the dispersion relation is obtained, whose solutions are analysed. The six real solutions for the possible propagation speeds (three positive, related to right-moving waves and three negative, related to left-moving waves) have magnitudes of different order. Upper and lower bounds for the previously mentioned roots are also given in terms of the coefficients of the equation. Subsequently, approximate formulae for the propagation speeds are derived. The importance of the DN operators is further illustrated in a separate analysis of the three-layer model with flat surface (rigid lid). The full nonlinear evolution equations are expressed again in terms of the DN operators, and the equations in the linear regime and the weakly nonlinear propagation regime (the Boussinesq approximation) are derived by a proper expansion of the DN operators. Limits to the two-layer free surface model are obtained as well. The obtained results are applicable to internal waves in lakes and in the ocean as well as to laboratory experiments with three superimposed fluid layers.

Organometallic layered materials have emerged as promising single-atom catalysts for oxygen reduction and evolution reactions, but their practical use has been limited by insufficient electrochemical stability. Here, we present a density functional theory study clarifying the relationship between catalytic activity and stability in organometallic single-atom catalysts with metal-N$_4$ (MN$_4$) and metal-O$_4$ (MO$_4$) coordination. We compare graphene-embedded MN$_4$ motif and phthalocyanine-like frameworks with MO$_4$-coordination frameworks, including M$_4$(OHPTP)$_2$ and M$_3$(HHTP)$_2$ (M = Mn, Fe, Co, Ni, Cu, Zn). Stability is assessed by surface Pourbaix analysis, while activity is evaluated using the computational hydrogen electrode method. MN$_4$ systems show competitive overpotentials but suffer strong pH-dependent instability. In contrast, MO$_4$ frameworks exhibit enhanced robustness across wide pH ranges while maintaining good catalytic performance. A proposed stability descriptor enables direct comparison across systems, identifying MO$_4$ coordination structures, particularly M$_4$(OHPTP)$_2$ (M = Zn, Co) as optimal for balancing activity and stability in practical electrocatalysis.

Quantum data hiding asks how much distinguishing power can be lost when global measurements are restricted to local measurements and classical communication. In this work, we establish sharp results and improved bounds for several natural classes of restricted measurements. For bipartite systems on $\mathbb C^n\otimes\mathbb C^m$, we prove that the optimal data-hiding ratios against separable and LOCC measurements are both $\min\{n,m\}$. This result follows from a stronger result that, for every $2\le p\le\infty$, the largest centered Schatten $p$-ball whose associated binary measurements are implementable by finite-round LOCC has radius $\min\{n,m\}^{2/p-1}$. This strengthens the classic separable-ball theorems, while also providing an explicit finite-round LOCC implementation. For Alice-first one-way LOCC with Alice's local dimension equal to $n$, we prove that the optimal ratio is $(1+o(1))n$, with the upper bound obtained from a Gaussian rank-one POVM. For local operations without communication, we improve the universal upper bound to $(\pi\sqrt3/4+o(1))\min\{n,m\}$.

In this work we investigate the inversion accuracy of stellar magnetic fields through the analysis of spectropolarimetric data. We performed several noise free tests to untangle the impact among the atmospheric and magnetic parameters in the data analysis. Using a single spectral line, we found that under ideal scenario, without noise, the magnetic parameters can be recovered with very high accuracy, while some of the atmospheric ones show a considerable incertitude. If multi-line profiles are considered instead, then the accuracy of the recovered atmospheric parameters increases significantly. Nonetheless, it is quite common that for the inversion of stellar spectropolarimetric data, the atmospheric parameters and the stellar inclination angle of the star are fixed; we show that this procedure could induce very high errors in the inference of the magnetic properties, specially in what concerns to fix the inclination angle. We show that even small deviations from the true inclination angles could have as consequence that the recovery of the magnetic properties of the star are no longer reliable. This is because we demonstrate that given a set of Stokes profiles observed along the rotational phase, they can be satisfactorily fitted regardless of the assumed stellar inclination angle, thereby revealing a degeneracy in the solution. Although this work validates the solution generation solely for a de-centered dipolar geometry, a comparable degeneracy is anticipated when modeling the magnetic field with higher order spherical harmonics, an effect that remains to be formally characterized.

We apply time-reversal symmetry to quantum codes and show that it imposes parity selection rules on the physical error algebra. A time-reversal-invariant logical qubit on an odd number of spins is a Kramers doublet, forcing every even-weight Pauli to act as a scalar. Consequently, all even-weight Knill–Laflamme conditions hold automatically, so single-qubit error detection implies correction. We then reinterpret the Rains shadow enumerator through time reversal: each coefficient is a sum of error-resolved overlaps between a code and its time-reversed image.

The precision of transport observables can be bounded by the entropy production and the activity of the transport process via kinetic and thermokinetic uncertainty relations. In linear bosonic systems, such uncertainty relations can provide tight bounds when the activity is replaced by a local activity of the measurement contact of interest—even in the strong-coupling regime. How much nonlinearities (or interactions) impact the validity and predictiveness of these local bounds and how much this impact depends on the concrete definition of activity are open questions that we address for two experimentally relevant model systems, a harmonic oscillator network and the intrinsically nonlinear spin-boson model. We thereby provide experimentally testable predictions on how nonlinearities impact or even break local kinetic and thermokinetic precision bounds.

We develop a fully quantized theory of nonlinear Compton scattering driven by a single-mode quantum field. Exact quantum-Volkov states retain pump depletion, back-action, and final-state correlations through displaced or squeezed-displaced Fock-state ladders. A finite Fock-state pump produces discrete photon-transfer edges and a terminal spectral cutoff. In the bright, weakly depleted regime, the exact theory reduces to a Wigner-function weighted-average of scattering probabilities evaluated at fixed complex field amplitudes, with ordinary and generalized Bessel functions describing the harmonic structure for circular and linear polarization, respectively. For squeezed coherent light, the squeezing angle controls the high-energy emission through photon-number fluctuations.

Field theories whose potentials have noninteger power laws $\alpha$ have found many applications, but are often claimed to have no lift to quantum field theory except as effective models. We define quantum lifts by expanding the classical potential in Hermite polynomials and then normal ordering at a mass scale shifted by a parameter $\beta$. We find that when $\alpha>2$, for sufficiently large $\beta$, the vacuum state can be perturbatively expanded in usual Fock states. We apply this to the following problem. The $\sigma=4$ Pöschl-Teller model has a $\phi^{5/2}$ potential. As the third derivative of the potential diverges in each vacuum, one expects the three point interactions to diverge in the vacuum. The model's kink has three shape modes and the least bound mode extends so far into the vacuum that its probability of being excited by radiation apparently diverges. We show that a deformation $\beta$ of order the meson mass or larger is sufficient to tame this divergence, although it nonetheless results in an excitation probability which is enhanced by a $\beta$-dependent fractional power of the inverse coupling.

We benchmark electromagnetic transitions and moments (electric quadrupole and magnetic dipole) in angular-momentum projected-after-variation Hartree-Fock calculations against full configuration-interaction diagonalization results in a shell model basis. For such a simple approximation we find reasonably good agreement, including for many odd-$A$ and odd-odd nuclides. As previous work on excitation spectra found, results are frequently improved in cases with shape coexistence. Here we considered select cases from the $sd$- and $pf$-valences spaces. While electric quadrupole moments and transitions are, as one might expect, frequently (though not always) well reproduced, especially in even-even nuclides, magnetic dipole moments and transitions are overall better than expected. This continues the benchmarking of projected Hartree-Fock as a simple yet effective alternative to full configuration-interaction as well as an underlying foundation for many other many-body methods.

We establish an integral basis for the B-brane central charges of certain Calabi-Yau fourfold flops and derive exact expressions for their monodromies using the grade restriction rule and window categories of the associated gauged linear sigma models. The monodromy is interpreted as an EZ twist associated with the contraction of an exceptional surface onto a curve of conifold singularities. We further illustrate a decomposition of the EZ twist into spherical twists for families of splitting configurations of the sixtic Calabi-Yau fourfold and a complete intersection in grassmannian.

We compute and test analytic models for the plunging region dynamics, thermodynamics, and magnetic fields against dedicated 3D global general relativistic magnetohydrodynamics (MHD) simulations of thin accretion discs around black holes across the spin range, using the code ATHENAK. We find that the dynamics of the plunging fluid closely resembles that of a gravity-dominated geodesic plunge, with the best agreement at low spins. Additionally, we find good agreement between the thermodynamic framework and the simulated quantities across the spin range. Finally, we develop a new model for the magnetic fields in the plunging region that assumes a fixed geodesic inflow, into which the magnetic fields are frozen. Overall, our simulations are in good concordance with this model, albeit with some discrepancies that suggest a degree of non-ideal MHD dissipation. In addition, we investigate how the MHD stresses in the plunging region depend on the black hole spin, interpreting our results through the lens of our flux-freezing model. We find that the magnitude of the stress increases as the black hole spin is increased in the prograde direction. This question is of particular importance for observers who wish to determine the black hole spin from X-ray measurements of the inner accretion disc, since a low-stress, high-spin solution is degenerate with a high-stress, low-spin solution. The spin-stress relationship that we report is approximately orthogonal to the contour of degenerate spin-stress pairings, indicating that the degeneracy is not fundamental. We show this explicitly for the case of M33 X-7.

We study holographic entanglement entropy in 3-dimensional AdS gravity with conformal boundary conditions which fix the conformal class of the boundary metric and its extrinsic curvature, $K$, while leaving the Weyl mode dynamical. Extending Lewkowycz-Maldacena-Dong's replica construction, we derive the corresponding holographic entanglement entropy formula. We show that the fluctuating Weyl mode does not contribute additional entropy. The entropy of the full boundary is therefore the Bekenstein-Hawking entropy, and the entropy of a boundary subregion continues to obey the Ryu-Takayanagi prescription, namely, the area of a minimal surface divided by $4G_N$. We carry out explicit calculations for global AdS, rotating and non-rotating BTZ geometries. For an interval in AdS$_3$ we find that the $K$-dependent holographic entanglement entropy is governed by $c_m=\frac{3 \ell}{2 G_N}.$ For a thermal state at high conformal temperatures we find that, the entropy is governed by $c_{\rm eff}=\frac{3 \ell}{2 G_N} \frac{K \ell- \sqrt{K^2 \ell^2-4}}{2}$, the same effective central charge that governs the Cardy-like density of states, in agreement with previous results in the literature. Finally, we also compute the entanglement entropy directly from the conjectured dual boundary theory - a holographic CFT coupled with time-like Liouville theory and deformed by a marginal $T \bar{T}$ like operator - and find $S_{EE} =\frac{c_{\rm eff}}{3} \ln\!\left(\frac{2 R \sin\phi_0}{\epsilon}\right) .$ This result for the state with no operator insertions (vacuum state ), provides an independent boundary realization of $c_{\mathrm{eff}}$ while clarifying that this state is not the state dual to global AdS.

Scientific analyses increasingly use flexible neural networks, but their thousands of correlated parameters make it challenging to interpret the associated uncertainties. Here we develop a low-dimensional posterior for the fitted function itself, for scientific neural surrogates trained with second-order optimization. Linearizing the fitting procedure with respect to the randomized residual rows gives a measurement-to-function transport, the linear map, assembled from the converged Jacobians and Gauss–Newton curvature, that carries measurement perturbations into the function perturbations that refitting would produce. Its leading singular functions define coherent deformation modes. Independent Gaussian coefficients then generate smooth function draws, so that any derived quantity, including those requiring derivatives or integrals of the draw, inherits the posterior. The construction distinguishes repeated-experiment covariance from the local Gauss–Newton/Laplace posterior and propagates both to correlated quantities of scientific interest. The result is conditional on the fit's declared choices (architecture, hyperparameters, active set, and optimization branch), and every fit is certified as converged by checking that a further optimization step would change the fitted predictions by less than a chosen small fraction of the measurement errors. Our primary example is an 800-parameter phase-space distribution function fit for a mock stellar disk. Four uncertainty coordinates, two orders of magnitude fewer than the fitted parameters and stable under refinement of the force basis, capture 99% of the vertical-force posterior variance, and 4000 coherent draws propagate through the force, total-density, surface-density, and frequency calculations in 0.8s. The method provides a highly efficient route to uncertainty propagation for derivative-dependent scientific inference.

Starting from the Standard Model Lie algebra $\mathfrak{g}_{\mathrm{SM}} = \mathfrak{sl}_3 \oplus \mathfrak{sl}_2 \oplus \mathbb{C}$ sitting inside the complex Lie algebra $\mathfrak{e}_7$, we show how to decompose $\mathfrak{e}_7$ into the direct sum of a Lie subalgebra containing $\mathfrak{g}_{\mathrm{SM}}$ and three 32-dimensional subspaces, each of which forms the same representation of $\mathfrak{g}_{\mathrm{SM}}$ as one generation of fermions and their antiparticles. The setting is due to Nasmith, and much of the mathematics is that underlying the $\mathrm{E}_7$ generation unification of Kugo and Yanagida. New features include the derivation, in which as many results as possible rely only on the embedding $\mathfrak{g}_{\mathrm{SM}} \subset \mathfrak{e}_7$, and also the description of each 32-dimensional subspace as a copy of the exterior algebra $\Lambda\mathbb{C}^5$.

The inspiral and merger of two supermassive black holes (SMBHs) releases immense energy in low-frequency gravitational waves (GWs). Recent pulsar timing array (PTA) observations of the stochastic nHz GW background (GWB) are consistent with a SMBH binary origin. GW data from PTAs and from the upcoming Laser Interferometer Space Antenna (LISA) can probe late-stage binary evolution where electromagnetic constraints are scarce. However, the complexity of the relevant astrophysics necessitates a well optimized approach. I argue that a key physical quantity to constrain with PTAs is the orbital semi-major axis at which binary inspiral transitions from the astrophysical to the GW-dominated regime ($a_{\rm GW}$). This quantity should be treated as a free parameter in analysis of the GWB. Using this premise, I present a simple analytic framework for modeling SMBH binary inspiral in an "inside-out" fashion. At orbital separations slightly larger than $a_{\rm GW}$, a power-law scaling for the astrophysical inspiral timescale is assumed, while the outermost phase (prior to the PTA regime) is simply modeled via a delay time. I show that the GWB spectral shape and amplitude are most sensitive to $a_{\rm GW}$ (normalized to $10^9 M_{\odot}$, equal-mass binaries and expressed in gravitational units), with weaker dependence on the inner power-law index and the outer delay time. The GWB is largely insensitive to the mass and mass-ratio scaling of $a_{\rm GW}$ and to the boundary between the inner and outer astrophysical inspiral regimes. I compare with models for gas- and stellar-driven binary inspiral and discuss implications for LISA and for GW source parameter inference.

GW Orionis is a triple stellar system with a disk featuring three misaligned dust rings. We present ALMA molecular line data of CO isotopologues, revealing a streamer feeding the disk in $^{12}$CO and $^{13}$CO. Through multi-pointing observations, we find the streamer extends to $\sim30''$ on-sky ($\sim12,000$~AU) and estimate a mass of 1.6 M$_{\rm Jup}$ using $^{13}$CO. Fitting the morphology and kinematics of the streamer, we estimate the mass infall timescale of 0.04 Myrs and a mass infall rate of $3.6\times10^{-8}$~M$_{\odot}$~yr$^{-1}$, approximately an order of magnitude lower than the stellar accretion rate. Our best-fit trajectory shows that the streamer meets the disk at the outermost dust ring and that the streamer's angular momentum vector is closely aligned with this outermost ring within $\approx3^\circ$, in contrast to the $\approx32^\circ$ misalignment with the innermost ring, suggesting the streamer is the likely cause of the misalignment. However, the total angular momentum of the streamer is smaller than that of GW Ori's disk; this, together with the low accretion rate, indicates that we are probably witnessing the end stages of infall. Total Power observations reveal bright emission connecting the streamer to the surrounding star-forming region, with a projected distance falling well within the Bondi-Hoyle radius, implying the streamer could have originated through Bondi-Hoyle accretion as GW Ori moves through its natal cloud. Together, these results suggest that GW Ori remains dynamically linked to its parental cloud through ongoing accretion, with the streamer serving as the likely driver of its misaligned disk structure.

For more than three centuries, Newton's Second Law (F=ma) has governed mechanics with undisputed success, yet its epistemic authority has rested on empirical adequacy alone. That empirical contingency vanishes under two physical principles - the Principle of Excluded Perpetual Motion (PEPM) and the Weak Equivalence Principle (WEP) - from which the law emerges as a structural necessity of admissible mechanics. Under the PEPM constraint, Suppes' operational measurement protocol grounds gravitational mass and force as independent primitives. The fusion of Stevin's static and Galileo's kinematic inclined-plane analyses establishes F/a as a well-defined, object-intrinsic quantity - the operational definition of inertial mass. The WEP compels the equivalence of inertial and gravitational mass without presupposing Newton's Second Law. Substituting this equivalence into the definition of inertial mass yields the law as a theoretical identity between independently defined quantities. The derivation is anchored in gravity because weight uniquely bridges statics and kinematics, yet the result is independent of the underlying force mechanism. The derivation carries structural consequences: modified-inertia formulations of MOND are inadmissible under the PEPM-WEP constraint; the location-invariance of the Kibble-balance realization of the SI kilogram is secured on first principles; and under the PEPM alone, torsion-balance and free-fall experiments constitute equally direct tests of the WEP. More fundamentally, Newton's Second Law is not an irreducible axiom of mechanics, but a structural consequence of deeper physical principles: energy conservation and the Einstein Equivalence Principle.

We develop a phase space electronic structure view of the solid state, where electronic bands are parameterized by both nuclear position $\mathbf{Q}$ and nuclear momentum $\mathbf{\Pi}$ (rather than the standard practice of only $\mathbf{Q}$). Within this phase space, non-Born-Oppenheimer electronic structure context, we prove a nuclear wavevector ($\mathbf{q}$)-dependent version of Nafie's equality relating the change in electronic momentum as a function of nuclear momentum, $\partial \langle\mathbf{p}\rangle/\partial \mathbf{\Pi}_q$, to the change in electronic position as a function of nuclear position, $\partial \langle\mathbf{r}\rangle/\partial \mathbf{Q}_q$. Furthermore, we show how information about electron-phonon interactions, specifically nuclear-induced electronic momentum, can be extracted from simple band structure calculations – without Berry curvature calculations.

Topologically ordered phases naturally realize quantum error correction through nonlocal encoding of quantum information. More recently, conformal field theories have been shown to realize approximate quantum error-correcting codes, but such constructions generally require fine tuning to criticality. Here we introduce a family of approximate quantum error-correcting codes realized by the chiral edges of two-dimensional topologically ordered phases. The proposed encoding combines the robustness of a gapped topological bulk with the flexibility of gapless edge conformal field theories. To characterize its robustness, we study coherent-information loss under local erasure. We derive an exact expression relating coherent-information loss to relative entropy, reducing the recoverability problem to universal properties of the edge theory. This leads to power-law scaling of coherent-information loss with the size of the erased region. We further show that, for geometrically local erasures near one edge, the two-dimensional chiral edge code is at least as robust as the dimensionally reduced CFT code, and is strictly more robust in several representative examples. For Abelian code subspaces, we further construct a power-law-range recovery map supported on the erased region together with a power-law-range buffer; this recovery map depends only on the code subspace, not on the unknown encoded state. We provide numerical calculations for lattice realizations of compact free boson and Ising CFT examples that support the theoretical predictions of the power-law exponents.

Megamaser distances can be measured without using the traditional distance ladder. As such, they provide an independent probe of the local expansion rate, quantified by the Hubble constant $H_0$. We re-analyze megamaser distance and redshift data to obtain a new, more accurate, estimate of $H_0$. The main improvement in our analysis is the use of a new velocity field reconstruction to correct redshifts for peculiar velocities. This reconstruction utilizes constrained cosmological simulations in addition to redshift survey data to more accurately capture both coherent flows as well as nonGaussian individual galaxy motions. We argue that previous estimates of $H_0$ from megamaser data were susceptible to bias due to peculiar velocities. By correcting for peculiar motions using this new reconstruction we obtain a value of $H_0$ that is more consistent with the value from the Cosmic Microwave Background (CMB) than that of the distance ladder, although consistent with both, whereas previous results showed consistency with the distance ladder and tension with the CMB at greater than $2\sigma$. Our results suggest that the Hubble tension may be due to some heretofore undetermined systematic in the distance ladder rather than new physics.

We report the detection of an extended 21-cm parsec-scale \ion{H}{i} structure toward the Mira variable V420\,Vul using archival Galactic Arecibo L-band Feed Array survey data. The emission exhibits a spatially coherent but intensity-asymmetric morphology that nevertheless retains a globally symmetric kinematic profile centered near $v_{\mathrm{LSR}} \sim 47.6\,\mathrm{km\,s^{-1}}$. At an adopted distance of $\sim 1.9$\,kpc, the structure extends over $\sim 20$\,pc, implying a dynamical timescale of order $10^6$\,yr. Although the total \ion{H}{i} mass ($\sim 70\,\mathrm{M_\sun}$) indicates that the atomic gas reservoir is heavily dominated by the ambient interstellar medium rather than pristine stellar ejecta, the spatially resolved spectra and position-velocity diagrams reveal an underlying symmetric velocity framework centered on the star. We interpret this as the dynamical imprint of the stellar wind preferentially channeling through a porous ambient cloud, demonstrating that cohesive kinematic records of late-stage stellar mass loss can be preserved over parsec scales and megayear timescales despite dominant interstellar coupling.

Lorentz symmetry and gauge symmetry constitute the mathematical cornerstones of modern physics, yet their ultimate physical origins remain elusive. From the standpoint of a constructive interpretation, this paper demonstrates that both symmetry structures can emerge isomorphically from a unified classical source: dynamical constraints on wave-packet excitations in a continuous elastic substrate medium (SM). Neither symmetry is posited as fundamental, nor does their emergence rely on quantization. Three core results are established. First, taking the transverse wave speed of a homogeneous, isotropic SM as the benchmark under a conventionalist synchronization scheme, Minkowski-type spacetime arises isomorphically, with Lorentz transformations as effective coordinate transformations between inertial frames. This reinterprets the Michelson–Morley null result: observers are composite wave-packet excitations, and medium-induced kinematic corrections are encoded in their measurement frameworks. Second, for wave packets endowed with $SU(N)$ intrinsic symmetry, the requirement of identity invariance drives the SM to spontaneously generate gauge fields. This requires invariant equivalence classes of intrinsic states under propagation, yielding gauge structures isomorphic to Yang-Mills theory. The gauge group $SU(N)$ is uniquely determined by the number of stable normal modes supported by the medium. Third, through the same conventionalist measurement protocols, inhomogeneous distributions of the SM emerge isomorphically as curved spacetime geometry, governed by Einstein-type field equations from variational extremization of the medium's deformation free energy. This paper advances a unified interpretive account of the physical origin underlying the mathematical structures of both Relativity and the Standard Model.

Syndrome-measurement timing is usually treated as a fixed clock cycle of a quantum error-correcting code. For quantum memories, however, the inter-round interval is itself an optimizable control parameter: measuring too rarely allows idling errors to accumulate, whereas measuring too often introduces measurement-induced faults. We propose a phenomenological logical-noise model for this trade-off and analytically show that the optimal syndrome-measurement interval is inversely proportional to the code distance and that this produces an exponential reduction of logical-error rates in the distance relative to constant-interval schedules. Furthermore, for time-dependent idling noise, we develop an adaptive timing strategy based on the measured syndrome activity that outperforms every fixed-interval protocol, with largest gains for short but strong noise bursts. Simulations of rotated surface-code memories with matching decoding validate the phenomenological model, the distance-dependent optimum, and the adaptive-strategy improvement. Moreover, with the experimental noise parameters reported by Google in Nature 638 (2025), our model predicts reductions in logical-error rates per unit time of up to $40\%$.

Non-Gaussian states can exhibit large quantum Fisher information (QFI) in quantum sensing. In optical systems, however, its generation is often probabilistic via the boson-sampling type conditional operation and thus its generation rate is limited. This probabilistic generation of non-Gaussian resource should be taken into account for evaluation of the sensing performance. Then a natural question arising is whether the use of heralded probabilistic non-Gaussian states is better than that of the original deterministic Gaussian states for quantum sensing. In this paper, we answer to this question for single-parameter phase-estimation. By using photon-number conservation in passive linear optical systems, we show that heralded state preparation before parameter encoding can be mapped to a postselection problem after parameter encoding for phase estimation. This mapping allows the success probability of heralding to be included naturally in the metrological performance. We introduce an effective quantum Fisher information (EQFI), defined as the success-probability-weighted QFI of the heralded outputs, and prove that it cannot exceed the QFI of the original Gaussian inputs. The result highlights the importance of resource counting in quantum sensing toward better understanding of the resource efficient advantage of optical quantum sensing.