Papers

Casimir forces, arising from quantum and thermal fluctuations, depend strongly on the electromagnetic susceptibilities of the interacting materials. Here, we theoretically investigate the Casimir force between two graphene sheets separated by a nanometer-thin layer of liquid water. We find that deviations from the bulk case can be as large as 24 %, mostly due to the static susceptibility components. This effect does not decrease monotonically as a function of the layer thickness: it increases up to a maximum at 70 nm and it slowly declines to the bulk limit only at 1 micron. This is due to two competing effects: on one hand, the anisotropy decreases with the layer thickness; on the other hand, the relative contribution of the most anisotropic, static susceptibility components increases.

We study complex geodesic actions and heat-kernel resurgence on isotropic Heisenberg groups. For real endpoints with $r>0,y\ne0$, the nonzero finite singularities reached by analytic continuation of the minimizing-saddle Borel germ are exactly the finite complex action differences. For nonresonant endpoints, we construct row-finite directional Stokes operators and compute the positive-ray Stokes matrix and its logarithm explicitly; the primitive alien support can be strictly smaller than the full Borel singular support. Near the vertical axis, we obtain uniform two-term large-order asymptotics from the nearest Borel singularity. Cubic resonances admit uniform $A_2$ confluence formulas. We also identify the combination of resurgent sectors selected by the original Fourier contour. Positive Borel summation is exact at horizontal endpoints. At nonzero isotropic complex endpoints, no finite normal trajectories exist, but the signed vertical action lattice is the complete limiting spectrum. The action and Stokes structures are independent of the dimension on isotropic $H^n$.

Phase change materials (PCMs) can enable non-volatile optical memory through the large refractive index and extinction coefficient contrast between crystalline and amorphous states. Among them, $\mathrm{Sb}_{2}\mathrm{Se}_{3}$ combines low optical attenuation at telecom wavelengths, making it promising for low-loss programmable phase shifters. Its non-volatility is particularly useful for cryogenic systems, where power dissipation and thermal load constrain scalability. However, its optical properties at cryogenic temperatures remains poorly understood. Here, we report the first cryogenic optical characterization of $\mathrm{Sb}_{2}\mathrm{Se}_{3}$ integrated on a foundry silicon photonic platform from 4K to 300K for both crystalline and amorphous states. We observe that the magnitude of the thermo-optic coefficient decreases upon cooling, whereas the optical attenuation changes only weakly for both the amorphous and crystalline phases. We report the stability of the material upon repeated thermal cycling. These measurements provide the material parameters and stability required to design low-loss, non-volatile photonic memory elements for scalable cryogenic information processing.

Strong and weak symmetries and their spontaneous breaking distinguish different forms of symmetry and order in mixed states. We show that complete one- and two-point correlation functions, equivalently all two-site reduced density matrices, determine exact strong symmetry for continuous onsite unitary actions of connected groups: states with identical correlations have the same strong symmetry and character. We also present an algorithm to determine the maximal connected strong-symmetry sub-Lie group and its character from two-point correlations. Because such correlations are more accessible than full-state tomography, the algorithm is readily applicable to experiments ranging from condensed-matter systems to quantum simulators and circuits. We also identify group and representation-specific cases in which fewer correlations suffice.

In the framework of non-relativistic quantum chromodynamics (NRQCD), we systematically investigate the inclusive and exclusive production processes of spin-singlet \(^1S_0\) and spin-triplet \(^3S_1\) toponium at future muon colliders and in Pb–Pb ultraperipheral collisions (Pb–Pb UPC). Using the Coulomb-plus-linear potential and solving the Schrödinger equation, we obtain the wave function at the origin as $|R_{t\bar{t}}(0)|^2 = 2.507\ \text{GeV}^3$. The scattering cross sections and various kinematic distributions for two types of processes are calculated, and the corresponding event yields are estimated based on the expected integrated luminosities. Our study indicates that the detection prospects for toponium production through the aforementioned processes are unfavorable.

We develop a multiscale approach for incorporating molecular-scale transport information into computationally efficient models of ion transport through nanopores. A radially varying effective diffusion coefficient profile is fitted to radial conductivity profiles obtained from explicit-water molecular dynamics (MD) simulations. The fitting is performed within the NP+LEMC framework, which combines the Nernst–Planck equation with Local Equilibrium Monte Carlo to account for ion correlations beyond mean-field approximation. We apply the approach to NaCl, CaCl$_2$, and their mixtures in a negatively charged silica nanopore. The resulting diffusion coefficient profiles reproduce the radial current distributions of the MD simulations, including the strong suppression of ionic mobility near the pore wall that cannot be captured by a spatially constant diffusion coefficient inside the pore. NaCl and CaCl$_2$ exhibit qualitatively different transport behavior: the former is cation selective due to enhanced near-wall Na$^+$ conduction, whereas the latter shows weak anion selectivity because strongly bound Ca$^{2+}$ ions have strongly suppressed mobility near the surface. For NaCl–CaCl$_2$ mixtures, preferential Ca$^{2+}$ binding leads to nonlinear changes in ionic conductance. The approach establishes a bridge between experimentally relevant device behavior and computationally efficient reduced models, with explicit-water MD providing the molecular-scale information that can be incorporated into the effective transport coefficients.

Mobile interstitial atoms redistribute while defects migrate, complicating prediction of defect kinetics and leading to contradictory reports of acceleration and retardation. We formulate defect activation in a grand-canonical ensemble at fixed interstitial chemical potential and define a pathway free-energy landscape $\Delta G(\Lambda;T,\mu)$ and the corresponding activation free energy $\Delta G^{\ddagger}$. We compute these quantities using both hyperplane-constrained thermodynamic integration via a mean force relation and a two-state chemical-potential integration, denoted TSCPI. The latter requires sampling only the initial and transition states; a single chemical-potential integration then yields $\Delta G^{\ddagger}(T,\mu)$ across a wide $\mu$ range, enabling rapid mapping over temperature and chemical potential. Applied to vacancy diffusion in FCC, BCC, and HCP metals with H (including in plane and cross plane diffusion in Zr) and in BCC W with He, both free energy routes agree with diffusion coefficients from molecular dynamics mean square displacements. The resulting maps reveal regimes of suppression and enhancement, including a crossover from suppression to enhancement with increasing hydrogen concentration. A site occupancy analysis links barrier shifts to state dependent site spectrum changes and transferable interstitial interaction terms.

In an antiferromagnet, areas with different orientations of the antiferromagnetic Néel vector, which plays the role of the order parameter, can coexist, thus forming antiferromagnetic domains separated by domain walls. This suggests that antiferromagnets can possess the functionalities of magnetic storage media. Whether one can benefit from these functionalities crucially depends on the availability of efficient means for deterministic control of antiferromagnetic domain walls. Here, we demonstrate an approach to deterministically control domain walls in the van der Waals antiferromagnet Ni-doped $MnPS_3$ via dynamic engineering of the crystal lattice. By resonantly exciting a pair of nearly degenerate orthogonal infrared-active $A_u$ and $B_u$ phonon modes with circularly polarized mid-infrared light, we induce helicity-dependent reconfiguration of 180{\deg} antiferromagnetic domains, providing evidence for a phonon-induced effective field conjugate to the Néel order parameter. The domain kinetics exhibit a pronounced helicity asymmetry governed by the interplay between domain-wall elasticity and defect-mediated pinning, enabling small phonon-driven perturbations to accumulate into stable domain transformations. Our results establish dynamic lattice control and defect engineering as means for deterministic control of antiferromagnetic order.

We construct gauge-origami systems on the toric Calabi–Yau fourfold $\mathcal{C}\times\mathbb{C}$ from its brane brick model. Brick matchings and phase boundaries determine elementary D6- and D4-brane framings, respectively, realizing the magnificent-four, tetrahedron-instanton, and spiked-instanton sectors in a unified framed quiver quantum mechanics. We define their partition functions by Jeffrey–Kirwan residues and describe the fixed points in terms of colored BPS crystals. General gauge-origami configurations are obtained by combining these elementary sectors through their common fractional D0-brane quiver. This construction provides a first step toward gauge origami on general toric Calabi–Yau fourfolds.

Measurements of the angular distributions of Z boson-decay leptons at the Large Hadron Collider (LHC) are of interest in QCD studies and precision electroweak measurements. Z boson production at the LHC is dominated by quark-gluon processes and the quark-antiquark process accounts for only 40% of the cross section. We investigate the theoretical predictions (using the POWHEG-minnlops event generator) for the difference in the angular distributions of $ pp \to \gamma^{*}/Z \to \ell^+\ell^-$ ($ \mu^+\mu^-$ or $e^{+}e^{-}$) events produced via quark-antiquark, quark-gluon , and gluon-gluon processes. The study is done for proton-proton collisions at the Large Hadron Collider (LHC) at $\sqrt{s} = 13$ TeV. We investigate the angular coefficients $A_0$ and $A_2$ (for $\theta_{CS}$ and $\phi_{CS}$ distributions in the Collins-Soper frame) for the different processes as a function of the Z boson rapidity, transverse momentum and final state jet multiplicity, and propose how these can be investigated experimentally at the LHC.

In many soft-matter and biological systems, task completion relies on the cumulative arrival of multiple searchers rather than the speed of a single pioneer. The completion kinetics are therefore set not only by the first arrival, but by the full ordered sequence of first-passage times. Here, we determine how stochastic resetting optimizes these ordered arrivals for all arrival ranks. We construct an exact finite-$N$ reference for non-interacting Brownian searchers and obtain the mean ordered first-passage time $\langle T_{(k)} \rangle$ and its optimal resetting rate $r_k^*$. For searchers with identical initial conditions, $r_k^*$ increases monotonically with arrival rank and, with increasing population size, approaches the known large-$N$ quantile limit where a finite optimum appears only above a critical rank fraction $\phi_c \simeq 0.412$. Spatial heterogeneity qualitatively reorganizes this sequence, shifting its maximum from late to early ranks even without particle interactions. We then compare this baseline with Brownian colloid experiments, interacting active Brownian particles, and a collective autochemotactic search with persistent environmental memory. Across these systems, sensitivity to resetting increases strongly with arrival rank, while deviations from appropriate non-interacting references reveal the influence of direct interactions, finite return overhead, and environmental memory. Our results show that optimal resetting in multiparticle search is governed by the required completion rank and must be evaluated relative to protocol- and geometry-matched baselines.

This series of papers aims to establish a universal generalized Brillouin zone (GBZ) theory for higher-dimensional non-Hermitian systems. As the starting point of this series, we emphasize a fundamental question: while the conventional one-dimensional (1D) GBZ condition, $|\beta_p| = |\beta_{p+1}|$, is well known to fail in two dimensions, how does this breakdown actually occur as a system gradually crosses over from 1D to 2D? Investigating this question reveals that the existing 1D GBZ theory itself remains incomplete. In this first paper, we therefore systematically review the 1D spectral approach and clarify where the underlying difficulties lie. Our work identifies the key challenges that motivate the wavefunction approach developed in Paper~II.

Stellar associations are difficult clustering targets because position, kinematics and extinction carry different physical units, different uncertainties and different discriminatory power. We extend the Extended Minimum Spanning Tree (XMST) framework without forcing these observables into a single metric. Three-dimensional spatial connectivity first defines candidate parent structures (XMST-S1), transverse kinematics then tests those parents for dynamically distinct populations (XMST-S3), and visual extinction provides a final reddening refinement (XMST-S2). Across 1000 Monte Carlo realisations, XMST-S1 produced a better purity–completeness balance than the eight predefined three-dimensional HDBSCAN configurations tested, although neither method reliably separated a deliberately superimposed pair using spatial information alone. Applying kinematics before reddening increased mean Jaccard similarity to 0.8354 and resolved the overlapping pair in 98.6 per cent of realisations. The S3 null experiment produced only five accepted subdivisions among 106,265 tested groups. Across 1000 paired reddening-uncertainty realisations, increasing uncertainty reduced the mean number of accepted S2 subdivisions from 4.224 to 1.982, while mean Jaccard similarity changed only from 0.8074 to 0.7993. Direct XMST-S3 uncertainty tests showed negligible practical degradation for transverse-velocity errors up to $0.5~\mathrm{km\,s^{-1}}$ per component, with larger errors progressively suppressing kinematic refinement. In a label-blind repartition of 2,551 stars from 56 published OB associations, median best-match Jaccard similarity increased from 0.6535 after spatial clustering to 0.8861 after complete refinement, with 22 associations recovered identically. The main result is that physically different observables can refine an existing spatial hierarchy without redefining its me

Equilibrium phase transitions are conventionally categorized into first-order and continuous phase transitions. Far from equilibrium, many new transitions emerge during the real-time evolution of quantum systems. One such transition is the temporal entanglement transition (TET) characterized by the nonanalyticity of the entanglement spectrum. So far, all TETs occur through a linear crossing of the leading Schmidt levels in different symmetry sectors, resembling a first-order transition in equilibrium. A natural question is whether a continuous TET, featured by entanglement spectrum touching, is possible. In a periodically driven transverse $J_1$-$J_2$ Ising chain, we show that two such TETs can merge into a critical touching, where the leading levels meet tangentially without exchanging, realizing the temporal analog of a continuous phase transition. Near the critical frequency, the temporal separation of the two TETs vanishes continuously and its derivative with respect to frequency diverges, a nonanalytic signature that is absent in a single first-order TET. This finite-frequency touching arises from the interplay between a weak symmetry-preserving perturbation of the product initial state and Floquet corrections. Further extending the frequency scan reveals a second critical touching at a higher frequency, and the two critical frequencies enclose a finite window with no TET. These features can be understood from a second-order Floquet Hamiltonian and persist across a broad range of coupling ratios, establishing the critical touching as a distinct form of TET.

In this work, we construct models compatible with ACT constraints on inflation in the framework of $f\left(Q, \tilde R\right)$ gravity, with $f(R)$ gravity coupled to a scalar field. The $f\left(Q, \tilde R\right)$ theory is equivalent to $f(Q, B)$ gravity models or $f(Q, C)$ gravity where $B$ or $C$ is the difference between $Q$ and the scalar curvature $\tilde R$ in Einstein's gravity, so, $B=Q-\tilde R$ or $C=\tilde R - Q$. Using appropriate reconstruction techniques compatible with $f\left(Q, \tilde R\right)$ theory, we propose two functional behaviors of the Hubble rate $H$ that satisfy the constraints, and we construct models that realize these behaviors of the Hubble rate $H$ using $f\left(Q, \tilde R\right)$ gravity and $f(R)$ gravity coupled with a scalar field. We also discuss the reheating stage after inflation. Although the scenario of $f(R)$ gravity coupled with a scalar field is well-known, since the model can be rewritten in the form of Einstein's gravity coupled with two scalar fields, the non-trivial problem occurs in the $f\left(Q, \tilde R\right)$ gravity case, because the number of dynamical degrees of freedom in $f(Q)$ gravity is not settled.

Overcoming the approximately 60~mV/dec Boltzmann limit of the subthreshold swing remains a central challenge for low-power nanoelectronics. Negative-capacitance field-effect transistors address it by amplifying the channel potential, but their effectiveness is constrained by capacitance matching and by the quantum capacitance of conventional channels. Here we model a negative-capacitance bandgap-change field-effect transistor (NC-BCFET), in which the ferroelectric gate stack instead amplifies the electric field that opens the bandgap of the channel, using experimentally proven materials: bilayer graphene as a channel with an electrically tunable bandgap and Al$_{0.55}$Sc$_{0.45}$N as the negative-capacitance ferroelectric. Our self-consistent framework couples a four-band tight-binding Hamiltonian with GW-corrected screening, a quasistatic Landau–Devonshire ferroelectric response, and ballistic Landauer–Büttiker transport. Negative capacitance amplifies the interlayer potential difference, compressing the switching window 37-fold relative to a dielectric-gated control. At 300~K, the optimized NC-BCFET achieves a subthreshold swing of 15~mV/dec, four times below the Boltzmann limit, improving to 2.5~mV/dec at 100~K. The room-temperature on/off ratio is limited to $\sim 10^{2}$ by the bandgap of bilayer graphene. The concept extends directly to materials with larger field-tunable bandgaps, where deep subthermionic switching and high on/off ratios can be achieved together at room temperature.

The cosmic evolution of galactic bars offers key insights into the dynamical history of disk galaxies. However, studies of high-redshift bars are severely hampered by observational effects such as resolution degradation and surface brightness dimming. To quantify these biases and establish a robust methodology of bar detection and measurement for high-redshift galaxies, we develop an automated pipeline integrating isophotal ellipse fitting and Fourier decomposition. We benchmark its performance using a comprehensive set of mock observations generated by artificially redshifting high-quality images of local barred galaxies to match the background and resolution of HST ($z \approx 0.5-3$) and JWST ($z \approx 1-6$) observations. We find that applying standard bar detection criteria derived from local galaxies to high-redshift data results in a severe underestimation of the bar fraction, missing $>50%$ of bars at $z>0.5$ in HST imaging and a similar fraction at $z>2$ in JWST imaging. Using adaptive, redshift-dependent criteria optimized via mock data achieves recovery rates above $60%$ out to $z \approx 3$ for HST and $z \approx 6$ for JWST. The ellipse fitting method significantly outperforms Fourier decomposition in measurement reliability. While ellipse fitting systematically underestimates bar length by $\sim 4%$–$36%$ due to surface brightness dimming, this bias is consistent and correctable ($\sigma \approx 0.88$–$2.22$); in contrast, the Fourier method is prone to catastrophic failures ($\sigma \approx 2.40$–$6.14$) in the regime of low signal-to-noise ratio. We propose a standardized workflow that prioritizes mock-derived adaptive criteria and ellipse fitting, providing quantitative correction factors and empirical relations that enable future studies to recover intrinsic bar statistics from raw observations.

NLO simulations are essential for LHC physics analyses but are expensive, as they are not only slow but also lead to negative weights, which imply the need to simulate much larger samples of events. Folding is a powerful technique to reduce negative weights but is itself expensive. In this paper I propose “vectorized folding” as a new idea to speed up these calculations using SIMD and GPUs, and I present its CUDACPP-based implementation for MG5aMC in MadVfold, including its extension for unfolded NLO event generation. Preliminary results show overall speedups around 6x to 9x with folding and 3x without it. This work is based on a test-centric, LLM-assisted software development process.

Three dimensional Earth-Moon transfers usually consume more fuel than planar ones, but are needed depending on the latitude of the launch site and the desired inclination of the final lunar orbit. A systematic search of the optimal 3D transfers represents a true challenge due the dimension of the parameter set to span. In this paper, we propose a new method to design 3D transfers using a tangential velocity constraint for the burns, modeled using the overdetermined constraints technique based on the Theory of Functional Connections for an optimal search of solutions in a numerically efficient way. The developed method is applied here for a systematic study of optimal 3D Earth-Moon transfers, but could be used to design any type of 3D maneuvers.

We present a physics–informed neural solver for the generalized Falkner–Skan boundary-value problem that combines an exact boundary–admissible trial representation with adaptive regional residual balancing (ARRB). The three prescribed boundary conditions are embedded analytically, eliminating boundary-condition penalty terms while allowing the finite–domain streamfunction value and wall shear to be determined by the governing equation. The residual is divided into wall, middle, and tail regions, and a physical global residual is reconstructed from regional mean-squared errors using region-length fractions. Safeguarded exponential–moving–average inverse–gradient coefficients adaptively balance the regional contributions during Adam optimization. A deterministic 800-point residual monitor is used for checkpoint selection, followed by two deterministic L–BFGS stages minimizing the physical global residual. The method is tested on the Blasius, favourable-pressure–gradient Falkner–Skan, and Pohlhausen cases. For \((\beta_0,\beta_1)=(0.75,0.50)\), the predicted wall shear is \(f''(0)=0.8997161394\), compared with the finite-domain reference \(0.8997168085\), giving an absolute error of \(6.691\times10^{-7}\). The residual MSE is \(6.357\times10^{-9}\), while the relative \(L_2\) errors in \(f'\) and \(f''\) are \(2.848\times10^{-6}\) and \(4.188\times10^{-5}\). A matched single–seed ablation shows that ARRB reduces residual MSE by 52.81% relative to global–residual training and by 50.24% relative to equal-regional weighting. Wall–shear errors are reduced by 77.30% and 72.37%, respectively. These results support ARRB as an accuracy-oriented residual-conditioning strategy, while multi–seed experiments remain necessary to quantify optimization variability.

Background: During the navigation of Rosetta's first Earth flyby in 2005, a small yet unexplained asymptotic velocity increase was detected in the departing leg, necessitating inserting an artificial prograde delta-V at perigee in the orbit determination. Similar instances of this phenomenon have been observed in several missions. However, subsequent Rosetta Earth flybys did not exhibit this effect. Despite numerous investigations of the - so called Earth flyby anomaly - over the last decades, the underlying cause remains unresolved. Idea: To address the problem, we perform an Orbit Determination using ESOC's new system for Deep Space orbit determination, utilising the original radiometric tracking data and spacecraft model. This approach enables the incorporation of additional physical effects in the flight trajectory, with the aim of identifying the root cause of the anomaly. Results: We successfully reproduced the anomaly using the new orbit determination software. Subsequent analysis ruled out explanations involving Earth ephemeris errors, gravitational field modelling, relativistic contributions, and propagator configurations. Additional dynamical variations, such as the solar radiation pressure or albedo radiation, were evaluated but found insufficient to account for the observed discrepancy. Outlook: During investigations of Earth's albedo effect, a possible explanation for an artificial velocity increase was identified. Albedo-induced illumination on thermally sensitive spacecraft surfaces could have triggered outgassing, consistent in direction and magnitude with documented outgassing events during Rosetta's cruise phase. A detailed attitude analysis further strengthens this theory and provides conclusive results, also in comparison to Rosetta's other Earth flybys.

The influence of photon fields of local sources (LS) on the formation of the cosmic ray (CR) energy spectrum (E0) is considered. A model for the formation of irregularities in the CR spectrum, based on the local source model, is proposed. It is shown that the CR spectrum can be formed as a sum of partial spectra formed near local CR sources during the passage of primary cosmic radiation (PCR) through the photon fields of the sources. Local sources can be the most active stars of various types of variability in the stellar population, - from dwarfs to hypergiants. Studies have shown that the so-called "bump" near E0 = 100 PeV is formed in the photon fields of Mira-type variable stars, which are typically multiple stellar systems, consisting of a red giant and a white dwarf.

We propose that the $248\,\mathrm{keV}$ nuclear-recoil candidate reported by LUX–ZEPLIN can arise from the endothermic hyperfine excitation of composite dark matter. Rather than requiring two distinct dark-sector particles, the inelasticity of scattering arises from a hyperfine transition between the pseudoscalar and vector states of a single dark hadron. In a PQ-augmented dark QCD framework, the parity-conserving vacuum suppresses dangerous elastic scattering, while axion emission depletes the relic excited-state population. Endothermic excitation near the Galactic kinematic edge then naturally produces a localized high-energy recoil peak. We find that sub-TeV-scale dark matter with a hyperfine splitting of a few hundred keV can yield an order-one event rate in the LZ high-recoil window. This interpretation offers a possible form of dark-matter hyperfine spectroscopy, with complementary tests from dark-photon searches and future recoil-spectrum measurements.

A potential path forward is Quantum Machine Learning (QML), which aims to leverage quantum computing in conjunction with classical machine learning to enhance computing efficiency and the expressiveness of models. In this paper, two different quantum classifiers - Variational Quantum Classifier (VQC) and Quantum Kernel Support Vector Machine (QSVM) - are compared with three classical classifiers as baseline classifiers - Logistic Regression, Support Vector Machine (SVM), and a Multi-Layer Perceptron (MLP) - on the Breast Cancer Wisconsin dataset. The quantum circuits were created in the PennyLane framework and simulated on a classical backend. However, in terms of accuracy, classical Logistic Regression performed better with an accuracy of 97.8%, classical SVM and QSVM with an accuracy of 95.6% each, although the Quantum VQC achieved a lower accuracy of 88.9% and had a recall of 100% for the benign class, though it correctly identified only 12 of the 17 malignant cases (a malignant-class recall of approximately 70.6%). The drawback of quantum models is the higher training time; however, since the quantum circuit needs to be classically simulated, the quantum SVM took 23.29 seconds compared to less than 0.01 seconds for the classical linear models. These results indicate that for small structured datasets, classifiers based on quantum computing have not yet surpassed well-tuned classical counterparts. In some respects (e.g., benign-class recall), they perform competitively, though not on malignant-class recall, where the VQC in particular performed worse than the classical baselines, which is worth further investigation on real quantum computers.

The dark photon $A'$ is widely considered as the mediator of dark matter $\chi$. In the conventional non-resonance benchmark scenario with $m_{A'}/m_\chi=3$, the kinetic mixing $\epsilon$ required to match the observed dark matter relic density is typically ruled out by the combined constraints from the direct detection, indirect detection, collider, and other relevant experiments. However, if a delayed decay of the inflaton creates the low-temperature reheating, the additional entropy production dilutes the dark matter relic density. As a result, a significantly smaller $\epsilon$ becomes sufficient to match the observation, which allows the dark matter to escape the present multi-experimental bounds. In this paper, we investigate the dark matter production under the influence of a low reheating temperature $T_{\rm rh}$ within the dark photon $A^\prime$ portal framework, where $A^\prime$ mediates the interaction between dark matter $\chi$ and the SM particles. We systematically explore the viable and promising parameter space for complex scalar, Dirac, and Majorana fermion dark matter under the combined experimental constraints, and compare the distinctions among these three scenarios.

We identify a directional tangency mechanism responsible for anomalous far-field decay in Schrödinger equations. For constant-coefficient operators, we introduce a directional decomposition of the limiting resolvent based on the geometry of the Fermi surface and the observation direction. In two dimensions, we show that an analytic source produces a super-algebraically small tangency contribution, whereas a transverse non-analyticity located on the directional tangency set generates an algebraic contribution of order \(R^{-(2\alpha+1)}\). Shifting the singularity away from the tangency set restores super-algebraic decay, showing that geometric alignment is essential to the anomalous behavior. We further construct a bounded, decaying real-valued potential for which the same mechanism occurs in the first Born correction through the effective source \(Vu_0\). In a suitable long-range regime, the resulting tangency contribution decays more slowly than the conventional two-dimensional far-field term.

We establish a resolvent factorization of the hyperbolic projection associated with the finite-range dual operators, by a kernel with exponential off-diagonal decay. As an application, we prove that, for every irrational frequency and every analytic potential, each subcritical Type I energy satisfying the gap-labelling condition is an endpoint of an open spectral gap. This confirms the conjecture of Ge–Jitomirskaya–You [GJY,You] in the subcritical regime.

Quantum teleportation and Bell measurements are considered in a noisy relay setting. We introduce two quantum relay-channel models with closed-form capacity formulas, motivated by the canonical quantum communication protocols of teleportation and superdense coding. In both models, the sender transmits a qubit, while the relay observes side information about the Pauli errors that occur in the channel and communicates with the receiver through an orthogonal rate-limited link. We develop a compress-forward coding scheme in which the relay compresses the Pauli-error sequence into bins and sends the bin index to the receiver. The receiver uses this partial error information to reduce the effective channel noise before quantum decoding. We show that this strategy is optimal by establishing matching converse bounds for both models.

With the rapid development of quantum computers, proofs of quantumness have recently become an interesting research direction. However, in current schemes for proofs of quantumness, quantum provers face the risk of being maliciously exploited by classical verifiers. Through malicious strategies in interaction with quantum provers, classical verifiers could solve some instances of hard problems that arise from the specific scheme in use. This is due to the lack of formalization that prevents malicious verifiers from extracting useful information in proofs of quantumness. To address this issue, we formalize zero-knowledge proofs of quantumness. Intuitively, the zero-knowledge property necessitates that the information gained by the classical verifier from interactions with the quantum prover should not surpass what can be simulated using a simulated classical prover interacting with the same verifier. As a result, the new zero-knowledge notion can prevent a malicious verifier from exploiting quantum advantage. We find that the classical zero-knowledge proof is sufficient to compile some existing proofs of quantumness schemes into zero-knowledge proofs of quantumness schemes. It appears to be more general to require zero-knowledge proof on the verifier side instead of the prover side. This helps to regulate the verifier's behavior from malicious to be honest-but-curious. As a result, both parties will play not only one role in the proofs of quantumness but also the dual role in the classical zero-knowledge proof. Specifically, Shor's factoring-based scheme and the learning with errors-based scheme in [Brakerski et al., FOCS, 2018] can be transformed into zero-knowledge proofs of quantumness by requiring an extractable non-interactive zero-knowledge argument on the verifier side. Zero-knowledge proofs of quantumness can thus be viewed as an enhanced security notion for proofs of quantumness.

Heavy-quark production in deep-inelastic scattering probes the gluon distribution, and the precision of current and future data requires predictions beyond next-to-leading order. We calculate the even Mellin moments $N = 2$ to $22$ of the next-to-leading-order heavy-quark coefficient functions for $F_2$ and $F_L$, retaining the full heavy-quark mass dependence. This includes the gluon channel, for which no analytic result is available. They provide a test of the parametrisations used in phenomenology: at a representative kinematic point these are accurate to better than one per cent in the gluon channel, whereas in the quark channels we find deviations of up to $20\%$ over a wide range of Mellin moments, signalling significant differences in the corresponding $x$-space distributions. As a new result at next-to-next-to-leading order, the lowest moment $N = 2$ has been determined exactly.