We investigate whether early- and late-time dark energy could arise from a single scalar field. Adopting a bottom-up perspective, we first identify the sequence of dynamical regimes that any unified scenario must traverse to account for both an early dark energy phase relevant for pre-recombination solutions of the Hubble tension and the late-time acceleration of the Universe. We derive the corresponding requirements on the scalar energy density and equation of state. We then adopt a complementary top-down perspective and translate these requirements into constraints on the phase-space structure of minimally coupled scalar fields with tracking-like dynamics. We show that satisfying all requirements necessitates a potential with three distinct slopes, arranged in a steep-steeper-shallow hierarchy. This conclusion remains unchanged in the presence of conformal couplings to dark matter. These results place strong constraints on attempts to construct unified models of early- and late-time dark energy. We discuss implications for model-building.

Rydberg atoms are promising for microwave (MW) sensing and control, but full local MW characterization remains difficult. Existing methods generally do not provide self-calibrated reconstruction of the three-dimensional vector field, which is valuable for both atom-based sensing and in-situ field characterization in complex electromagnetic environments. We propose and implement multi-level, Zeeman-resolved Rydberg electromagnetically induced transparency (EIT) spectroscopy in a laser-cooled atomic ensemble. We extract the three polarization amplitudes from a single spectrum and show that the MW polarization components give rise to closed interferometric loops within the atoms' internal Hilbert space, enabling extraction of their relative phases. Moreover, it is self-calibrated and requires no external reference MW fields, with MW parameters largely separable from one another and from other experimental parameters. These features make it broadly applicable to dedicated sensing platforms as well as quantum optics and quantum information experiments.

Commuting Hamiltonians lie at the boundary between classical constraint satisfaction and quantum many-body physics, exhibiting rich quantum structure while remaining more tractable than general noncommuting models. In contrast, physical Hamiltonians are rarely exactly commuting, which naturally motivates the study of almost commuting Hamiltonians. Despite their relevance, the implications of approximate commutation are only poorly understood. In this work, we show how to efficiently approximate any almost commuting $2$-local qubit Hamiltonian by a commuting one: we give a locality-preserving algorithmic rounding technique that maps any $2$-local Hamiltonian $H=\sum_{i=1}^m h_i$ with $\|[h_i,h_j]\| \leq ε$ to a nearby Hamiltonian $\hat{H}$ whose terms pair-wise commute, and which is within overall distance $\|H-\hat{H}\| = O(m\,ε^{1/6})$. As a consequence, we show that $δ$-approximations to the ground energy for $ε$-almost commuting $2$-local qubit Hamiltonians lie in $\mathsf{NP}$ when $δ\gg mε^{1/6}$, extending the classical containment well beyond the commuting setting. Finally, we present two applications of our rounding framework: Gibbs sampling and fast Hamiltonian simulation for almost commuting systems.

We present a comprehensive multi-wavelength study of GRB 260310A / SN 2026fgk, a nearby ($z=0.153$), long-duration gamma-ray burst (GRB) with an exceptionally underluminous prompt $γ$-ray emission and a Comptonized spectrum. It is located at the edge of a blue host galaxy with a projected distance of 15 kpc, which is one of the largest offsets reported for a long GRB. The bright optical afterglow, with dense coverage from COLIBRÍ, likely peaked at a few to several hours post-burst, followed by a shallow decay not expected from canonical afterglow models. Both the optical and X-ray light curves show a brief chromatic plateau from $4-7$ days and a more standard decay thereafter only terminated with a rebrightening at $\sim20$ days. We demonstrate that this feature is best described by a combination of emission from the Ic-BL supernova, as identified in GTC spectra, and a late-time refreshed shock. The broadband optical to X-ray spectral energy distribution is well described by synchrotron emission from the forward shock, while the radio observations demand an additional emission component. We model the afterglow using (a) an on-axis uniform jet from a dirty fireball with late-time energy injection and (b) a misaligned jet with power-law angular structure, both having material emitting along our line-of-sight (LOS) moving with an initial Lorentz factor of $Γ_0\sim20-35$. Had this GRB occurred at a more typical redshift ($z\gtrsim0.5$), its prompt emission would likely have remained undetected by current $γ$-ray monitors while its optical afterglow would still have been readily detectable, placing it observationally among orphan afterglows or gamma-ray quiet fast X-ray transients.

Even in cases where quantum linear solvers provide significant speedup compared to their classical counterparts, their performance depends on some of the same parameters. In particular, the condition number of the matrix which is to be inverted is a decisive parameter. A well known classical, and now quantum, remedy is to precondition the linear system $A x = b$ by premultiplying it by a matrix $H$ in such a way that the condition number of $HA$ is significantly smaller than the condition number of $A$. In this work, we focus on a family of preconditioners called domain decomposition. First, we prove that it is feasible to apply quantum domain decomposition. We provide upper bounds for the block-encoding parameters of the Poisson problem discretized by the finite element method and preconditioned by the two-level Additive Schwarz preconditioner (one of the most fundamental domain decomposition techniques). From these bounds, we deduce the complexity of the quantum linear system solver. Second, we focus on a particular choice of local solver within the domain decomposition preconditioner by applying recent work by [Deiml and Peterseim, \textit{Math. Comput.}, 2025] on the Bramble--Pasciak--Xu (BPX) preconditioner. Finally, we provide details on how the operators are implemented.

We introduce two-body nuclear conditional probabilities that allow the definition of an intrinsic reference frame and the multipole moments of angular-momentum-$J$-conserving states. This enables the characterization of quadrupole deformations of states with $J\leq1/2$, which are not accessible via spectroscopic one-body quadrupole moments. We illustrate the method with nuclear density functional theory (DFT) calculations for $J=0$ states of $^{16}$O and $^{20}$Ne, the latter obtained by restoring rotational symmetry of prolate or oblate intrinsic configurations. We show that the two-body quadrupole shape characterizations are not equal to the one-body moments obtained from broken-symmetry states, mainly because of Pauli repulsion effects. Calculations of two-body multipole moments can be performed within various theoretical frameworks, but their experimental determination requires measuring two-body correlations.

Stellar radiation zones play a key role in the long-term magneto-rotational and chemical evolution of stars. As parts of the oceans and of the atmosphere of the Earth, their dynamics is controlled by the Archimedean buoyancy force and the Coriolis acceleration. They are the seat of an efficient extraction of angular momentum and of a mild mixing of chemicals. In this context, particle tracing in recent nonlinear hydrodynamical equatorial numerical simulations of stellar radiation zones where internal gravity waves (hereafter IGWs) are propagating led to the measurement of an effective diffusivity following the prescriptions derived by Garcia-Lopez & Spruit and by Zahn for the inflectional instability of the vertical shear of low-frequency IGWs. However, the associated instability criteria are not fullfiled. This effective diffusivity is found to scale as the squared velocity of IGWs for every rotation rates. Other dependences have also been derived in the literature, for instance in the case of the Stokes displacement. To interpret these results, we propose to explore the parameterisation for the mixing of particles, which has been proposed for the oceans. A foundation stone in physical oceanography is the so-called Osborn & Cox energetic balance that leads to an effective dyapicnal diffusivity for the transport of matter that scales as the ratio of the dissipation of the fluctuating flows over the squared Brunt-Väisälä stratification frequency. We demonstrate that this diffusivity is equivalent to the eddy diffusivity derived by Zahn for the inflectional instability of the vertical shear applied to low-frequency IGWs. This allows us to characterize the corresponding energetic balance where the power extracted by the waves from the mean flows is balanced by their dissipation and by the power produced by their buoyancy flux, which triggers mixing, for any rotation rate.

We study intersecting surface operators in 6d holomorphic field theories with the aim of unraveling associated quantum integrable structures. We first study the intersections of surface operators in 6d holomorphic Chern-Simons theory on $\mathbb{C}^3$. Computing their correlation function, we find a local operator at the intersection of the surface operators with a form reminiscent of the leading nontrivial term in the quasi-classical expansion of a rational $R$-matrix, as predicted by Costello. We provide evidence that this $R$-matrix-like operator satisfies a Yang-Baxter-type relation. We then derive the associated coproduct of the chiral algebra supported by surface operators from their OPE. We also study intersecting surface operators in 6d holomorphic BF theory and derive the local leading form of the corresponding $R$-matrix-like operator. When this theory is placed on twistor space, where it describes the self-dual sector of 4d Yang-Mills theory, this operator is expected to provide a local building block for quantum integrable structures anticipated in that setting.

A central lesson of gravity is that local observables are ill-defined. Coordinates themselves are a redundancy of description, so any particular point in spacetime is only meaningful once defined relationally by clocks, rulers, or asymptotic data. Despite extensive formal work on this subject, explicit calculations of the resulting gravitationally-dressed observables are more scarce. In this paper we perturbatively compute dressed matrix elements of local operators in electrodynamics and general relativity, including both potential and radiative photons and gravitons. Our expressions indicate that dressing is not ornamental: it universally induces kinematic singularities that can substantively reshape observables. We further show how dressing is mathematically equivalent to gauge fixing, as demonstrated by a dynamical temporal gauge in which the gauge-fixing vector is itself a geodesic fluid.

The altermagnetic materials have emerged as model systems for studying spin split electronic structures, yet controlled epitaxial growth on technologically relevant substrates remains challenging. Among the known candidates, MnTe stands out as a prominent altermagnetic material owing to its layered structure and high Neel temperature. Here, we report the molecular beam epitaxy (MBE) growth of high quality alpha MnTe thin films on GaAs(111)B substrates and provide a comprehensive analysis of the growth evolution and structural properties. Raman spectroscopy reveals multiple vibrational features of alpha MnTe including modes near 121, and 140 1/cm. Combined with first principles phonon calculations, these features are identified as the Raman-active phonons of the hexagonal NiAs type lattice. Our results show that the high crystalline quality of MBE grown alpha MnTe enables the complete experimental resolution of all symmetry allowed Raman active phonon modes, highlighting epitaxial alpha MnTe as a robust thin film platform for investigating altermagnetism and its lattice coupled excitations.

We present a quantitative theory for simulating the electrically detected magnetic resonance (EDMR) of silicon vacancy-related spin pairs in silicon carbide using steady-state Lindblad master equations. In our theory, we consider V1a and V2a deep level silicon vacancies near the (0/-) charge state transition level in proximity to a previously identified nitrogen-related complex, the incomplete K-center, due to the hyperfine, spin structure, and Landé g factor of the shallow state. Our theory describes recent room temperature measurements attributed to V1a silicon vacancies, with reasonable extracted parameters for defect spin coherence times and electrical transport rates. At lower temperatures we predict that the shallow level hyperfine structure may be spectrally resolvable. Finally, we predict the EDMR spectrum of V2a silicon vacancy-related spin pairs and predict that two-photon, double quantum transitions of the silicon vacancy's negative charge state can be electrically read-out for enhanced magnetic field sensing.

The symmetric simple exclusion process (SSEP) is a paradigmatic model of classical non-equilibrium dynamics. Exact results for large deviations of particle current in the SSEP have been obtained in various settings using integrability-based methods. In this Article, we discuss how these results are modified in the presence of localized slow bonds. We consider three conventional geometries: (a) a finite one-dimensional lattice weakly coupled to unequal reservoirs at its boundaries, (b) a semi-infinite one-dimensional lattice weakly coupled to a boundary reservoir, and (c) an infinite one-dimensional lattice with localized slow bonds near the origin. For each case, we present exact expressions for the large deviation function of current and validate them through rare-event simulations based on the cloning algorithm. In connection with our results, we present an elementary derivation of the exact large deviation function for the current in the semi-infinite SSEP, complementing recent results obtained through more elaborate techniques.

Emission from X-ray binaries in the hard spectral state is dominated by high-energy radiation attributed to the Compton scattering of seed photons. The prevalent model of the Comptonization by hot electrons or pairs faces the problem of rapid radiative cooling of the emitting particles. A proposed alternative mechanism is the Comptonization by scattering off fast plasmoids formed during magnetic reconnection. In this work, we simulate a simplified model of the plasmoid chain with Monte Carlo radiation transport and report on spectropolarimetric properties. We find that the Comptonization off trans-relativistic bulk plasmoids is not only able to reproduce the 100 keV spectral cutoff, but furthermore produces X-rays that are above 1 keV strongly polarized perpendicular to the reconnection layer. The polarization is stronger than that from the Comptonization by an isotropic hot plasma owing to the confinement of the motion of the scattering plasmoids in the plane of the reconnection layer. The dependence of polarization on azimuthal viewing angle is discussed, along with possible locations for the plasmoid chain in an equatorial current sheet or the sheath of the black hole's relativistic jet.

Bayesian inverse design provides a principled framework for inferring aerodynamic geometries from sparse flow observations while quantifying uncertainty. However, its practical use in computational fluid dynamics (CFD) is severely limited by the cost of repeated high-fidelity simulations required for gradient-based Markov chain Monte Carlo (MCMC) sampling. While surrogate models are commonly proposed to reduce this cost, their effect on posterior geometry and uncertainty, especially for shock-dominated flows, remains poorly understood. In this work, we demonstrate that neural operator surrogates can be embedded directly within the MCMC inference loop while preserving posterior structure. Using a fully Bayesian inverse formulation of quasi-one-dimensional nozzle flow, we demonstrate that geometry parameterization plays a decisive role in identifiability and posterior conditioning, with cubic B-splines yielding stable and physically meaningful uncertainty estimates. Building on this formulation, a Deep Operator Network trained on CFD-generated data is substituted for the CFD solver within a No-U-Turn Sampler, while keeping the likelihood model, priors, and sampling configuration unchanged. Across sparse to fully observed regimes, surrogate-based inference reproduces the posterior geometry and uncertainty trends of the CFD reference. As a result of surrogate integration, total inference time is reduced to under one second, corresponding to a speedup exceeding three orders of magnitude. In addition, a direct inverse neural operator is examined as a deterministic alternative for inverse design, enabling single-shot geometry reconstruction without posterior sampling. These results demonstrate that neural operator-accelerated Bayesian inference enables practical, uncertainty-aware inverse design workflows for aerodynamic applications.

Helicity is a universal quantity describing the internal rotation of an object or a field. Whether it characterizes fundamental properties such as the spin of elementary particles or leads to practical consequences such as the toxicity or harmlessness of chiral molecules, defining and measuring it is essential. However, this remains ambiguous in the case of chiral photonic systems such as plasmonic nanoparticles or photonic metasurfaces, where contrary to common knowledge, the observation of circularly polarized dependent optical properties is not a relevant measure for the helicity. We demonstrate experimentally and theoretically that the helicity can be rigorously defined and measured in a nanophotonic system emitting circularly polarized light after excitation in the near-field by a focused electron beam. In the case of a model system composed of two plasmonic dipoles (Born-Kuhn systems), we show that the helicity of photonic modes takes on a very intuitive form and can be simply measured by symmetrizing the geometry of excitation and detection. The method could be extended to a variety of chiral photonic systems, whose locally enhanced properties make them promising for the engineering of local chirality.

We study Krylov complexity in BMN Plane Wave Matrix Model at large mass deformation. We consider various consistent reductions of the matrix model that allow us to perform a Hamiltonian analysis which leads to different notions of the Krylov complexity. In the first part of the paper, we study the Krylov state complexity considering systematic reduction of $N=3$ and $N=4$ representations of the matrix model, which reveals a universal characteristic scaling for the Lanczos coefficients and fix them completely in terms of the mass deformation parameter. In the second part of the paper, we study the Krylov operator growth in the matrix model and compute the corresponding Lanczos coefficients. In both cases, we observe a \emph{linear} scaling of Lanczos coefficients with the mass parameter. The early time growth in Krylov complexity receives quadratic correction due to the presence of the massive deformation in the matrix model. Our analysis reveals that such massive corrections appear at same order in time for both the notion of the Krylov complexity.

We use multiband real space Green's functions computed using open-boundary conditions for clean GaN to exactly solve the potential-scattering Dyson equation to obtain the electronic structure of single nitrogen and gallium vacancies. From these vacancy solutions, we compute the local density of states as well as the Fermi contact and anisotropic contributions to the hyperfine field in the vicinity of the defect. These quantities directly affect electrically-detected magnetic resonance signals, which can be used to identify these defects when present in GaN devices.

We investigate an extension of $Λ$CDM in which a fraction of cold Dark Matter (DM) decays into invisible dark radiation (DR) around the radiation-matter equality epoch, together with a non-standard dark energy (DE) equation of state characterized by $w_0$. The decaying DM component modifies the early expansion history and reduces the sound horizon at baryon drag, while the DE alters the expansion rate at the late times. A comprehensive analysis combining \texttt{Planck 2018+ACT DR6+DESI DR2+CMB lensing} datasets has been carried out to explore the viability of this framework in addressing the $H_0$ tension. This model yields a Hubble constant of $H_0 = 69.83 \pm 0.98~\mathrm{km\,s^{-1}\,Mpc^{-1}}$, reducing the discrepancy with SH0ES measurement to ${\sim}2.2σ$ and local distance network measurement (H0DN) to ${\sim}2.9σ$. Further, considering \texttt{SH0ES} and \texttt{Pantheon+}, the inferred value of the Hubble constant becomes $H_0 = 70.20 \pm 0.66~\mathrm{km\,s^{-1}\,Mpc^{-1}}$. The Bayesian evidence suggests that this framework offers a fit to the relevant cosmological datasets at a statistically similar level as $Λ$CDM. It is observed that correlated early- and late-time modifications to the cosmological expansion history provide a more effective route to reducing the $H_0$ tension than either class of modification alone.

We give a complete classification of the eternal solutions for the KPZ fixed point. Each of these is a (possibly infinite) patching together of the known eternal solutions, called Busemann functions. The resulting evolution of the KPZ fixed point exhibits a shock at each of the boundaries between the different Busemann functions. Moving forward in time, the shocks coalesce, while moving backwards in time, additional shocks can form. We describe several geometric properties of this tree of shocks.

Magnetic ordering in quasicrystals has recently emerged as a fertile ground for discovering unconventional magnetic states beyond the framework of periodic crystals. However, elucidating the microscopic origin of such states remains challenging due to the intrinsic aperiodicity of quasicrystals. Here, we address this issue by investigating the prototypical Tsai-type quasicrystal approximant Cd6Tb, which preserves the essential local geometry and connectivity of icosahedral quasicrystals while allowing detailed structural and magnetic characterization due to its translational periodicity. Using neutron diffraction measurements, we find a noncoplanar multi-k magnetic ground state composed of Ising-like Tb moments arranged on a network of corner-sharing octahedra, the ingredients required to host octahedral spin-ice physics. Remarkably, only one third of the Tb moments develop long-range magnetic order, whereas the remaining moments display strongly reduced static order accompanied by persistent spin dynamics on microsecond timescales, as evidenced by muon spin rotation. This coexistence of ordered and fluctuating moments constitutes a potential realization of magnetic fragmentation - a key prediction of octahedral spin-ice physics - in a quasicrystal-related material.

Simulating fermionic systems on qubit hardware involves many nonlocal interactions, and efficient routing of these interactions is critical to the overall cost of fermionic simulation algorithms. Recent works reduce this Jordan-Wigner routing overhead to polylogarithmic depth under all-to-all connectivity, but degrade to $O(\sqrt{N}\,\mathrm{polylog}\,N)$ for $N$ fermionic modes on 2D nearest-neighbor architectures. We present a fermionic permutation protocol tailored to 2D grid architectures that achieves the optimal $O(\sqrt{N})$ depth with $O(N\sqrt{N})$ nearest-neighbor gates and no ancilla qubits, mid-circuit measurements, or classical feedforward. This matches the $Ω(\sqrt{N})$ lower bound, which holds even when $O(N)$ ancillas and classical feedforward are permitted. We further construct an $O(\sqrt{N})$-depth transformation between the Jordan-Wigner, Bravyi-Kitaev, and Parity encodings on the 2D grid via a Hilbert-curve layout, extending our result to all three encodings. Benchmarks on the fermionic fast Fourier transform and Trotter simulation of sparse SYK model demonstrate consistent reduction in depth, spacetime volume, and infidelity for system sizes $N \gtrsim 100$ in the early fault-tolerant regime.

Creating images from noise is image generation; reconstructing fine details from coarse inputs is super-resolution. Despite their practical differences, both can be understood as reversing information loss across scales. We introduce $\textbf{SKILD}$, a $\textbf{S}$cale-invariant $\textbf{K}$-Space $\textbf{I}$mage $\textbf{L}$earning $\textbf{D}$iffusion model that unifies generation and continuous super-resolution within a single unconditional framework. Both natural images and critical physical systems exhibit scale invariance, and we leverage it to design a forward process that attenuates image content from fine to coarse scales while injecting spectrum-matched Gaussian noise, making scale an explicit coordinate of the diffusion dynamics. The same trained reverse process performs generation and continuous super-resolution by varying only the starting timestep: $\textit{no task-specific architecture, no conditioning branch, no classifier-free guidance, no retraining per scale factor}$. Empirically, SKILD reaches FID $2.65$ and Inception Score $9.63$ on unconditional CIFAR-10, performs $2\times$--$8\times$ super-resolution on ImageNet from a single unconditional checkpoint while outperforming conditional models across perceptual metrics, and reconstructs critical Ising models whose connected four-point correlations closely track the ground truth.

The polarization of starlight and thermal dust emission, resulting from non-spherical grains aligned with the interstellar magnetic field (B-field), act as a powerful tool to trace the B-field morphologies and strengths in molecular clouds and constrain the grain alignment mechanisms and grain properties. The exact alignment mechanisms of grains is not yet fully clear. However, the leading theory is the alignment induced by RAdiative Torques (RATs), known as RAT theory. In this work, we use optical polarization observations of background stars projected towards nine of Bright-Rimmed Clouds (BRCs) and Cometary Globules(CGs) to study the polarization efficiencies and the alignment mechanisms of the grains in the direction towards the outer diffuse envelopes of these clouds. We use distance and extinction data of the stars from Gaia EDR3 and StarHorse 2 Catalogue. We study the variations of the degree and position angle of polarization, and the extinction, as functions of distance of the stars. For some of the clouds, we find discrete enhancement of the extinction at certain distances along with an increase in polarization degree, signifying the presence of polarizing dust layers. We estimate the polarization efficiency of grains towards each of the clouds. We find that it decreases with increasing extinction, and also shows a slight increase with dust temperature for some clouds associated with more ordered magnetic field orientations, providing an implication for the alignment of grains by RATs. Whereas, for some other clouds, the decrease in the polarization efficiency with extinction may be caused by more fluctuations in the magnetic field orientations.

We develop a time-domain numerical framework for global scalar wave scattering in Minkowski spacetime. The main contribution is an exact conformal matching of three compactified regions: a past hyperboloidal domain attached to $\mathscr I^-$, a Penrose domain covering a neighborhood of spatial infinity $i^0$, and a future hyperboloidal domain attached to $\mathscr I^+$. The matching surfaces are identical conformal hypersurfaces in the adjacent charts. This yields a global evolution scheme connecting $\mathscr I^-$, the neighborhood of $i^0$, and $\mathscr I^+$ without artificial timelike outer boundaries and without interpolation between scri-fixing gauges. We implement the construction for spherically symmetric scalar waves, including free propagation, localized linear scattering potentials such as the Pöschl--Teller potential, and semilinear wave equations with cubic, quintic, and septic nonlinearities. The numerical experiments demonstrate stable propagation across the matching interfaces, direct extraction of radiation at $\mathscr I^+$, and fourth-order convergence for the free and linear-potential tests. The quintic and septic nonlinear tests exhibit approximately fourth-order convergence and recover the expected late-time tail rates. The cubic case, by contrast, shows only first-order convergence, revealing a limitation of our treatment near compactified boundaries when the conformally rescaled nonlinear source remains non-vanishing. These results validate the conformal matching strategy for long-time simulations, while identifying the boundary regularity issues that must be addressed using a more robust treatment of spatial infinity.

Biomolecular condensates play essential roles in cellular processes, and recent efforts have focused on understanding their assembly and rational design principles. In this study, we have employed an explicit-solvent minimal statistical mechanical model based on the lattice-gas Hamiltonian with quenched disorder -- which mimics crowders -- to investigate how protein-solvent and protein-crowder interactions influence condensate phase behavior and morphology. The computed phase diagrams reveal rich behavior, including upper critical solution temperature (UCST), closed-loop, and reentrant type transitions under varying protein-solvent interactions at both equilibrium and out-of-equilibrium conditions. We elucidated the origin of these phase behavior changes and examined the role of protein-crowder interactions in modulating condensed phase morphology and stability. We further extended this model to binary protein mixtures where we studied the phase behavior in the presence and absence of quenched disorder. Without disorder, the system exhibits diverse phase-separated morphologies -- partially wetted, fully wetted, segregative, and associative -- with phase boundaries delicately sensitive protein-solvent interactions. The introduction of quenched disorder (or crowder) leads to a broader spectrum of complex morphologies, dictated by the interplay among protein-protein, protein-solvent, and protein-crowder interaction parameters. In general, this work underscores that protein-solvent and protein-crowder interactions, together with protein-protein interactions, can act as key regulatory parameters for modulating condensate morphology. These insights may guide future computational and experimental studies of liquid-liquid phase separation in biomolecular systems aimed at designing stimuli-responsive condensates.

We inspect $\mathfrak{su}(n)$ forms, providing greater detail for $n=2,3$, as a toy model for a field theory in finite dimensions and with gauge symmetries. Relying on homological perturbation theory, we show that there are no scattering amplitudes with trivalent tree-level diagrams, except for the interaction vertex, thus extending a known argument of Cattaneo--Mnëv to arbitrary $n$. In contrast to this, we show how to obtain non-trivial higher products when transferring to a larger space of fields.

Quantum control is essential for quantum information science and technology, yet designing high-fidelity control protocols remains challenging due to complex optimization landscapes, hardware noise, and long pulse sequences. Existing numerical solvers often require problem-specific engineering and produce opaque control amplitudes, while naive large language models (LLMs) lack the physical consistency and long-horizon precision for reliable quantum control synthesis. Here we introduce VF-QCTRL, a physics-informed large language model framework for general quantum control that combines symbolic reasoning with optimization to propose analytic control ansätze and coherently refine their parameters through feedback. To systematically evaluate LLM-driven quantum control, we develop QCTRL-BENCH, a benchmark spanning sixteen tasks across single- and multi-qubit systems, closed and open quantum dynamics, noiseless and noisy settings, and both analytic and numerical protocols. Across the benchmark, VF-QCTRL demonstrates strong universality, accuracy, efficiency, and interpretability: it applies to generic quantum control systems without task-specific training, achieves performance competitive with or exceeding state-of-the-art conventional solvers in both noiseless and noisy regimes with query efficiency, exhibits favorable inference-time scaling and pulse resolution scaling, and derives physically interpretable analytical protocols directly from prompts. Our results establish physics-informed LLM-based quantum control as a promising paradigm for accurate, efficient, interpretable, and training-free quantum control protocol design across a broad range of quantum systems.

Modern atomistic spin simulations combine long stochastic trajectories, thermodynamic sampling, static optimization and multi-image transition-path workflows, all of which rely on repeated evaluation of spin Hamiltonians and become computationally prohibitive on the large lattices required for three-dimensional magnetic textures. We introduce SpinX, a GPU-native atomistic spin simulation framework built around a unified Hamiltonian interface and multiple user-selectable computational backends. Its core is a crystallographic sublattice decomposition that reformulates translationally invariant spin interactions as multi-channel tensor convolutions, enabling dense, sparse and FFT-based convolution backends, while irregular systems are handled by pair-list evaluation and long-range dipolar fields by reciprocal-space FFT. Implemented in JAX, SpinX supports deterministic and stochastic Landau-Lifshitz-Gilbert dynamics, Monte Carlo sampling, static optimization, dynamical spectroscopy and string and geodesic nudged elastic band transition-path calculations on heterogeneous accelerator platforms. A validated mixed-precision mode combines fp32 field evaluation with fp64 spin-state propagation. We validate SpinX against analytical single-spin dynamics, finite-size thermodynamics of bcc Fe and transverse dynamic structure factors. Performance benchmarks show peak throughput exceeding 10 billion spin-site operations per second on a single accelerator and aggregate single-node workloads of over 1 billion atomic spins. Applying this framework to an exchange-stabilized magnetic hopfion, we uncover two competing annihilation channels on a million-spin atomistic lattice: a previously reported axial-collapse pathway and a distinct lateral-rupture pathway with a different transition morphology and activation barrier.(Due to arXiv's limit, the abstract shown here is a shortened version)

We analyze the $K^-p\to K^+Ξ^-$ and $K^-p\to K^0Ξ^0$ processes in the energy region $1.8<\sqrt{s}<2.8$ GeV within an effective Lagrangian approach. The $Λ(1800)$ and $Σ(2250)$ resonances, along with the ground states $Σ$ and $Λ$, are included. Additionally, a possible $J^P=3/2^-$ $Σ^*$ or $Λ^*$ resonance with a mass around 1.9 GeV and a width of approximately 200 MeV is introduced to describe the structure at 2.0 GeV in the total cross section and reproducing the threshold behavior. The two possible solutions corresponding to $Σ^*(3/2^-)$ and $Λ^*(3/2^-)$ cannot be distinguished by the existing data. Predictions for the polarization of the final-state $Ξ$ and the cross section of $K^-n \to K^0Ξ^-$ are compared with the experimental data, we find that the results of solution-II with $Λ^*(3/2^-)$ are much better. We also discuss the possible interpretations of the introduced $3/2^-$ hyperon as a pentaquark candidate, e.g. an $S$-wave $KΞ(1530)$ hadronic molecule. However, since the polarization data suffer from rather large uncertainties, more data inputs are needed in future experiments, for example, J-PARC, HIAF and JLab.

We study the relation between the Bogoliubov-de Gennes equation and the Ginzburg-Landau equation for a BCS model without external fields. While previous rigorous derivations of Ginzburg-Landau theory from BCS theory have focused on energies and minimizers, here we consider arbitrary critical points in the relevant energy regime. For temperatures close to the critical temperature, we prove that every sufficiently small solution of the BdG equation admits an asymptotic factorization into a microscopic Cooper-pair profile and a macroscopic order parameter. The latter satisfies the Ginzburg-Landau equation up to an error that vanishes in the scaling limit. Our analysis relies on a Birman-Schwinger reformulation of the BdG equation, a Lyapunov-Schmidt type reduction, and semiclassical estimates at low regularity.