We construct orthogonality relations in the Separation of Variables framework for the sl(2) sector of planar N=4 supersymmetric Yang-Mills theory. Specifically, we find simple universal measures that make Q-functions of operators with different spins vanish at all orders in perturbation theory, prior to wrapping corrections. To analyze this rank-one sector, we relax some of the assumptions thus far considered in the Separation of Variables framework. Our findings may serve as guidelines for extending this formalism to other sectors of the theory as well as other integrable models

Quantum instruments describe both the classical output and the updated quantum state in a measurement process. To do this in a non-trivial way, instruments must have the capability to interact coherently with the state that they measure. Here, we develop a resource theory for instruments. We consider a relevant quantifier of the separation between interactive and non-interactive instruments and show that it admits three distinct operational interpretations in terms of quantum information tasks. These concern (i) the preservation of maximally entangled states after a local measurement, (ii) the average ability to preserve random states after measurement, and (iii) the ability to recover the classical information generated from measuring half of a maximally entangled state. We also introduce a natural set of allowed operations and show that the third task fully characterises the resource content of instruments. Our general framework reproduces as special cases established resource theories for channels and measurements.

We investigate nonclassical photon-bundle correlations in the quantum Rabi model and its extended cases, using the quantum dressed master equation. By tuning the light--matter coupling strength at finite temperature, the quantum Rabi model exhibits controllable nonclassical transitions between two-photon bundle bunching and antibunching, allowing for the two-photon bundle emission and statistics. We further introduce anisotropic coupling and nonlinear Stark interactions, which enrich the photon statistical behaviors and provide additional tunability of photon-bundle correlations. Extreme correlation behaviors are found to be closely linked to excited-state quantum phase transitions, suggesting a potential pathway for predicting and exploiting excited-state phenomena. These effects can be controlled solely by tuning intrinsic system parameters, without the need for an external modulating field. The quantum Rabi model family thus provides a flexible and experimentally feasible platform for high-purity photon bundle generation and controllable multi-photon sources.

Purpose: To create modular solutions for interactive real-time MRI using reconstruction algorithms implemented in BART. Methods: A new protocol for streaming of multidimensional arrays is presented and integrated into BART. The new functionality is demonstrated using examples for cardiac interactive real-time MRI based on radial FLASH, where iterative reconstruction is combined with advanced features such as dynamic coil compression and gradient-delay orrection. We analyze the latency of the reconstruction and measure end-to-end latency of the full imaging process. Results: Reconstruction pipelines with iterative reconstruction and advanced functionality were built in a modular way using scripting. Latency measurements demonstrate latency sufficient for interactive real-time MRI, on the order of 30 ms for BART processing and network transfer time, or 200 ms for end-to-end latency including acquisition, vendor processing, and display. Conclusion: With the new streaming capabilities, real-time reconstruction pipelines can be assembled using BART in a flexible way, enabling rapid prototyping of advanced applications such as interactive real-time MRI.

The advancement in quantum technology has brought the implementation of Grover's Search attack on cybersecurity algorithms much closer to reality. For such tasks, the Hilbert space has to be designed to make the relation between the input and output of these cryptographic algorithms in quantum circuits. Also, these algorithms are tested on current quantum simulators such as Qiskit, where memory constraints and limited processing power are hurdles. Here, we present an easy-to-implement method using a conventional arithmetic number field approach which can be applied to quantum circuits by CNOT and Toffoli gates, while focusing on resource constraints. Also, we give a Python code that can generate a Qiskit code for the quantum implementation of similar cryptographic S-boxes using the CNOT and 3-Tofflie gates by using simple logic presented in this paper.

These notes provide a detailed and self-contained exposition of basic theory of CP maps and continuous-time Markovian evolution.The infinite-dimensional (separable) setting is handled as an extension of the finite-dimensional one.The treatment stands on two legs.For the finite-dimensional part, a basis-free version of the Choi-Jamiolkowski isomorphism called simply Jamiolkowski transform.And, for the extension, the ground matrix element topology (GMET), which does for the superoperators on trace-class operators what the weak-operator topology does for bounded operators on a Hilbert space. Background in open quantum systems or quantum information theory is not assumed.

Identification of the particle interaction potential is a challenging and important task in dusty plasma, colloids, and smart materials as it allows the characterization of structure formation and helps predict phase transitions. With the advent of machine learning methods, this interaction can be extracted from particle position data, leading to a generalizable expression which is applicable in different systems. Methods such as sparse regression aim to provide a physically interpretable model that can generalize well, while avoiding unnecessary complexity due to overfitting. In this work, we present the use of the Sparse Identification of Nonlinear Dynamics (SINDy) with the weak formulation to learn equations of motion for noisy data from simple simulations of two dust particles interacting with a Yukawa (shielded Coulomb) potential. The application of these methods to experimental dusty plasma data is discussed, particularly in the case of simulation data and glass box experiments in RF discharge gravity environments and DC discharge microgravity environments, such as the Plasmakristall-4 (PK-4) experiment.

A proper-time method for constructing models of dynamic gravitational-wave fields is presented. Using the proper-time method, analytical (not numerical) models of secondary gravitational waves are constructed as perturbative solutions of linearized field equations against the background of the exact wave solution of Einstein's equations for the vacuum in the Bianchi VI universe in a privileged wave coordinate system. Relations for the proper time of test particles against the background of a strong gravitational wave are used. The analytical form of the metric components for secondary gravitational waves is found from compatibility conditions for the field equations. From the field equations, an explicit form of ordinary differential equations and their solutions is obtained for functions included in small corrections to the metric for secondary gravitational waves. It is shown that there exists a continuum of gravitational wave parameters for which the perturbative solutions are stable.

Single-photon sensitive detectors like Silicon Photomultipliers are widely used in many medical imaging applications. By using detectors with position resolutions, it is possible to build compact photodetector readouts with reduced number of channels, but still preserving position resolution and gamma-rays imaging capabilities. In this work, we present the advantage of using a Deep Neural Networks (DNNs) light position reconstruction applied to a 2x2 array of linearly-graded SiPMs (LG-SiPMs), to minimize the distortions on the reconstructed event maps. Our approach significantly enhances both the resolution and linearity of position detection compared to the nominal reconstruction formula based on the device architecture. Remarkably, the DNN-based reconstruction boosts the number of resolved areas (pixels) by a factor of 5.7 to 12.1 (depending the training splitting used) allowing for a higher level of precision and performance in light detection.

We develop a general theory of Landau-Zener (LZ) tunneling in a two-level system with amplitude-dependent, sign-reversible nonlinear coupling, distinguishing it fundamentally from conventional on-site nonlinearity. Through a combination of analytical and phase-space analysis, we show that beyond a critical interaction strength, the nonlinear coupling fundamentally reshapes the adiabatic energy landscape, introducing a topological twisted and knotted structure. This structure leads to a complete breakdown of the standard exponential LZ formula, even in the adiabatic limit. Central to this anomalous behavior is the emergence of a black-hole-like fixed point, which acts as a universal attractor: upon traversing the critical region, all quantum trajectories converge to this fixed point, irreversibly erasing any memory of the initial state. From this fixed-point picture, we derive an exact analytical expression for the adiabatic tunneling probability, revealing a characteristic power-law dependence on both linear and nonlinear coupling strength. Our work establishes a paradigmatic framework for nonlinear-coupling-induced anomalous adiabaticity breaking and offers a universal mechanism for state control in driven quantum and wave systems.

Neutrino oscillations probe the quantum gravity interface in unique ways. While gravitational effects on neutrinos are well studied in general relativity and torsion based geometries, the symmetric teleparallel regime where gravity stems solely from non-metricity, with zero curvature and torsion has remained uncharted. In this work, we perform the first analysis of neutrino oscillations in such a spacetime. Using the reduced Kerr metric in coincident gauge for the slowly rotating and weakly gravitating spherical Sun, we derive the Dirac Hamiltonian from the generalized Dirac equation and compute the accumulated phase of neutrino mass eigenstates. There are six free coupling constants in our model. Based on certain observational inputs, we inferred upper bounds on our arbitrary coupling constants. This allowed us to simplify the otherwise cumbersome calculations to some extent. Ultimately, we computed the phase differences that play a crucial role in solar neutrino oscillations and analyzed the contributions arising from our arbitrary coupling constants. Our results establish neutrino oscillations as a novel probe of non-metricity and open a new avenue for testing symmetric teleparallel gravity through astrophysical observations.

Stupendously large astrophysical black holes (SLABs) are hypothetical black holes with masses of more than a trillion Suns. Because observable consequences of their existence have only recently been seriously considered, there have been relatively few constraints on their abundance. This work motivates a simple yet powerful constraint on SLABs: their huge shadows are visible against the cosmic microwave background. SLABs could thus appear as negative sources in microwave data. In fact, the shadow of a SLAB with a fixed mass becomes easier to detect with increasing redshifts past $1.6$ where the angular diameter distance starts falling. The limits are powerful enough to rule out SLABs of mass $\gtrsim 10^{17}\ M_{\odot}$ within the last scattering surface, and imply $Ω_{BH} \lesssim 10^{-5}$ for masses $10^{15}$--$10^{18}\ M_{\odot}$. I also discuss the effects of accretion and their implications for the limits: SLAB growth, positive accretion luminosity, and obscuring material.

We considered the Inverse Compton Scattering (ICS) of charged particles onto photons whose distribution is a Black Body Radiation (BBR) deriving the exact energy and angular differential distribution in the general case and in its most useful expansions. These results can be successfully applied in high energy accelerators experiments to evaluate the ICS contribution from the thermal photons in the cavity as well as in astrophysics where the ICS of cosmic rays plays a relevant role in a variety of phenomena. In particular we show how our formulae reproduce the ICS energy spectrum recently measured at LEP, how it could be considered a key tool in explaining the Gamma Ray Bursts (GRB) , SGRs energy spectrum. Finally we predicted the presence of a low gamma flux, nearly detectable at hundred of TeV from SNRs SN1006 as well as, at lower energy (tens TeV, due to gamma ray cascading in cosmic BBR), from relic extragalactic highest cosmic rays sources born by jets in AGN,as blazars 3C279,Mrk421,Mrk 501.

We consider the gravitational clustering of a multicomponent fluid in an expanding Newtonian universe, taking into account the mutual gravitational interactions of the medium. We obtain a set of exact and approximate solutions for two fluid components and for several fluid components: primordial hydrogen and helium or cosmological massive neutrinos of different mass and/or velocity distribution may be described by these solutions. The ratio between the two fluid perturbations, even if originally equal to unity, changes monotonically with time; this phenomenon leads to different epochs for nonlinear clustering that may be reflected into different epochs of galaxy formation. Additional note: see also D. Fargion (Nuovo Cimento 65,1981,316), L.V. Solov'eva & I.S. Nurgaliev (Sov. Astron. 29(3),1985,267-272), L.V. Solov'eva & A.A. Starobinskiy (Sov. Astron. 29(4),1985,367-371), I.S. Nurgaliev (Sov. Astron. Lett. 12(2),1986,73-76) and compare with astro-ph/9605133.

Valley splitting in strained Si/SiGe quantum wells is a central parameter for silicon spin qubits and is commonly described with envelope-function and effective-mass theories. These models provide a computationally efficient continuum description and have been shown to agree well with atomistic approaches when the confinement potential is slowly varying on the lattice scale. In modern Si/SiGe heterostructures with atomically sharp interfaces and engineered Ge concentration profiles, however, the slowly varying potential approximation underlying conventional (local) envelope-function theory is challenged. We formulate an exact multi-valley envelope-function model by combining Burt-Foreman-type envelope-function theory, which does not rely on the assumption of a slowly varying potential, with a valley-sector decomposition of the Brillouin zone. This construction enforces band-limited envelopes, which satisfy a set of coupled integro-differential equations with a non-local potential energy operator. Using degenerate perturbation theory, we derive the intervalley coupling matrix element within this non-local model and prove that it is strictly invariant under global shifts of the confinement potential (choice of reference energy). We then show that the conventional local envelope model generically violates this invariance due to spectral leakage between valley sectors, leading to an unphysical energy-reference dependence of the intervalley coupling. The resulting ambiguity is quantified by numerical simulations of various engineered Si/SiGe heterostructures. Finally, we propose a simple spectrally filtered local approximation that restores the energy-reference invariance exactly and provides a good approximation to the exact non-local theory.

Quantum learning from state samples is often benchmarked in a fixed-budget paradigm, relating error to a prescribed number of copies. We instead adopt a stopping-time viewpoint: in minimal-feedback learning, the learning completion can be defined by an online run-length certificate extracted from a one-bit-per-copy record. As an instantiation, we analyze single-shot measurement learning (SSML), introduced in [Phys. Rev. A 98, 052302 (2018)] and [Phys. Rev. Lett. 126, 170504 (2021)], which tunes a unitary and halts after $M_H$ consecutive successes. Viewing the halting as a sequential certification linking the observed counter to infidelity, we derive sample-complexity bounds that separate search (driving success probability toward unity) from certification (run statistics of consecutive successes). The resulting trade-off among $M_H$, dimension $d$, and one-bit reliability clarifies when performance is control-limited versus certificate-limited. With label-flip noise probability $q$, we find a sharp feasibility threshold: once $qM_H \gtrsim 1$, the expected halting time grows exponentially, making the learning completion impractical even under ideal control. More broadly, this shows that under severely constrained feedback, the certification can dominate sample complexity and small label noise becomes the information bottleneck. Finally, the near-optimal accuracy enabled by run-length certification aligns with the quantum-state-estimation (and equivalently, no-cloning) limits, expressed in the stopping-time terms.

Characterization of the dynamics of an impurity immersed in a quantum medium is vital for fundamental understanding of matter as well as applications in modern day quantum technologies. The case of strong and long-ranged interactions is of particular importance here, as it opens the possibility to leverage quantum correlations in controlling the system properties. Here, we consider a charged impurity moving in a bosonic gas and study its properties out of equilibrium. We extract the stationary momentum of the ion at long times, which is nonzero due to the superfluid nature of the medium, and the effective mass which stems from dressing the impurity with the host atoms. The nonlinear evolution leads not only to emission of density waves, but also momentum transfer back to the ion, resulting in the possibility of oscillatory dynamics.

While correlated phenomena of flat bands have been extensively studied in twisted systems, the ordered states that emerge from interactions in the intrinsic flat bands of kagome lattice materials remain largely unexplored. The newly discovered kagome metal CsCr3Sb5 offers a unique and rich platform for this research, as its multi-orbital flat bands at the Fermi surface result in a complex interplay of pressurized superconductivity, antiferromagnetism, a structural phase transition, and density wave orders. Here, using ultrafast optical techniques, we provide strong spectroscopic evidence for a charge density wave transition in CsCr3Sb5, resolving previous ambiguities. Crucially, we identify rotational symmetry breaking that manifests as a three-state Potts-type nematicity. Our elastoresistance measurements directly demonstrate the electronic origin of this order, as the rotational-symmetry-breaking E2g component of the elastoresistance shows a divergent behaviour around the transition temperature. This exotic nematicity results from the lifting of degeneracy of the multi-orbital flat bands, akin to phenomena seen in certain iron-based superconductors. Our study pioneers the investigation of ultrafast dynamics in flat-band systems at the Fermi surface, offering new insights into the interactions between multiple elementary excitations in strongly correlated systems.

Interference effects are an important consequence of a correct description in physics theories within and beyond the Standard Model (SM) of particle physics. However, many current theoretical descriptions as well as experimental searches neglect such effects, which can, among others, lead to an incorrect description of e.g. kinematical distributions, at least within the context of UV-complete models. In this review, I briefly discuss the current status and most common descriptions as well as existing studies of such effects, where I focus on models with extended scalar searches.

Photoluminescent color centers in diamond and hexagonal boron nitride (hBN) are powerful nanoscale solid-state quantum sensors that are explored in a plethora of quantum technologies. Methods for integrating them into macroscopic structures that improve their sensitivity and enable their large-scale deployment are highly sought after. Here, we demonstrate cavity-enhanced photoluminescence (PL) of fluorescent nanodiamonds (FNDs) and hBN nanoparticles (NPs) embedded in polymer-based thin-film optical cavities on the centimeter scale. The cavity resonances efficiently modulate the spectral PL peak position of nitrogen-vacancy (NV) centers in FNDs across the NV PL spectrum and lead to an up to 2.9-fold Purcell-enhancement of the NV PL decay rate. The brightness of hBN NPs increases by up to a factor of three and the PL decay rate is enhanced by up to 13-fold inside the cavities. Finally, we find a 4.8 times improved magnetic field sensitivity of 20 nm FNDs in thin-film cavities due to cavity-enhanced optically detected magnetic resonance contrast and PL brightness. Our study demonstrates a low-cost and scalable method for the fabrication of quantum sensor-doped thin-film cavities, which is an important step toward the development of advanced quantum sensing technologies.

While geostrophy remains the simplest and most practical balance to extract velocity information from sea-surface height anomaly (SSHa), confusions remain within the oceanographic community to what extent this balance can be applied to altimetric observations with the launch of the Surface Water and Ocean Topography (SWOT) satellite. Given the limited temporal resolution of SWOT, many studies have resorted to claiming that the spatially filtered SSHa fields correspond to the geostrophic component. This introduces the ambiguity of which spatial scale to choose. Here, we build upon the recent developments in internal tide (IT) corrections (Yadidya et al., 2025) and apply a dynamic mode decomposition (DMD)-based method introduced by Lapo et al. (2025) to robustly extract the geostrophic component associated with sub-inertial frequencies from the SWOT one-day-repeat orbit; we distribute the global dataset as a public good. We provide the joint probability density function (PDF) of vorticity and strain, and spectra of SSHa at a few cross-over regions.

Active galactic nucleus (AGN) powered jets can accelerate cosmic ray electrons, leading to the observed radio synchrotron emission. To simulate this emission, jet dynamics in galaxy clusters must be coupled to electron spectral modelling. We run magneto-hydrodynamic (MHD) simulations of a single AGN jet outburst in a Perseus-like galaxy cluster and adopt a sub-grid model for the acceleration of cosmic ray protons and electrons at unresolved internal shocks in the jet. We evolve cosmic ray electron spectra along Lagrangian trajectories using the Fokker-Planck solver Crest and compute the non-thermal emission using Crayon+. The resulting total electron spectrum reaches a steady-state slope at high momenta, with a gradually decreasing normalization over time, while the lower-momentum portion continues to resemble a freely cooling spectrum. The interaction of the jets with the turbulent cluster environment inflates lobes which rise buoyantly, induce amplification of the magnetic fields and uplift old cosmic ray populations in the wake of the bubbles. We connect radio spectral indices to electron injection ages: at a given radio frequency, weaker magnetic fields are illuminated by higher momenta electrons, whose age is determined by the last injection event. On the other hand, stronger magnetic fields are illuminated by lower momenta electrons, whose age is determined by the maximum energy injection event in the past. This powerful approach allows us to relate the underlying MHD properties to electron spectra and the resulting radio synchrotron emission, thereby enabling us to infer the underlying physics from observed radio properties.

Frequency-bin encoding offers tremendous potential in quantum photonic information processing, in which a single waveguide can support hundreds of lightpaths in a naturally phase-stable fashion. This stability, however, comes at a cost: arbitrary unitary operations can be realized by cascaded electro-optic phase modulators and pulse shapers, but require nontrivial numerical optimization for design and have thus far been limited to discrete tabletop components. In this article, we propose, formalize, and computationally evaluate a new paradigm for universal frequency-bin quantum information processing using acousto-optic scattering processes between distinct transverse modes. We show that controllable phase matching in intermodal processes enables 2$\times$2 frequency beamsplitters and transverse-mode-dependent phase shifters, which together comprise cascadable FRequency-transverse-mODe Operations (FRODOs) that can synthesize any unitary via analytical decomposition procedures. Modeling the performance of both random gates and discrete Fourier transforms, we demonstrate the feasibility of high-fidelity quantum operations with existing integrated photonics technology, highlighting prospects of parallelizable operations achieving 100\% bandwidth utilization. Our approach is realizable with CMOS technology, opening the door to scalable on-chip quantum information processing in the frequency domain.

The data post-processing gain is an important parameter for exposure time calculations used to inform the design of the Habitable Worlds Observatory (HWO). Assuming azimuthally symmetric noise properties is a common simplifying assumption for such simulations, which neglects the patchy nature of the residual diffracted starlight; i.e., speckles. Fortunately, patchiness might prove to be an opportunity that improves the overall sensitivity of observatory assuming photon-noise limited speckle subtraction. We illustrate this effect in the context of angular differential imaging (ADI), which is one of the possible observing strategies being considered for the detection and characterization of exo-Earth with HWO. We show that combining observations of two observatory roll angles leads to a gain in signal-to-noise greater than $\sqrt{2}$ when the patchy starlight dominates other noise sources. The gain can be closer to x2 when the starlight dominates the noise budget by more than an order of magnitude. In other words, combining good and bad observations is better than combining two average ones. This statement is very general as it is a direct consequence of combining data with a weighted mean. It applies more broadly to any combination of observations with varying noise level.

The variational quantum eigen solver (VQE), has been widely used to find the ground state energy of different Hamiltonians with no analytical solutions and are classically difficult to compute. In our work, we have used VQE to identify the phase transition boundary for an infinite order phase transition. We use long-range XXZ (LRXXZ) chain for our study. In order to probe infinite order phase transition, we propose to utilise the ground state energy obtained from VQE. The idea rests on the argument that VQE requires an ansatz circuit; therefore, the accuracy of the VQE will rely on this ansatz circuit. We have designed this circuit such that the estimated ground state energy is sensitive to the phase it is evaluated in. It is achieved by applying the constraint that the net spin remains constant throughout the optimisation process. Consequently, the ansatz works in a certain phase where it gives relatively small random error, as it should, when compared to the error in ground state energy calculations of the other phases, where the ansatz fails. By identifying these changes in the behaviour of the error in ground state energy using VQE, we were able to determine the phase boundaries. Using exact diagonalisation, we also compare the behaviour of the energy gradient and energy gap across both the phase transition boundaries for this model. Further, by increasing the depth of the optimisation circuit, we also accurately evaluate the ground energy of the LRXXZ chain for the value of coupling constant, J equal to -1

Bell inequality tests based on high-dimensional entanglement usually require measurements that can resolve multiple possible outcomes. However, the implementation of high-dimensional multi-outcome measurements is often only emulated via a collection of ``click or no-click'' measurements. This reduction of multi-outcome measurements to binary-outcome measurements opens a loophole in high-dimensional tests Bell inequalities which can be exploited by local hidden variable models [Tavakoli et al., Phys. Rev. A 111, 042433 (2025)]. Here, we close this loophole by using four-dimensional photonic path-mode entanglement and multi-outcome detection. We test both the well-known Collins-Gisin-Linden-Massar-Popescu inequality and a related Bell inequality tailored for maximally entangled states in high-dimension. We observe violations that are large enough to also rule out any quantum model based on entanglement of lower dimension, thereby demonstrating genuinely high-dimensional nonlocality free of the binarisation loophole.

This study investigates the dynamics of quantum information and computational resources using a tractable model of coupled harmonic oscillators. We precisely characterize the interplay between mutual information, synchronization, and circuit complexity, demonstrating that they serve as complementary yet distinct measures of quantum correlations. Our analysis reveals how coupling strength, detuning, and external magnetic fields modulate these quantities, with synchronization and mutual information exhibiting marked divergence in nonlinear regimes. By employing exact Gaussian methods, we compute the circuit depth required to prepare target states and connect increased fidelity to more regular dynamical behavior. Furthermore, we analyze single-ion transport in a harmonic trap, comparing sudden and adiabatic protocols. We introduce a nonadiabaticity metric to quantify the fidelity-complexity trade-off, showing that smooth control sequences significantly minimize operational errors by suppressing excitations. These results provide a refined understanding of quantum correlations and offer concrete principles for optimizing control strategies in quantum technologies.

Estimating molecular ground-state energies is a central application of quantum computing, requiring both the preparation of accurate quantum states and efficient energy readout. Understanding the effect of hardware noise on these experiments is crucial to distinguish errors that have low impact, errors that can be mitigated, and errors that must be reduced at the hardware level. We ran a state preparation and energy measurement protocol on an ion-trap quantum computer, without any non-scalable off-loading of computational tasks to classical computers, and show that leakage errors are the main obstacle to chemical accuracy. More specifically, we apply adiabatic state preparation to prepare the ground state of a six-qubit encoding of the H3+ molecule and extract its energy using a noise-resilient variant of iterative quantum phase estimation. Our results improve upon the classical Hartree-Fock energy. Analyzing the effect of hardware noise on the result, we find that while coherent and incoherent noise have little influence, the hardware results are mainly impacted by leakage errors. Absent leakage errors, noisy numerical simulations show that with our experimental settings we would have achieved close to chemical accuracy, even shot noise included. These insights highlight the importance of targeting leakage suppression in future algorithm and hardware development.

We study rotating hybrid stars, with particular emphasis on the effect of spin on the deconfinement phase transition and star properties. Our analysis is based on a hybrid equation of state with a phase transition from hadronic matter containing hyperons to color-superconducting quark matter, where the quark phase is modeled within a relativistic density functional approach. By varying the strength of the vector repulsion and diquark pairing couplings in the microscopic quark Lagrangian, we construct a set of hybrid star sequences with different quark-matter onset densities. This framework ensures consistency with astrophysical and gravitational wave constraints on mass, radius, and tidal deformability.

Recently the ARCA array detector published the down-ward-horizontal event: the KM3-230213A. It appeared as the most energetic neutrino ever observed: about 200 PeV (2 10^17 eV) up to EeV (10^18 eV) energy. This huge value, is puzzling. It is not statistically consistent with several upper bound derived by two greater and longer life detectors: by IceCube and in particular by AUGER array. Asymmetry in recent IceCube neutrino alert tracks upward and downward at same horizontal angles as ARCA one, suggest that they are mostly polluted atmospheric muon bundles. This paucity also disfavor the skimming neutrino interpretation by ARCA. We suggest that the array floating and bending in the deep sea may lead, sometime, to a misleading geometry that is pointing to a wrong arrival angle direction: a much less horizontal muon (neutrino) track respect to a much real one, more inclined and vertical, due to atmospheric muon bundle or charmed single event. Contrary to present argument, if such a rare event would be soon rediscovered in data or re-observed, it would open the road to a new guaranteed Tau neutrino Astronomy. At EeV energy such upward tau air-showers should shine AUGER telescopes or blaze future satellite in Space. A previous model in astrophysics considered energetic neutrino E>>100 EeV, neutrino scattering, onto cosmic, relic, light mass ones. Their ultra-relativistic Z boson resonance formation and its decay in flight would produce hadron UHECR relics around tens-hundred EeV energy. Explaining how sources located at far distances, above the usual GZK hundred Mpc, cut off ones, may shine and cluster in AUGER or TA data.