We investigate Turing instability and pattern formation in two-dimensional domains for two reaction-diffusion models, obtained as diffusive limits of kinetic equations for mixtures of monatomic and polyatomic gases. The first model is of Brusselator type, which, compared with the classical formulation, presents an additional parameter whose role in stability and pattern formation is discussed. In the second framework, the system exhibits standard nonlinear diffusion terms typical of predator-prey models, but differs in reactive terms. In both cases, the kinetic-based approach proves effective in relating macroscopic parameters, often set empirically, to microscopic interaction mechanisms, thereby rigorously identifying admissible parameter ranges for the physical description. Furthermore, weakly nonlinear analysis and numerical simulations extend previously known one-dimensional results and reveal a wider scenario of spatial structures, including spots, stripes, and hexagonal arrays, that better reflect the richness observed in real-world systems.

We review lattice results related to pion, kaon, $D$-meson, $B$-meson, and nucleon physics with the aim of making them easily accessible to the nuclear and particle physics communities. More specifically, we report on the determination of the light-quark masses, the form factor $f_+(0)$ arising in the semileptonic $K \to \pi$ transition at zero momentum transfer, as well as the decay constant ratio $f_K/f_\pi$ and its consequences for the CKM matrix elements $V_{us}$ and $V_{ud}$. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of $SU(2)_L\times SU(2)_R$ and $SU(3)_L\times SU(3)_R$ Chiral Perturbation Theory. We review the determination of the $B_K$ parameter of neutral kaon mixing as well as the additional four $B$ parameters that arise in theories of physics beyond the Standard Model. For the heavy-quark sector, we provide results for $m_c$ and $m_b$ as well as those for the decay constants, form factors, and mixing parameters of charmed and bottom mesons and baryons. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. We review the status of lattice determinations of the strong coupling constant $\alpha_s$. We consider nucleon matrix elements, and review the determinations of the axial, scalar and tensor bilinears, both isovector and flavor diagonal. Finally, in this review we have added a new section reviewing determinations of scale-setting quantities.

In this paper we study the perturbations of the charged, dilaton black hole, described by the solution of the low energy limit of the superstring action found by Garfinkle, Horowitz and Strominger. We compute the complex frequencies of the quasi-normal modes of this black hole, and compare the results with those obtained for a Reissner-Nordström and a Schwarzschild black hole. The most remarkable feature which emerges from this study is that the presence of the dilaton breaks the \emph{isospectrality} of axial and polar perturbations, which characterizes both Schwarzschild and Reissner-Nordström black holes.

We provide the ultimate precision attainable in spectroscopy of a quantum emitter using single-photon pulses. We find the maximum for estimating the linewidth to be independent of the details of the emitter's bare Hamiltonian while that for the detunings not to be so. We also identify optimal pulse shapes attaining these precisions.

We present a numerical calculation of the Lee-Yang and Fisher zeros of the 2D Ising model using multi-point Padé approximants. We perform simulations for the 2D Ising model with ferromagnetic couplings both in the absence and in the presence of a magnetic field using a cluster spin-flip algorithm. We show that it is possible to extract genuine signature of Lee Yang and Fisher zeros of the theory through the poles of magnetization and specific heat, using multi-point Padé method. We extract the poles of magnetization using Padé approximants and compare their scaling with known results. We verify the circle theorem associated to the well known behaviour of Lee Yang zeros. We present our finite volume scaling analysis of the zeros done at $T=T_c$ for a few lattice sizes, extracting to a good precision the (combination of) critical exponents $\beta \delta$. The computation at the critical temperature is performed after the latter has been determined via the study of Fisher zeros, thus extracting both $\beta_c$ and the critical exponent $\nu$. Results already exist for extracting the critical exponents for the Ising model in 2 and 3 dimensions making use of Fisher and Lee Yang zeros. In this work, multi-point Padé is shown to be competitive with this respect and thus a powerful tool to study phase transitions.

We study the lattice N=1 Wess-Zumino model in two dimensions and we construct a sequence $\rho^{(L)}$ of exact lower bounds on its ground state energy density $\rho$, converging to $\rho$ in the limit $L\to\infty$. The bounds $\rho^{(L)}$ can be computed numerically on a finite lattice with $L$ sites and can be exploited to discuss dynamical symmetry breaking. The transition point is determined and compared with recent results based on large-scale Green Function Monte Carlo simulations with good agreement.

We consider the speed planning problem for a vehicle moving along an assigned trajectory, under maximum speed, tangential and lateral acceleration, and jerk constraints. The problem is a nonconvex one, where nonconvexity is due to jerk constraints. We propose a convex relaxation, and we present various theoretical properties. In particular, we show that the relaxation is exact under some assumptions. Also, we rewrite the relaxation as a Second Order Cone Programming (SOCP) problem. This has a relevant practical impact, since solvers for SOCP problems are quite efficient and allows solving large instances within tenths of a second. We performed many numerical tests, and in all of them the relaxation turned out to be exact. For this reason, we conjecture that the convex relaxation is always exact, although we could not give a formal proof of this fact.

Understanding the electronic structure of actinide materials is crucial for both fundamental research and nuclear applications. The partially filled 5f shells exhibit complex behavior due to strong correlations and ligand hybridization, requiring advanced spectroscopic techniques. Here, we report on the development and application of high-resolution valence-band resonant inelastic x-ray spectroscopy (VB-RIXS) experiments at the uranium M$_{4,5}$ edges (3551 and 3725\,eV). We present data of UO$_2$, a well-established model actinide compound. VB-RIXS is particularly well suited for probing the 5f-shell electronic structure, as it probes, in contrast to core-to-core RIXS, excitations without leaving a high-energy core hole in the final state. In VB-RIXS, we achieve energy resolutions of 50\,meV (M$_5$) and 90\,meV (M$_4$), enabling the resolution of multiplet excitations and crystal-field effects, as well as charge-transfer and fluorescence-like features with unprecedented clarity. As such, high resolution VB-RIXS offers direct insights into both low-energy, near ground-state properties and high-energy hybridization and covalency effects. Our results demonstrate the power of VB-RIXS as a versatile and powerful tool for probing the strongly correlated electronic structure of actinide materials, providing essential input for quantitative modeling and the validation of theoretical concepts.

In a previous study, the flavor-changing fermion-graviton interactions have been analyzed in the framework of the standard model, where analytical results for the relevant form factors were obtained at the leading order in the external fermion masses. These interactions arise at one-loop level by the charged electroweak corrections to the fermion-graviton vertex, when the off-diagonal flavor transitions in the corresponding charged weak currents are taken into account. Due to the conservation of the energy-momentum tensor, the corresponding form factors turn out to be finite and gauge invariant when external fermions are on-shell. Here we extend this previous analysis by including the exact dependence on the external fermion masses. Complete analytical results are provided for all the relevant form factors to the flavor-changing fermion-graviton transitions.

We search for gravitational-wave signals associated with gamma-ray bursts detected by the Fermi and Swift satellites during the second half of the third observing run of Advanced LIGO and Advanced Virgo (1 November 2019 15:00 UTC-27 March 2020 17:00 UTC).We conduct two independent searches: a generic gravitational-wave transients search to analyze 86 gamma-ray bursts and an analysis to target binary mergers with at least one neutron star as short gamma-ray burst progenitors for 17 events. We find no significant evidence for gravitational-wave signals associated with any of these gamma-ray bursts. A weighted binomial test of the combined results finds no evidence for sub-threshold gravitational wave signals associated with this GRB ensemble either. We use several source types and signal morphologies during the searches, resulting in lower bounds on the estimated distance to each gamma-ray burst. Finally, we constrain the population of low luminosity short gamma-ray bursts using results from the first to the third observing runs of Advanced LIGO and Advanced Virgo. The resulting population is in accordance with the local binary neutron star merger rate.

In the Wigner-covariant rest-frame instant form of dynamics it is possible to develop a relativistic kinematics for the N-body problem. The Wigner hyperplanes define the intrinsic rest frame and realize the separation of the center-of-mass. Three notions of {\it external} relativistic center of mass can be defined only in terms of the {\it external} Poincaré group realization. Inside the Wigner hyperplane, an {\it internal} unfaithful realization of the Poincaré group is defined. The three concepts of {\it internal} center of mass weakly {\it coincide} and are eliminated by the rest-frame conditions. An adapted canonical basis of relative variables is found. The invariant mass is the Hamiltonian for the relative motions. In this framework we can introduce the same {\it dynamical body frames}, {\it orientation-shape} variables, {\it spin frame} and {\it canonical spin bases} for the rotational kinematics developed for the non-relativistic N-body problem.

We consider the speed planning problem for a vehicle moving along an assigned trajectory, under maximum speed, tangential and lateral acceleration, and jerk constraints. The problem is a nonconvex one, where nonconvexity is due to jerk constraints. We propose a convex relaxation, and we present various theoretical properties. In particular, we show that the relaxation is exact under some assumptions. Also, we rewrite the relaxation as a Second Order Cone Programming (SOCP) problem. This has a relevant practical impact, since solvers for SOCP problems are quite efficient and allows solving large instances within tenths of a second. We performed many numerical tests, and in all of them the relaxation turned out to be exact. For this reason, we conjecture that the convex relaxation is always exact, although we could not give a formal proof of this fact.

The Tokeneer project was an initiative set forth by the National Security Agency (NSA, USA) to be used as a demonstration that developing highly secure systems can be made by applying rigorous methods in a cost effective manner. Altran Praxis (UK) was selected by NSA to carry out the development of the Tokeneer ID Station. The company wrote a Z specification later implemented in the SPARK Ada programming language, which was verified using the SPARK Examiner toolset. In this paper, we show that the Z specification can be easily and naturally encoded in the {log} set constraint language, thus generating a functional prototype. Furthermore, we show that {log}'s automated proving capabilities can discharge all the proof obligations concerning state invariants as well as important security properties. As a consequence, the prototype can be regarded as correct with respect to the verified properties. This provides empirical evidence that Z users can use {log} to generate correct prototypes from their Z specifications. In turn, these prototypes enable or simplify some verificatio activities discussed in the paper.

A quantum control protocol is proposed for the creation of NOON states with $N$ ultracold bosonic atoms on two modes, corresponding to the coherent superposition $\vert N,0\rangle + \vert 0,N\rangle$. This state can be prepared by using a third mode where all bosons are initially placed and which is symmetrically coupled to the two other modes. Tuning the energy of this third mode across the energy level of the other modes allows the adiabatic creation of the NOON state. While this process normally takes too much time to be of practical usefulness, due to the smallness of the involved spectral gap, it can be drastically boosted through counterdiabatic driving which allows for efficient gap engineering. We demonstrate that this process can be implemented in terms of static parameter adaptations that are experimentally feasible with ultracold quantum gases. Gain factors in the required protocol speed are obtained that increase exponentially with the number of involved atoms and thus counterbalance the exponentially slow collective tunneling process underlying this adiabatic transition. Besides optimizing the protocol speed, our NOON state preparation scheme achieves excellent fidelities that are competitive for practical applications.

In ABJ(M) theory, we propose a matrix model for the exact evaluation of BPS Wilson loops on a latitude circular contour, so providing a new weak-strong interpolation tool. Intriguingly, the matrix model turns out to be a particular case of that computing torus knot invariants in $U(N_1|N_2)$ Chern-Simons theory. At weak coupling we check our proposal against a three-loop computation, performed for generic framing, winding number and representation. The matrix model is amenable of a Fermi gas formulation, which we use to systematically compute the strong coupling and genus expansions. For the fermionic Wilson loop the leading planar behavior agrees with a previous string theory prediction. For the bosonic operator our result provides a clue for finding the corresponding string dual configuration. Our matrix model is consistent with recent proposals for computing Bremsstrahlung functions exactly in terms of latitude Wilson loops. As a by-product, we extend the conjecture for the exact $B^{\theta}_{1/6}$ Bremsstrahlung function to generic representations and test it with a four-loop perturbative computation. Finally, we propose an exact prediction for $B_{1/2}$ at unequal gauge group ranks.

We report the results of a search for a narrow resonance in electron-positron events in the invariant mass range of 150-950 GeV/c^2 using 1.3 fb^-1 of ppbar collision data at sqrt(s) = 1.96 TeV collected by the CDF II detector at Fermilab. No significant evidence of such a resonance is observed and we interpret the results to exclude the standard model-like Z' with a mass below 923 GeV/c^2 and the Randall-Sundrum graviton with a mass below 807 GeV/c^2 for k/M_pl=0.1, both at the 95% confidence level. Combining with di-photon data excludes the Randall-Sundrum graviton for masses below 889 GeV/c^2 for k/M_pl=0.1.

Many problems intractable on classical devices could be solved by algorithms explicitly based on quantum mechanical laws, i.e. exploiting quantum information processing. As a result, increasing efforts from different fields are nowadays directed to the actual realization of quantum devices. Here we provide an introduction to Quantum Information Processing, focusing on a promising setup for its implementation, represented by molecular spin clusters known as Molecular Nanomagnets. We introduce the basic tools to understand and design quantum algorithms, always referring to their actual realization on a molecular spin architecture. We then examine the most important sources of noise in this class of systems and then one of their most peculiar features, i.e. the possibility to exploit many (more than two) available states to encode information and to self-correct it from errors via proper design of quantum error correction codes. Finally, we present some examples of quantum algorithms proposed and implemented on a molecular spin qudit hardware.

Resolving quantum many-body problems represents one of the greatest challenges in physics and physical chemistry, due to the prohibitively large computational resources that would be required by using classical computers. A solution has been foreseen by directly simulating the time evolution through sequences of quantum gates applied to arrays of qubits, i.e. by implementing a digital quantum simulator. Superconducting circuits and resonators are emerging as an extremely-promising platform for quantum computation architectures, but a digital quantum simulator proposal that is straightforwardly scalable, universal, and realizable with state-of-the-art technology is presently lacking. Here we propose a viable scheme to implement a universal quantum simulator with hybrid spin-photon qubits in an array of superconducting resonators, which is intrinsically scalable and allows for local control. As representative examples we consider the transverse-field Ising model, a spin-1 Hamiltonian, and the two-dimensional Hubbard model; for these, we numerically simulate the scheme by including the main sources of decoherence. In addition, we show how to circumvent the potentially harmful effects of inhomogeneous broadening of the spin systems.

We report on a detailed investigation of the itinerant ferromagnets LaCoAsO, PrCoAsO and SmCoAsO performed by means of muon spin spectroscopy upon the application of external hydrostatic pressures $p$ up to $2.4$ GPa. These materials are shown to be magnetically hard in view of the weak dependence of both critical temperatures $T_{C}$ and internal fields at the muon site on $p$. In the cases $R$ = La and Sm, the behaviour of the internal field is substantially unaltered up to $p = 2.4$ GPa. A much richer phenomenology is detected in PrCoAsO instead, possibly associated with a strong $p$ dependence of the statistical population of the two different crystallographic sites for the muon. Surprisingly, results are notably different from what is observed in the case of the isostructural compounds $R$CoPO, where the full As/P substitution is already inducing a strong chemical pressure within the lattice but $p$ is still very effective in further affecting the magnetic properties.

We compute the exact all-orders perturbative expansion for the partition function of 2d $\mathrm{SU}(2)$ Yang-Mills theory on closed surfaces around higher critical points. We demonstrate that the expansion can be derived from the lattice partition function for all genera using a distributional generalization of the Poisson summation formula. We then recompute the expansion directly, using a stationary phase version of supersymmetric localization. The result of localization is a novel effective action which is itself a distribution rather than a function of the supersymmetric moduli. We comment on possible applications to A-twisted models and their analogs in higher dimensions.