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We consider a second order difference equation with operator-valued coefficients. More precisely, we study either compact or trace class perturbations of the discrete Laplacian in the Hilbert space of bi-infinite square-summable sequence with entries in a fixed Hilbert space. We discuss its continuous and discrete spectrum, as well as properties of the associated scattering matrix., Comment: 47 pages

We show that circularly polarized lasers create plasmas with long-lasting ring-shaped weakly relativistic momentum distributions which, in the presence of an ambient magnetic field, are prone to the electron cyclotron maser instability. Theoretical results and particle-in-cell simulations show that current laser technology can effectively induce field ionized tailored distribution functions and probe the electron cyclotron maser in controlled conditions, providing direct experimental evidence to coherent radiation processes driven by ring-shaped or Landau inverted momentum distributions of relevance in extreme astrophysical conditions.

In this paper, we study time-like geodesics around a spherically symmetric black hole in Kalb-Ramond (KR) gravity, characterized by the parameter $l$, which induces spontaneous Lorentz symmetry breaking. The geodesic equations and effective potential are derived to investigate the influence of $l$. We calculate the marginally bound orbits and innermost stable circular orbits, analyzing the parameter's impact. Periodic orbits are computed numerically and classified within the standard taxonomy, revealing significant effects of $l$ on their momentum and energy. Additionally, we explore an extreme mass ratio inspiral system under the adiabatic approximation to derive gravitational waveforms emitted by an object orbiting a supermassive black hole in KR gravity. These waveforms reflect the distinctive characteristics of periodic orbits and highlight the influence of $l$. With advancements in gravitational wave detection, these results offer insights into black holes influenced by Lorentz symmetry-breaking fields., Comment: 16 pages, 10 figures

This work tackles the problem of spectral characterization of a class of infinite matrices arising from the modelling of small oscillations in a system of interacting particles. The class of matrices under discussion corresponds to the infinite Marchenko-Slavin class. The spectral functions of these matrices are completely characterized and an algorithm is provided for the reconstruction of the matrix from its spectral function. The techniques used in this work are based on recent results for the spectral characterization of infinite band symmetric matrices with so-called degenerations., Comment: 22 pages 3 figures

Relativistic plasmas in strong electromagnetic fields exhibit distinct properties compared to classical plasmas. In astrophysical environments, such as neutron stars, white dwarfs, AGNs, and shocks, relativistic plasmas are pervasive and are expected to play a crucial role in the dynamics of these systems. Despite their significance, both experimental and theoretical studies of such plasmas have been limited. Here, we present the first ab initio high-resolution kinetic simulations of relativistic plasmas undergoing synchrotron cooling in a highly magnetized medium. Our results demonstrate that these plasmas spontaneously generate coherent linearly polarised radiation (independently of the electron/positron ratio), in a wide range of parameters, via the electron cyclotron maser instability, with radiative losses altering the saturation of this instability. This enables the plasma to continously amplify coherent radiation for significantly longer durations of time. These findings highlight fundamental differences in the behaviour of relativistic plasmas in strongly magnetized environments and align with astronomical phenomena, such as pulsar emission and Fast Radio Bursts.

We explore the phase diagram of the Mott metal-insulator transition (MIT), focusing on the effects of particle-hole asymmetry (PHA) in the single-band Hubbard model. Our dynamical mean-field theory (DMFT) study reveals that the introduction of PHA in the model significantly influences the critical temperature ($T_c$) and interaction strength ($U_c$), as well as the size of the co-existence region of metallic and insulating phases at low temperatures. Specifically, as the system is moved away from particle-hole symmetry, $T_c$ decreases and $U_c$ increases, indicating a suppression of the insulating phase and the strengthening of the metallic behavior. Additionally, the first-order transition line between metallic and insulating phases is better defined in the model with PHA, leading to a reduced co-existence region at $T

Generic equilibria are derived for turbulent relaxing plasmas via an entropy-maximization procedure that accounts for the short-time conservation of certain collisionless invariants. The conservation of these collisionless invariants endows the system with a partial `memory' of its prior conditions, but is imperfect on long time scales due to the development of a turbulent cascade to small scales, which breaks the precise conservation of phase volume, making this memory imprecise. The equilibria are still determined by the short-time collisionless invariants, but the invariants themselves are driven to a universal form by the nature of the turbulence. This is numerically confirmed for the case of beam instabilities in one-dimensional electrostatic plasmas, where sufficiently strong turbulence appears to cause the distribution function of particle energies to develop a universal power-law tail, with exponent -2., Comment: 11 pages, 7 figures

We consider a recently introduced extension of General Relativity dubbed as Cotton gravity (CG), based on the use of the Cotton tensor, to estimate the size of a new constant $\gamma$ appearing within a spherically symmetric, vacuum solution of the theory. Taking into account its non-asymptotically flat character, we use the inferred size of the central brightness depression of the supermassive object at the heart of the Milky Way galaxy (Sgr A*) by the Event Horizon Telescope to constrain at $2\sigma$ the CG parameter as $\gamma M \approx 3.5 \times 10^{-12}$. We study the potential observational consequences from the smallness of such a value using exact and numerical expressions for the deflection angle, optical images from optically and geometrically thin accretion disks, isoradials, and instability scales (Lyapunov index) of nearly bound geodesics associated to photon rings. Our results point towards the impossibility to distinguish between these two geometries using current and foreseeable techniques in the field of interferometric detection of optical sources., Comment: 13 pages, 8 figures

Recently, J. Harada proposed a theory relating gravity to the Cotton tensor, dubbed as ''Cotton gravity'' (CG). This is an extension of General Relativity such that every solution of the latter turns out to be a solution of the former (but the converse is not true) and, furthermore, it is possible to derive the cosmological constant as an integration constant within it. In this work we investigate CG by coupling it to both non-linear electrodynamics (NLED) and scalar fields. We study static and spherically symmetric solutions implementing a bouncing behaviour in the radial function so as to avoid the development of singularities, inspired by the Simpson-Visser black bounce and the Bardeen model, both interpreted as magnetic monopoles. We identify the NLED Lagrangian density and the scalar field potential generating such solutions, and investigate the corresponding gravitational configurations in terms of horizons, behaviour of the metric functions, and regularity of the Kretchsman curvature scalar. Our analysis extends the class of non-singular geometries found in the literature and paves the ground for further analysis of black holes in CG., Comment: 14 pages, 6 figures. V2: 16 pages, 6 figures. Discussion and references added; matches published version

Mobile robots, becoming increasingly autonomous, are capable of operating in diverse and unknown environments. This flexibility allows them to fulfill goals independently and adapting their actions dynamically without rigidly predefined control codes. However, their autonomous behavior complicates guaranteeing safety and reliability due to the limited influence of a human operator to accurately supervise and verify each robot's actions. To ensure autonomous mobile robot's safety and reliability, which are aspects of dependability, methods are needed both in the planning and execution of missions for autonomous mobile robots. In this article, a twofold approach is presented that ensures fault removal in the context of mission planning and fault prevention during mission execution for autonomous mobile robots. First, the approach consists of a concept based on formal verification applied during the planning phase of missions. Second, the approach consists of a rule-based concept applied during mission execution. A use case applying the approach is presented, discussing how the two concepts complement each other and what contribution they make to certain aspects of dependability., Comment: Language: German. Dieser Beitrag wird eingereicht in: "dtec.bw-Beitr\"age der Helmut-Schmidt-Universit\"at/Universit\"at der Bundeswehr Hamburg: Forschungsaktivit\"aten im Zentrum f\"ur Digitalisierungs- und Technologieforschung der Bundeswehr dtec.bw"

To achieve a flexible and adaptable system, capability ontologies are increasingly leveraged to describe functions in a machine-interpretable way. However, modeling such complex ontological descriptions is still a manual and error-prone task that requires a significant amount of effort and ontology expertise. This contribution presents an innovative method to automate capability ontology modeling using Large Language Models (LLMs), which have proven to be well suited for such tasks. Our approach requires only a natural language description of a capability, which is then automatically inserted into a predefined prompt using a few-shot prompting technique. After prompting an LLM, the resulting capability ontology is automatically verified through various steps in a loop with the LLM to check the overall correctness of the capability ontology. First, a syntax check is performed, then a check for contradictions, and finally a check for hallucinations and missing ontology elements. Our method greatly reduces manual effort, as only the initial natural language description and a final human review and possible correction are necessary, thereby streamlining the capability ontology generation process., Comment: \c{opyright} 2024 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works

In this work, we study timelike and lightlike geodesics in Kalb-Ramond (KR) gravity around a black hole with the goal of constraining the Lorentz symmetry-breaking parameter $l$. The analysis involves studying the precession of the S2 star periastron orbiting Sgr A* and geodesic precession around the Earth. The ratio of precession frequencies for General Relativity (GR) and KR gravity is computed, with Event Horizon Telescope (EHT) results providing a parameter range for the spontaneous symmetry-breaking of $-0.185022 \leq l \leq 0.060938$. Utilizing the geodesic precession frequency from the Gravity Probe B (GP-B), the $l$ parameter is further constrained to $-6.30714 \times 10^{-12} \leq l \leq 3.90708 \times 10^{-12}$, which is consistent with the Schwarzschild limits. Moreover, for timelike geodesics, the innermost circular orbit (ICO) and innermost stable circular orbit (ISCO) are determined and analyzed to illustrate the impact of the symmetry breaking term. Zoom-whirl obstructions are compared with the Schwarzschild solution. Lower and upper limits of the photon sphere for lightlike geodesics are established to demonstrate the influence of KR gravity on the photon sphere. Additionally, the shadow radius is determined for two observers, one situated at a finite distance from the KR black hole, and the other located at an infinite distance, to constrain the symmetry-breaking parameter $l$, with comparisons made to EHT results. The bounds for $l$ derived from constraints on the photon sphere radius for lightlike geodesics yield $-0.0700225 \leq l \leq 0.189785$ using EHT data. The findings of this paper align with experimental results in the $l \rightarrow 0$ limit., Comment: 11 pages, 4 figures. V2: 12 pages, 4 figures. Discussion and references added; matches published version

In this paper, we investigate the gravitational lensing effect for the Schwarzschild-like black hole spacetime in the background of a Kalb-Ramond (KR) field proposed in [K. Yang et. al., Phys. Rev. D 108 (2023) 124004]. The solution is characterized by a single extra parameter $l$, which is associated to the Lorentz symmetry breaking induced by the KR field. First, we calculate the exact deflection angle of massive and massless particles for finite distances using elliptic integrals. Then we study this effect in the weak and strong field regimes, discussing the correction of the KR parameter on the coefficients of the expansions in both limits. We also find that increasing $l$ decreases the deflection angle. Furthermore, we use the available data from the Sagittarius $A^{\star}$ object, which is believed to be a supermassive black hole at the center of our galaxy, to calculate relevant observables, such as, the image position, luminosity, and delay time. The values found could be potentially measured in the weak field regime, though for strong fields one would have to wait for the next generation of interferometers., Comment: 16 pages, 8 figures. V2: references added. arXiv admin note: text overlap with arXiv:2309.02658

Capability ontologies are increasingly used to model functionalities of systems or machines. The creation of such ontological models with all properties and constraints of capabilities is very complex and can only be done by ontology experts. However, Large Language Models (LLMs) have shown that they can generate machine-interpretable models from natural language text input and thus support engineers / ontology experts. Therefore, this paper investigates how LLMs can be used to create capability ontologies. We present a study with a series of experiments in which capabilities with varying complexities are generated using different prompting techniques and with different LLMs. Errors in the generated ontologies are recorded and compared. To analyze the quality of the generated ontologies, a semi-automated approach based on RDF syntax checking, OWL reasoning, and SHACL constraints is used. The results of this study are very promising because even for complex capabilities, the generated ontologies are almost free of errors., Comment: \c{opyright} 2024 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works

There is renewed interest in direct-drive inertial confinement fusion, following the milestone December 2022 3.15 MJ ignition result on the National Ignition Facility. A key obstacle is the control of the two plasmon decay instability. Here, recent advances in inhomogeneous turbulence theory are applied to the broadband parametric instability problem for the first time. A novel dispersion relation is derived for the two plasmon decay in a uniform plasma valid under broad-bandwidth laser fields with arbitrary power spectra. The effects of temporal incoherence on the instability are then studied. In the limit of large bandwidth, the well-known scaling relations for the growth rate are recovered, but it is shown that the result is more sensitive to the spectral shape of the laser pulse rather than to its coherence time. The range of wavenumbers of the excited plasma waves is shown to be substantially broadened, suggesting that the absolute instability is favoured in regions further away from the quarter critical density. The intermediate bandwidth regime is explored numerically -- the growth rate is reduced to half its monochromatic value for laser intensities of $10^{15} \, \text{W}/\text{cm}^{2}$ and relatively modest bandwidths of $5 \, \text{THz}$. The instability-quenching properties of a spectrum of discrete lines spread over some bandwidth have also been studied. The reduction in the growth rate is found to be somewhat lower compared to the continuous case but is still significant, despite the fact that, formally, the coherence time of such a laser pulse is infinite., Comment: 22 pages, 3 figures, Accepted for publication at the Journal of Plasma Physics

We study how radiation reaction leads plasmas initially in kinetic equilibrium to develop features in momentum space, such as anisotropies and population inversion, resulting in a ring-shaped momentum distribution that can drive kinetic instabilities. We employ the Landau-Lifshiftz radiation reaction model for a plasma in a strong magnetic field, and we obtain the necessary condition for the development of population inversion, we show that isotropic Maxwellian and Maxwell-J\"uttner plasmas, with thermal temperature $T>m_e c^2/\sqrt{3}$, will develop a ring-like momentum distribution. The timescales and features for forming ring-shaped momentum distributions, the effect of collisions and non-uniform magnetic fields are disscussed, and compared with typical astrophysical and laboratory plasmas parameters. Our results show the pervasiveness of ring-like momentum distribution functions in synchrotron dominated plasma conditions., Comment: 10 pages, 3 Figures, Under consideration for PoP

Multiband superconductors have featured one of the main challenges to achieve a comprehensive understanding of unconventional superconductivity. Here, the multiband character is studied separately as orbital and sublattice degrees of freedom, as they have different effects for the superconducting and magnetic or charge orders. We build on the framework of the matrix random-phase approximation (RPA), which accounts for the RPA Feynman diagrams and also vertex corrections, to treat the electron-electron interactions in an off-site degenerate Hubbard model. As a result, systems without a sublattice degree of freedom tend to be dominated by spin fluctuations, while systems with multiple sublattice sites and orbitals have the charge fluctuations favored. Finally, we explicitly demonstrate that the known suppression of the superconducting pairing strength $\lambda$ by spin fluctuations from repulsive interactions at zero momentum transfer $\boldsymbol{q}$ is countered by the finite-$\boldsymbol{q}$ pairing, which always improves $\lambda$., Comment: 10 + 6 pages, 2 figures

Mini-magnetospheres are small ion-scale structures that are well-suited to studying kinetic-scale physics of collisionless space plasmas. Such ion-scale magnetospheres can be found on local regions of the Moon, associated with the lunar crustal magnetic field. In this paper, we report on the laboratory experimental study of magnetic reconnection in laser-driven, lunar-like ion-scale magnetospheres on the Large Plasma Device (LAPD) at the University of California - Los Angeles. In the experiment, a high-repetition rate (1 Hz), nanosecond laser is used to drive a fast moving, collisionless plasma that expands into the field generated by a pulsed magnetic dipole embedded into a background plasma and magnetic field. The high-repetition rate enables the acquisition of time-resolved volumetric data of the magnetic and electric fields to characterize magnetic reconnection and calculate the reconnection rate. We notably observe the formation of Hall fields associated with reconnection. Particle-in-cell simulations reproducing the experimental results were performed to study the micro-physics of the interaction. By analyzing the generalized Ohm's law terms, we find that the electron-only reconnection is driven by kinetic effects, through the electron pressure anisotropy. These results are compared to recent satellite measurements that found evidence of magnetic reconnection near the lunar surface.

The geodesic method has played a crucial role in understanding the circular orbits generated by compact objects, culminating in the definition of the photon sphere, which was later generalized to a photon surface in arbitrary spacetimes. This new formulation extends the concept of the photon sphere in a broader sense, including dynamical spacetimes, as shown by the Vaidya solution. The photon surface essentially defines the null geodesics, which are originally tangent to the temporal surface, and keeps them confined to this surface. However, this formalism does not cover all classes of particles, and to overcome this limitation, a more comprehensive approach, denoted as the "massive particle surface", has been proposed that also accounts for charged massive particles. Indeed, the photon surface concept is recovered when the charge and mass of the particles are zero. In this work, we use these three formalisms to check the consistency of the results for the values of the radius of the photon sphere ($r_{ps}$) and the radius of the "innermost stable circular orbit" (ISCO) ($r_{\rm ISCO}$) for some gravitational models. In our results, the first model is described by conformal gravity, with the peculiarity that $g_{00}\neq-g_{11}^{-1}$. The second model, i.e. the Culetu solution, is developed by coupling General Relativity with nonlinear electrodynamics, which requires the consideration of the effective metric ($g_{\rm eff}^{\mu\nu}$) for geodesic approaches. Furthermore, we have also analysed the expressions for $r_{ps}$ and $r_{\rm ISCO}$ in a general static and spherically symmetric metric. Under these circumstances, we have found a discrepancy of $r_{ps}$ and $r_{\rm ISCO}$ obtained by the massive particle surface formalism as compared to the geodesic and photon surface formalisms., Comment: 15 pages, 1 figure; comments are welcome

In research of manufacturing systems and autonomous robots, the term capability is used for a machine-interpretable specification of a system function. Approaches in this research area develop information models that capture all information relevant to interpret the requirements, effects and behavior of functions. These approaches are intended to overcome the heterogeneity resulting from the various types of processes and from the large number of different vendors. However, these models and associated methods do not offer solutions for automated process planning, i.e. finding a sequence of individual capabilities required to manufacture a certain product or to accomplish a mission using autonomous robots. Instead, this is a typical task for AI planning approaches, which unfortunately require a high effort to create the respective planning problem descriptions. In this paper, we present an approach that combines these two topics: Starting from a semantic capability model, an AI planning problem is automatically generated. The planning problem is encoded using Satisfiability Modulo Theories and uses an existing solver to find valid capability sequences including required parameter values. The approach also offers possibilities to integrate existing human expertise and to provide explanations for human operators in order to help understand planning decisions., Comment: Presented at CAIPI Workshop at AAAI 2024

We explore the possibility of fully replacing a plasma physics kinetic simulator with a graph neural network-based simulator. We focus on this class of surrogate models given the similarity between their message-passing update mechanism and the traditional physics solver update, and the possibility of enforcing known physical priors into the graph construction and update. We show that our model learns the kinetic plasma dynamics of the one-dimensional plasma model, a predecessor of contemporary kinetic plasma simulation codes, and recovers a wide range of well-known kinetic plasma processes, including plasma thermalization, electrostatic fluctuations about thermal equilibrium, and the drag on a fast sheet and Landau damping. We compare the performance against the original plasma model in terms of run-time, conservation laws, and temporal evolution of key physical quantities. The limitations of the model are presented and possible directions for higher-dimensional surrogate models for kinetic plasmas are discussed., Comment: title changed, accepted for publication in Machine Learning: Science and Technology, code available at https://github.com/diogodcarvalho/gns-sheet-model

Global particle-in-cell (PIC) simulations of pulsar magnetospheres are performed with a volume, surface and pair production-based plasma injection schemes to systematically investigate the transition between electrosphere and force-free pulsar magnetospheric regimes. A new extension of the PIC code OSIRIS to model pulsar magnetospheres using a two-dimensional axisymmetric spherical grid is presented. The sub-algorithms of the code and thorough benchmarks are presented in detail, including a new first-order current deposition scheme that conserves charge to machine precision. It is shown that all plasma injection schemes produce a range of magnetospheric regimes. Active solutions can be obtained with surface and volume injection schemes when using artificially large plasma injection rates, and with pair production-based plasma injection for sufficiently large separation between kinematic and pair production energy scales., Comment: 19 pages, 18 figures, submitted to A&A

Magic-angle twisted bilayer graphene (MATBG) has been extensively explored both theoretically and experimentally as a suitable platform for a rich and tunable phase diagram that includes ferromagnetism, charge order, broken symmetries, and unconventional superconductivity. In this work, we investigate the intricate interplay between long-range electron-electron interactions, spin fluctuations, and superconductivity in MATBG. By employing a low-energy model for MATBG that captures the correct shape of the flat bands, we explore the effects of short- and long-range interactions on spin fluctuations and their impact on the superconducting (SC) pairing vertex in the Random Phase Approximation (RPA). We find that the SC state is notably influenced by the strength of long-range Coulomb interactions. Interestingly, our RPA calculations indicate that there is a regime where the system can traverse from a magnetic phase to the SC phase by \emph{increasing} the relative strength of long-range interactions compared to the on-site ones. These findings underscore the relevance of electron-electron interactions in shaping the intriguing properties of MATBG and offer a pathway for designing and controlling its SC phase., Comment: Revised and expanded version. 11 pages, 7 figures

The imaging by the Event Horizon Telescope (EHT) of the supermassive central objects at the heart of the M87 and Milky Way (Sgr A$^\star$) galaxies, has marked the first step into peering at the photon rings and central brightness depression that characterize the optical appearance of black holes surrounded by an accretion disk. Recently, Vagnozzi et. al. [S.~Vagnozzi, \textit{et al.} arXiv:2205.07787 [gr-qc]] used the claim by the EHT that the size of the {\it shadow} of Sgr A$^\star$ can be inferred by calibrated measurements of the bright ring enclosing it, to constrain a large number of spherically symmetric space-time geometries. In this work we use this result to study some features of the first and second photon rings of a restricted pool of such geometries in thin accretion disk settings. The emission profile of the latter is described by calling upon three analytic samples belonging to the family introduced by Gralla, Lupsasca and Marrone, in order to characterize such photon rings using the Lyapunov exponent of nearly bound orbits and discuss its correlation with the luminosity extinction rate between the first and second photon rings. We finally elaborate on the chances of using such photon rings as observational discriminators of alternative black hole geometries using very long baseline interferometry., Comment: 17 pages, 58 figures/images; v2: many comments and additions, version accepted for publication in Physical Review D

In order to react efficiently to changes in production, resources and their functions must be integrated into plants in accordance with the plug and produce principle. In this context, research on so-called capabilities and skills has shown promise. However, there are currently two incompatible approaches to modeling capabilities and skills. On the one hand, formal descriptions using ontologies have been developed. On the other hand, there are efforts to standardize submodels of the Asset Administration Shell (AAS) for this purpose. In this paper, we present ongoing research to connect these two incompatible modeling approaches. Both models are analyzed to identify comparable as well as dissimilar model elements. Subsequently, we present a concept for a bidirectional mapping between AAS submodels and a capability and skill ontology. For this purpose, two unidirectional, declarative mappings are applied that implement transformations from one modeling approach to the other - and vice versa., Comment: \c{opyright} 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works

This special session paper introduces the Horizon Europe NEUROPULS project, which targets the development of secure and energy-efficient RISC-V interfaced neuromorphic accelerators using augmented silicon photonics technology. Our approach aims to develop an augmented silicon photonics platform, an FPGA-powered RISC-V-connected computing platform, and a complete simulation platform to demonstrate the neuromorphic accelerator capabilities. In particular, their main advantages and limitations will be addressed concerning the underpinning technology for each platform. Then, we will discuss three targeted use cases for edge-computing applications: Global National Satellite System (GNSS) anti-jamming, autonomous driving, and anomaly detection in edge devices. Finally, we will address the reliability and security aspects of the stand-alone accelerator implementation and the project use cases., Comment: 10 pages, 2 figures, conference

An efficient approach that considers a high-intensity twisted laser of moderate energy (few J) is proposed to generate collimated proton bunches with multi-10-MeV energies from a double-layer hydrogen target. Three-dimensional particle-in-cell simulations demonstrate the formation of a highly collimated and energetic ($\sim 40$ MeV) proton bunch, whose divergence is $\sim 6.5$ times smaller compared to the proton bunch driven by a Gaussian laser containing the same energy. Supported by theoretical modeling of relativistic self-focusing in near-critical plasma, we establish a regime that allows for consistent acceleration of high-energetic proton bunches with low divergence under experimentally feasible conditions for twisted drivers., Comment: To be published in Physical Review Research, Accepted 10 February 2023, link: https://journals.aps.org/prresearch/accepted/17071Y71G3a1248f257a7662520350ece007b422f

A de Branges space $\mathcal B$ is regular if the constants belong to its space of associated functions and is symmetric if it is isometrically invariant under the map $F(z) \mapsto F(-z)$. Let $K_\mathcal{B}(z,w)$ be the reproducing kernel in $\mathcal B$ and $S_{\mathcal{B}}$ be the operator of multiplication by the independent variable with maximal domain in $\mathcal B$. Loosely speaking, we say that $\mathcal B$ has the $\ell_p$-oversampling property relative to a proper subspace $\mathcal A$ of it, with $p\in(2,\infty]$, if there exists $J_{\mathcal A\mathcal B}:\mathbb{C}\times\mathbb{C}\to\mathbb{C}$ such that $J(\cdot,w)\in\mathcal B$ for all $w\in\mathbb{C}$, \begin{equation*} \sum_{\lambda\in\sigma(S_{\mathcal B}^{\gamma})} \left(\frac{\lvert J_{\mathcal{A}\mathcal{B}}(z,\lambda)\rvert}{K_\mathcal{B}(\lambda,\lambda)^{1/2}}\right)^{p/(p-1)} <\infty, \quad\text{and}\quad F(z) = \sum_{\lambda\in\sigma(S_{\mathcal B}^{\gamma})} \frac{J_{\mathcal{A}\mathcal{B}}(z,\lambda)}{K_\mathcal{B}(\lambda,\lambda)}F(\lambda), \end{equation*} for all $F\in\mathcal A$ and almost every self-adjoint extension $S_{\mathcal B}^{\gamma}$ of $S_{\mathcal{B}}$. This definition is motivated by the well-known oversampling property of Paley-Wiener spaces. In this paper we provide sufficient conditions for a symmetric, regular de Branges space to have the $\ell_p$-oversampling property relative to a chain of de Branges subspaces of it., Comment: 18 pages, some minor corrections

Fast-exploding plasmas traveling though magnetized, collisionless plasmas can occur in a variety of physical systems, such as supernova remnants, coronal mass ejections, and laser-driven laboratory experiments. To study these systems, it is important to understand the coupling process between the plasmas. In this work, we develop a semi-analytical model of the parameters that characterize the strong collisionless coupling between an unmagnetized driver plasma and a uniformly and perpendicularly magnetized background plasma. In particular, we derive analytical expressions that describe the characteristic diamagnetic cavity and magnetic compression of these systems, such as their corresponding velocities, the compression ratio, and the maximum size of the cavity. The semi-analytical model is compared with collisionless 1D particle-in-cell simulations and experimental results with laser-driven plasmas, showing good agreement. The model allows us to provide bounds for parameters that are otherwise difficult to diagnose in experiments with similar setups.