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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

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

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

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

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

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

Teams of heterogeneous autonomous robots become increasingly important due to their facilitation of various complex tasks. For such heterogeneous robots, there is currently no consistent way of describing the functions that each robot provides. In the field of manufacturing, capability modeling is considered a promising approach to semantically model functions provided by different machines. This contribution investigates how to apply and extend capability models from manufacturing to the field of autonomous robots and presents an approach for such a capability model.

We propose a method to distinguish between trivial and topological, Majorana, zero-energy states in both short and long superconductor-normal-superconductor junctions based on Rashba nanowires using phase-biased equilibrium transport measurements. In particular, we show how the sawtooth profile of the supercurrent, due to the Majorana oscillation suppression in the topological phase for sufficiently long superconductor regions, leads to a strong signal in its zero-frequency susceptibility for a phase difference of $\phi=\pi$. This signal is notably insensitive to the chemical potential in the normal region, while trivial zero-energy states only causes signals in the susceptibility that is highly varying with the chemical potential, thus turning gating of the normal region into a simple experimental control knob. Furthermore, we obtain that, by tuning the junction transparency, critical currents in both short and long junctions undergo a reduction in the number of oscillations as a function of magnetic field only in the topological phase, an effect that find to be intimately linked to Majorana non-locality. Finally, we show that our results also hold at finite temperatures, thus highlighting their potential measurability under realistic experimental conditions., Comment: 12 pages, 7 figures. Published version

Parafermion bound states (PBSs) are generalizations of Majorana bound states (MBSs) and have been predicted to exist as zero-energy eigenstates in proximitized fractional quantum Hall edge states. Similarly to MBSs, a finite distance between the PBS can split the ground state degeneracy. However, parafermionic modes have a richer exchange statistics than MBSs, so several interaction terms are allowed by the underlying $\mathbb{Z}_{2n}$ symmetry, rendering the effective Hamiltonian governing a pair of PBSs at a finite distance nontrivial. Here, we use a combination of analytical techniques (semiclassical instanton approximation) and numerical techniques (quantum Monte Carlo simulations) to determine the effective coupling Hamiltonian. For this purpose, we go beyond the dilute one-instanton gas approximation and show how finite-size effects can give rise to higher-order parafermion interactions. We find excellent agreement between the analytical results and Monte Carlo simulations. We estimate that these finite-size corrections should be observable in some of the recently proposed experiments to observe PBSs in strongly correlated systems., Comment: 10 pages, 5 figures

Current challenges of the manufacturing industry require modular and changeable manufacturing systems that can be adapted to variable conditions with little effort. At the same time, production recipes typically represent important company know-how that should not be directly tied to changing plant configurations. Thus, there is a need to model general production recipes independent of specific plant layouts. For execution of such a recipe however, a binding to then available production resources needs to be made. In this contribution, select a suitable modeling language to model and execute such recipes. Furthermore, we present an approach to solve the issue of recipe modeling and execution in modular plants using semantically modeled capabilities and skills as well as BPMN. We make use of BPMN to model \emph{capability processes}, i.e. production processes referencing abstract descriptions of resource functions. These capability processes are not bound to a certain plant layout, as there can be multiple resources fulfilling the same capability. For execution, every capability in a capability process is replaced by a skill realizing it, effectively creating a \emph{skill process} consisting of various skill invocations. The presented solution is capable of orchestrating and executing complex processes that integrate production steps with typical IT functionalities such as error handling, user interactions and notifications. Benefits of the approach are demonstrated using a flexible manufacturing system., Comment: \c{opyright} 2022 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

Caroli-de Gennes-Matricon (CdGM) states are localized states with a discrete energy spectrum bound to the core of vortices in superconductors. In topological superconductors, CdGM states are predicted to coexist with zero-energy, chargeless states widely known as Majorana zero modes (MZMs). Due to their energy difference, current experiments rely on scanning tunneling spectroscopy methods to distinguish between them. This work shows that electrostatic inhomogeneities can push trivial CdGM states arbitrarily close to zero energy in non-topological systems where no MZM is present. Furthermore, the BCS charge of CdGM states is suppressed under the same mechanism. Through exploration of the impurity parameter space, we establish that these two phenomena generally happen in consonance. Our results show that energy and charge shifts in CdGM may be enough to imitate the spectroscopic signatures of MZMs even in cases where the estimated CdGM level spacing (in the absence of impurities) is much larger than the typical experimental level broadening., Comment: Revised and expanded version. 8 pages, 5 figures

Parafermions modes are non-Abelian anyons which were introduced as $\mathbb{Z}_N$ generalizations of $\mathbb{Z}_2$ Majorana states. In particular, $\mathbb{Z}_3$ parafermions can be used to produce Fibonacci anyons, laying a path towards universal topological quantum computation. Due to their fractional nature, much of theoretical work on $\mathbb{Z}_3$ parafermions has relied on bosonization methods or parafermionic quasi-particles. In this work, we introduce a representation of $\mathbb{Z}_3$ parafermions in terms of purely fermionic models operators in the t-J regime. We establish the equivalency of a family of lattice fermionic models written in the $t-J$ model basis with a Kitaev-like chain supporting free $\mathbb{Z}_3$ parafermonic modes at its ends. By using density matrix renormalization group calculations, we are able to characterize the topological phase transition and study the effect of local operators (doping and magnetic fields) on the spatial localization of the parafermionic modes and their stability. Moreover, we discuss the necessary ingredients towards realizing $\mathbb{Z}_3$ parafermions in strongly interacting electronic systems., Comment: Published version