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The resource theory of contextuality considers resourceful objects to be probabilistic data-tables, known as correlations or behaviors, that fail to have an explanation in terms of Kochen-Specker noncontextual models. In this work, we advance this resource theory, considering free operations to be noncontextual wirings (NCW). We show that all such wirings form a convex set. When restricted to Bell scenarios, we show that such wirings are not equivalent to local operations assisted by a common source of classical shared randomness (LOSR). The set of all NCW operations contains LOSR, but is strictly larger. We also prove several elementary facts about how different resources can be converted via NCW. As a concrete example, we show that there are pairs of behaviors that cannot be converted one into the other using NCW. Since resource conversion mathematically induces a pre-order over the set of all behaviors, our results reveal the intricate ordering induced by NCW in scenarios beyond Bell scenarios., Comment: 23 pages, 7 figures; supersedes arXiv:2210.03268. Comments are welcome

Off-road driving operations can be a challenging environment for human conductors as they are subject to accidents, repetitive and tedious tasks, strong vibrations, which may affect their health in the long term. Therefore, they can benefit from a successful implementation of autonomous vehicle technology, improving safety, reducing labor costs and fuel consumption, and increasing operational efficiency. The main contribution of this paper is the experimental validation of a path tracking control strategy, composed of longitudinal and lateral controllers, on an off-road scenario with a fully-loaded heavy-duty truck. The longitudinal control strategy relies on a Non-Linear Model Predictive Controller (NMPC), which considers the path geometry and simplified vehicle dynamics to compute a smooth and comfortable input velocity, without violating the imposed constraints. The lateral controller is based on a Robust Linear Quadratic Regulator (RLQR), which considers a vehicle model subject to parametric uncertainties to minimize its lateral displacement and heading error, as well as ensure stability. Experiments were carried out using a fully-loaded vehicle on unpaved roads in an open-pit mine. The truck followed the reference path within the imposed constraints, showing robustness and driving smoothness., Comment: Paper accepted at Journal of Control, Automation and Electrical Systems

Quantum batteries are quantum systems used to store energy to be later extracted by an external agent in the form of work to perform some task. Here we study the charging of a hybrid quantum battery via a collisional model mediated by an anti-Jaynes Cummings interaction obtained from an off-resonant Raman configuration. The battery is made of two distinct components: a stationary infinite dimensional single quantum system (e.g. an harmonic oscillator) and a stream of small dimensional ones (e.g. qutrits). The charging protocol consists of sequentially interacting the harmonic oscillator with each element of the stream, one at a time, under the action of an external energy source and the goal is to analyze how the charging of both the harmonic oscillator and the qutrits is affected by the correlation properties of the stream., Comment: 6 captioned figures

The utilization of artificial neural networks for representing quantum many-body wave functions has garnered significant attention, with enormous recent progress for both ground states and non-equilibrium dynamics. However, quantifying state complexity within this neural quantum states framework remains elusive. In this study, we address this key open question from the complementary point of view: Which states are simple to represent with neural quantum states? Concretely, we show on a general level that ground states of mean-field theories with permutation symmetry only require a limited number of independent neural network parameters. We analytically establish that, in the thermodynamic limit, convergence to the ground state of the fully-connected transverse-field Ising model (TFIM), the mean-field Ising model, can be achieved with just one single parameter. Expanding our analysis, we explore the behavior of the 1-parameter ansatz under breaking of the permutation symmetry. For that purpose, we consider the TFIM with tunable long-range interactions, characterized by an interaction exponent $\alpha$. We show analytically that the 1-parameter ansatz for the neural quantum state still accurately captures the ground state for a whole range of values for $0\le \alpha \le 1$, implying a mean-field description of the model in this regime., Comment: 10 pages,3 figures

Topology plays a fundamental role in our understanding of many-body physics, from vortices and solitons in classical field theory, to phases and excitations in quantum matter. Topological phenomena are intimately connected to the distribution of information content - that, differently from ordinary matter, is now governed by non-local degrees of freedom. However, a precise characterization of how topological effects govern the complexity of a many-body state - i.e., its partition function - is presently unclear. In this work, we show how topology and complexity are directly intertwined concepts in the context of classical statistical mechanics. In concrete, we present a theory that shows how the Kolmogorov complexity of a classical partition function sampling carries unique, distinctive features depending on the presence of topological excitations in the system. We confront two-dimensional Ising, Heisenberg, and XY models on several topologies and study the corresponding samplings as high-dimensional manifolds in configuration space, quantifying their complexity via the intrinsic dimension. While for the Ising and Heisenberg models the intrinsic dimension is independent of the real-space topology, for the XY model it depends crucially on temperature: across the Berezkinskii-Kosterlitz-Thouless (BKT) transition, complexity becomes topology dependent. In the BKT phase, it displays a characteristic dependence on the homology of the real-space manifold, and, for $g$-torii, it follows a scaling that is solely genus dependent. We argue that this behavior is intimately connected to the emergence of an order parameter in data space, the conditional connectivity, that displays scaling behavior., Comment: 12 pages, 8 figures

Spectral functions are central to link experimental probes to theoretical models in condensed matter physics. However, performing exact numerical calculations for interacting quantum matter has remained a key challenge especially beyond one spatial dimension. In this work, we develop a versatile approach using neural quantum states to obtain spectral properties based on simulations of the dynamics of excitations initially localized in real or momentum space. We apply this approach to compute the dynamical structure factor in the vicinity of quantum critical points (QCPs) of different two-dimensional quantum Ising models, including one that describes the complex density wave orders of Rydberg atom arrays. When combined with deep network architectures we find that our method reliably describes dynamical structure factors of arrays with up to $24\times24$ spins, including the diverging time scales at critical points. Our approach is broadly applicable to interacting quantum lattice models in two dimensions and consequently opens up a route to compute spectral properties of correlated quantum matter in yet inaccessible regimes., Comment: Published version

Quantum batteries are quantum systems that store energy which can then be used for quantum tasks. One relevant question about such systems concerns the differences and eventual advantages over their classical counterparts, whether in the efficiency of the energy transference, input power, total stored energy or other relevant physical quantities. Here, we show how a purely quantum effect related to the vacuum of the electromagnetic field can enhance the charging of a quantum battery. In particular, we demonstrate how an anti-Jaynes Cummings interaction derived from an off-resonant Raman configuration can be used to increase the stored energy of an effective two-level atom when compared to its classically driven counterpart, eventually achieving full charging of the battery with zero entropic cost.

Integrated circuit design automation tools are essential for the feasibility of complex designs with millions of transistors. One of the steps performed within the process is the routing of interconnections between components of a circuit. This problem, which also aims to optimize the utilization of connection resources, has been shown to be NP-Complete and requires heuristic algorithms to look for the best achievable solutions. In this work, we present a definition of this problem in context with a brief review of existing solutions in the literature. Then, we propose a methodology for the development of an original algorithm, which aims to differentiate itself, in certain domains, from the solutions already proposed., Comment: in Portuguese language

Resource theories constitute a powerful theoretical framework and a tool that captures, in an abstract structure, pragmatic aspects of the most varied theories and processes. For physical theories, while this framework deals directly with questions about the concrete possibilities of carrying out tasks and processes, resource theories also make it possible to recast these already established theories on a new language, providing not only new perspectives on the potential of physical phenomena as valuable resources for technological development, for example, but they also provide insights into the very foundations of these theories. In this work, we will investigate some properties of a resource theory for quantum contextuality, an essential characteristic of quantum phenomena that ensures the impossibility of interpreting the results of quantum measurements as revealing properties that are independent of the set of measurements being made. We will present the resource theory to be studied and investigate certain global properties of this theory using tools and methods that, although already developed and studied by the community in other resource theories, had not yet been used to characterize resource theories of contextuality. In particular, we will use the so called cost and yield monotones, extending the results of reference Quantum 4, 280 (2020) to general contextuality scenarios., Comment: Preliminary version, comments welcome

In this work, we study the efficiency of charging a quantum battery through optical pumping. The battery consists of a qutrit and it is connected to a natural thermal reservoir and an external coherent drive in the limit where its upper energy level can be adiabatically eliminated from the dynamics. In this scenario, the drive plus spontaneous emission optically pumps the intermediate energy level of the qutrit and the battery can be understood as being charged by an effective higher temperature reservoir that takes it out of equilibrium with the natural reservoir and stores useful energy in it. We also analyse the efficiency of using this battery and charging scheme as the work fluid of a two-stroke thermal machine. The thermal machine includes a fourth level through which work is extracted from the battery via a unitary transformation, therefore setting the limit of maximum efficiency of the machine., Comment: accepted in Phys. Rev. A

In quantum statistical mechanics, finite-temperature phase transitions are typically governed by classical field theories. In this context, the role of quantum correlations is unclear: recent contributions have shown how entanglement is typically very short-ranged, and thus uninformative about long-ranged critical correlations. In this work, we show the existence of finite-temperature phase transitions where a broader form of quantum correlation than entanglement, the entropic quantum discord, can display genuine signatures of critical behavior. We consider integrable bosonic field theories in both two- and three-dimensional lattices, and show how the two-mode Gaussian discord decays algebraically with the distance even in cases where the entanglement negativity vanishes beyond nearest-neighbor separations. Systematically approaching the zero-temperature limit allows us to connect discord to entanglement, drawing a generic picture of quantum correlations and critical behavior that naturally describes the transition between entangled and discordant quantum matter., Comment: 8 pages, 7 figures

Tagging facilitates information retrieval in social media and other online communities by allowing users to organize and describe online content. Researchers found that the efficiency of tagging systems steadily decreases over time, because tags become less precise in identifying specific documents, i.e., they lose their descriptiveness. However, previous works did not answer how or even whether community managers can improve the efficiency of tags. In this work, we use information-theoretic measures to track the descriptive and retrieval efficiency of tags on Stack Overflow, a question-answering system that strictly limits the number of tags users can specify per question. We observe that tagging efficiency stabilizes over time, while tag content and descriptiveness both increase. To explain this observation, we hypothesize that limiting the number of tags fosters novelty and diversity in tag usage, two properties which are both beneficial for tagging efficiency. To provide qualitative evidence supporting our hypothesis, we present a statistical model of tagging that demonstrates how novelty and diversity lead to greater tag efficiency in the long run. Our work offers insights into policies to improve information organization and retrieval in online communities.

As a tool for capturing irregular temporal dependencies (rather than resorting to binning temporal observations to construct time series), Hawkes processes with exponential decay have seen widespread adoption across many application domains, such as predicting the occurrence time of the next earthquake or stock market spike. However, practical applications of Hawkes processes face a noteworthy challenge: There is substantial and often unquantified variance in decay parameter estimations, especially in the case of a small number of observations or when the dynamics behind the observed data suddenly change. We empirically study the cause of these practical challenges and we develop an approach to surface and thereby mitigate them. In particular, our inspections of the Hawkes process likelihood function uncover the properties of the uncertainty when fitting the decay parameter. We thus propose to explicitly capture this uncertainty within a Bayesian framework. With a series of experiments with synthetic and real-world data from domains such as "classical" earthquake modeling or the manifestation of collective emotions on Twitter, we demonstrate that our proposed approach helps to quantify uncertainty and thereby to understand and fit Hawkes processes in practice.

The concept of thermal machines has evolved from the canonical steam engine to the recently proposed nanoscopic quantum systems as working fluids. The latter obey quantum open system dynamics and frequently operate in non-equilibrium conditions. However, the role of this dynamics in the overall performance of quantum heat engines remains an open problem. Here, we analyse and optimize the efficiency and power output of two-stage quantum heat engines fuelled by non-equilibrium steady states. In a charging first stage, the quantum working fluid consisting of a qutrit or two coupled qubits is connected to two reservoirs at different temperatures, which establish a heat current that stores ergotropy in the system; the second stage comprises a coherent driving force that extracts work from the machine in finite a amount of time; finally, the external drive is switched off and the machine enters a new cycle.

Quantum many-body systems are characterized by patterns of correlations that define highly-non trivial manifolds when interpreted as data structures. Physical properties of phases and phase transitions are typically retrieved via simple correlation functions, that are related to observable response functions. Recent experiments have demonstrated capabilities to fully characterize quantum many-body systems via wave-function snapshots, opening new possibilities to analyze quantum phenomena. Here, we introduce a method to data mine the correlation structure of quantum partition functions via their path integral (or equivalently, stochastic series expansion) manifold. We characterize path-integral manifolds generated via state-of-the-art Quantum Monte Carlo methods utilizing the intrinsic dimension (ID) and the variance of distances from nearest neighbors (NN): the former is related to dataset complexity, while the latter is able to diagnose connectivity features of points in configuration space. We show how these properties feature universal patterns in the vicinity of quantum criticality, that reveal how data structures {\it simplify} systematically at quantum phase transitions. This is further reflected by the fact that both ID and variance of NN-distances exhibit universal scaling behavior in the vicinity of second-order and Berezinskii-Kosterlitz-Thouless critical points. Finally, we show how non-Abelian symmetries dramatically influence quantum data sets, due to the nature of (non-commuting) conserved charges in the quantum case. Complementary to neural network representations, our approach represents a first, elementary step towards a systematic characterization of path integral manifolds before any dimensional reduction is taken, that is informative about universal behavior and complexity, and can find immediate application to both experiments and Monte Carlo simulations., Comment: 19 pages, 13 figures, version accepted for publication in Phys. Rev. X Quantum

Wikipedia, the largest encyclopedia ever created, is a global initiative driven by volunteer contributions. When the COVID-19 pandemic broke out and mobility restrictions ensued across the globe, it was unclear whether Wikipedia volunteers would become less active in the face of the pandemic, or whether they would rise to meet the increased demand for high-quality information despite the added stress inflicted by this crisis. Analyzing 223 million edits contributed from 2018 to 2020 across twelve Wikipedia language editions, we find that Wikipedia's global volunteer community responded remarkably to the pandemic, substantially increasing both productivity and the number of newcomers who joined the community. For example, contributions to the English Wikipedia increased by over 20% compared to the expectation derived from pre-pandemic data. Our work sheds light on the response of a global volunteer population to the COVID-19 crisis, providing valuable insights into the behavior of critical online communities under stress.

The development of control techniques to maintain vehicle stability under possible loss-of-control scenarios is essential to the safe deployment of autonomous ground vehicles in public scenarios. In this paper, we propose a tube-based guaranteed cost model predictive controller for autonomous vehicles able to avoid front and rear tire saturation and to track a provided reference trajectory up to the limits of handling of the vehicle. Such an approach ensures the vehicle will remain within its safe operational envelope; therefore, guaranteeing both stability and performance of the vehicle, including highly dynamic maneuvers that may be necessary for emergency conditions. We also propose a new conservative approximation of the nonlinear vehicle dynamics to a linear system subject to norm bounded multiplicative uncertainties and a new maximal robust controllable invariant set for vehicle dynamics. It consists of a larger feasible state-space region when compared to previously proposed invariant sets. Finally, we present both simulation and in-vehicle results of the performance of the proposed approach.

The objective of the first CARLA autonomous driving challenge was to deploy autonomous driving systems to lead with complex traffic scenarios where all participants faced the same challenging traffic situations. According to the organizers, this competition emerges as a way to democratize and to accelerate the research and development of autonomous vehicles around the world using the CARLA simulator contributing to the development of the autonomous vehicle area. Therefore, this paper presents the architecture design for the navigation of an autonomous vehicle in a simulated urban environment that attempts to commit the least number of traffic infractions, which used as the baseline the original architecture of the platform for autonomous navigation CaRINA 2. Our agent traveled in simulated scenarios for several hours, demonstrating his capabilities, winning three out of the four tracks of the challenge, and being ranked second in the remaining track. Our architecture was made towards meeting the requirements of CARLA Autonomous Driving Challenge and has components for obstacle detection using 3D point clouds, traffic signs detection and classification which employs Convolutional Neural Networks (CNN) and depth information, risk assessment with collision detection using short-term motion prediction, decision-making with Markov Decision Process (MDP), and control using Model Predictive Control (MPC)., Comment: 16 pages, 12 figures, preprint submitted to Journal of Systems Architecture

When a quantum system is subject to a thermal gradient it may sustain a steady non-equilibrium heat current, by entering into a so-called non equilibrium steady state (NESS). Here we show that NESS constitute a thermodynamic resource that can be exploited to fuel a quantum heat engine. This adds to the list of recently reported sources available at the nano-scale, such as coherence, entanglement and quantum measurements. We elucidate this concept by showing analytic and numerical studies of a two-qubits quantum battery that is alternatively charged by a thermal gradient and discharged by application of a properly chosen unitary gate. The presence of a NESS for the charging step guarantees steady operation with positive power output. Decreasing the duration of the charging step results in a time periodic steady state accompanied by increased efficiency and output power. The device is amenable to implementation with different nanotechnology platforms., Comment: 6 pages, 4 figures

Entanglement is known to serve as an order parameter for true topological order in two-dimensional systems. We show how entanglement of disconnected partitions defines topological invariants for one-dimensional topological superconductors. These order parameters quantitatively capture the entanglement that is possible to distill from the ground state manifold, and are thus quantized to 0 or log 2. Their robust quantization property is inferred from the underlying lattice gauge theory description of topological superconductors, and is corroborated via exact solutions and numerical simulations. Transitions between topologically trivial and non-trivial phases are accompanied by scaling behavior, a hallmark of genuine order parameters, captured by entanglement critical exponents. These order parameters are experimentally measurable utilizing state-of-the-art techniques., Comment: 6 pages, 8 figures. Supp Mat: 9 pages, 8 figures v2: Fused the two files into one, added a new section on disorder. Modifed the text and added relevant references. Now: 12 pages, 11 figures

We investigate the emergence of a myriad of phases in the strong coupling regime of the dipolar Hubbard model in two dimensions. By using a combination of numerically unbiased methods in finite systems with analytical perturbative arguments, we show the versatility that trapped dipolar atoms possess in displaying a wide variety of many-body phases, which can be tuned simply by changing the collective orientation of the atomic dipoles. We further investigate the stability of these phases to thermal fluctuations in the strong coupling regime, highlighting that they can be accessed with current techniques employed in cold atoms experiments on optical lattices. Interestingly, both quantum and thermal phase transitions are signalled by peaks or discontinuities in local moment-local moment correlations, which have been recently measured in some of these experiments, so that they can be used as probes for the onset of different phases.

We investigate a model of hard-core bosons with infinitely repulsive nearest- and next-nearest-neighbor interactions in one dimension, introduced by Fendley, Sengupta and Sachdev in Phys. Rev. B 69, 075106 (2004). Using a combination of exact diagonalization, tensor network, and quantum Monte Carlo simulations, we show how an intermediate incommensurate phase separates a crystalline and a disordered phase. We base our analysis on a variety of diagnostics, including entanglement measures, fidelity susceptibility, correlation functions, and spectral properties. According to theoretical expectations, the disordered-to-incommensurate-phase transition point is compatible with Berezinskii-Kosterlitz-Thouless universal behaviour. The second transition is instead non-relativistic, with dynamical critical exponent $z > 1$. For the sake of comparison, we illustrate how some of the techniques applied here work at the Potts critical point present in the phase diagram of the model for finite next-nearest-neighbor repulsion. This latter application also allows to quantitatively estimate which system sizes are needed to match the conformal field theory spectra with experiments performing level spectroscopy., Comment: 18 pages, 14 figures

According to data from the United Nations, more than 3000 people have died each day in the world due to road traffic collision. Considering recent researches, the human error may be considered as the main responsible for these fatalities. Because of this, researchers seek alternatives to transfer the vehicle control from people to autonomous systems. However, providing this technological innovation for the people may demand complex challenges in the legal, economic and technological areas. Consequently, carmakers and researchers have divided the driving automation in safety and emergency systems that improve the driver perception on the road. This may reduce the human error. Therefore, the main contribution of this study is to propose a driving simulator platform to develop and evaluate safety and emergency systems, in the first design stage. This driving simulator platform has an advantage: a flexible software structure.This allows in the simulation one adaptation for development or evaluation of a system. The proposed driving simulator platform was tested in two applications: cooperative vehicle system development and the influence evaluation of a Driving Assistance System (\textit{DAS}) on a driver. In the cooperative vehicle system development, the results obtained show that the increment of the time delay in the communication among vehicles ($V2V$) is determinant for the system performance. On the other hand, in the influence evaluation of a \textit{DAS} in a driver, it was possible to conclude that the \textit{DAS'} model does not have the level of influence necessary in a driver to avoid an accident., Comment: 14 pages, 27 figures

Digital image segmentation is the process of assigning distinct labels to different objects in a digital image, and the fuzzy segmentation algorithm has been successfully used in the segmentation of images from a wide variety of sources. However, the traditional fuzzy segmentation algorithm fails to segment objects that are characterized by textures whose patterns cannot be successfully described by simple statistics computed over a very restricted area. In this paper, we propose an extension of the fuzzy segmentation algorithm that uses adaptive textural affinity functions to perform the segmentation of such objects on bidimensional images. The adaptive affinity functions compute their appropriate neighborhood size as they compute the texture descriptors surrounding the seed spels (spatial elements), according to the characteristics of the texture being processed. The algorithm then segments the image with an appropriate neighborhood for each object. We performed experiments on mosaic images that were composed using images from the Brodatz database, and compared our results with the ones produced by a recently published texture segmentation algorithm, showing the applicability of our method.

Millions of users on the Internet discuss a variety of topics on Question-and-Answer (Q&A) instances. However, not all instances and topics receive the same amount of attention, as some thrive and achieve self-sustaining levels of activity, while others fail to attract users and either never grow beyond being a small niche community or become inactive. Hence, it is imperative to not only better understand but also to distill deciding factors and rules that define and govern sustainable Q&A instances. We aim to empower community managers with quantitative methods for them to better understand, control and foster their communities, and thus contribute to making the Web a more efficient place to exchange information. To that end, we extract, model and cluster user activity-based time series from $50$ randomly selected Q&A instances from the Stack Exchange network to characterize user behavior. We find four distinct types of user activity temporal patterns, which vary primarily according to the users' activity frequency. Finally, by breaking down total activity in our 50 Q&A instances by the previously identified user activity profiles, we classify those 50 Q&A instances into three different activity profiles. Our parsimonious categorization of Q&A instances aligns with the stage of development and maturity of the underlying communities, and can potentially help operators of such instances: We not only quantitatively assess progress of Q&A instances, but we also derive practical implications for optimizing Q&A community building efforts, as we e.g. recommend which user types to focus on at different developmental stages of a Q&A community.

We analyze the Chern-Simons-like term generation in the CPT-odd Lorentz-violating Yang-Mills theory interacting with fermions. Moreover, we study the anomalies of this model as well as its quantum stability. The whole analysis is performed within the algebraic renormalization theory, which is independent of the renormalization scheme. In addition, all results are valid to all orders in perturbation theory. We find that the Chern-Simons-like term is not generated by radiative corrections, just like its Abelian version. Additionally, the model is also free of gauge anomalies and quantum stable., Comment: 16 pages. No figures. Final version to appear in the Eur.Phys.J.C

The noninteracting electronic structures of tight binding models on bipartite lattices with unequal numbers of sites in the two sublattices have a number of unique features, including the presence of spatially localized eigenstates and flat bands. When a \emph{uniform} on-site Hubbard interaction $U$ is turned on, Lieb proved rigorously that at half filling ($\rho=1$) the ground state has a non-zero spin. In this paper we consider a `CuO$_2$ lattice (also known as `Lieb lattice', or as a decorated square lattice), in which `$d$-orbitals' occupy the vertices of the squares, while `$p$-orbitals' lie halfway between two $d$-orbitals. We use exact Determinant Quantum Monte Carlo (DQMC) simulations to quantify the nature of magnetic order through the behavior of correlation functions and sublattice magnetizations in the different orbitals as a function of $U$ and temperature. We study both the homogeneous (H) case, $U_d= U_p$, originally considered by Lieb, and the inhomogeneous (IH) case, $U_d\neq U_p$. For the H case at half filling, we found that the global magnetization rises sharply at weak coupling, and then stabilizes towards the strong-coupling (Heisenberg) value, as a result of the interplay between the ferromagnetism of like sites and the antiferromagnetism between unlike sites; we verified that the system is an insulator for all $U$. For the IH system at half filling, we argue that the case $U_p\neq U_d$ falls under Lieb's theorem, provided they are positive definite, so we used DQMC to probe the cases $U_p=0,U_d=U$ and $U_p=U, U_d=0$. We found that the different environments of $d$ and $p$ sites lead to a ferromagnetic insulator when $U_d=0$; by contrast, $U_p=0$ leads to to a metal without any magnetic ordering. In addition, we have also established that at density $\rho=1/3$, strong antiferromagnetic correlations set in, caused by the presence of one fermion on each $d$ site., Comment: 10 pages, 14 figures

In this work we study the issue of gauge anomalies in Lorentz-violating QED. To do so, we opt to use the Becchi-Rouet-Stora-Tyutin formalism within the algebraic renormalization approach, reducing our study to a cohomology problem. Since this approach is independent of the renormalization scheme, the results obtained here are expected to be general. We find that the Lorentz-violating QED is free of gauge anomalies to all orders in perturbation theory., Comment: 17 pages

In this work, we employ algebraic renormalization technique to show the renormalizability to all orders in perturbation theory of the Lorentz and CPT violating QED. Essentially, we control the breaking terms by using a suitable set of external sources. Thus, with the symmetries restored, a perturbative treatment can be consistently employed. After showing the renormalizability, the external sources attain certain physical values, which allow the recovering of the starting physical action. The main result is that the original QED action presents the three usual independent renormalization parameters. The Lorentz violating sector can be renormalized by nineteen independent parameters. Moreover, vacuum divergences appear with extra independent renormalization. Remarkably, the bosonic odd sector (Chern-Simons-like term) does not renormalize. One-loop computations are also presented and compared with the existing literature., Comment: 24 pages, 4 figures. arXiv admin note: text overlap with arXiv:1404.4846

We investigate the harmonic-trap control of size and shape of Mott regions in the Fermi Hubbard model on a square optical lattice. The use of Lanczos diagonalization on clusters with twisted boundary conditions, followed by an average over 50-80 samples, drastically reduce finite-size effects in some ground state properties; calculations in the grand canonical ensemble together with a local-density approximation (LDA) allow us to simulate the radial density distribution. We have found that as the trap closes, the atomic cloud goes from a metallic state, to a Mott core, and to a Mott ring; the coverage of Mott atoms reaches a maximum at the core-ring transition. A `phase diagram' in terms of an effective density and the on-site repulsion is proposed, as a guide to maximize the Mott coverage. We also predict that the usual experimentally accessible quantities, the global compressibility and the average double occupancy (rather, its density derivative) display detectable signatures of the core-ring transition. Some spin correlation functions are also calculated, and predict the existence N\'eel ordering within Mott cores and rings., Comment: 5 pages, 6 figures