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A bstract We prove that higher-dimension operators contribute positively to the entropy of a thermodynamically stable black hole at fixed mass and charge. Our results apply whenever the dominant corrections originate at tree level from quantum field theoretic dynamics. More generally, positivity of the entropy shift is equivalent to a certain inequality relating the free energies of black holes. These entropy inequalities mandate new positivity bounds on the coefficients of higher-dimension operators. One of these conditions implies that the charge-to-mass ratio of an extremal black hole asymptotes to unity from above for increasing mass. Consequently, large extremal black holes are unstable to decay to smaller extremal black holes and the weak gravity conjecture is automatically satisfied. Our findings generalize to arbitrary spacetime dimension and to the case of multiple gauge fields. The assumptions of this proof are valid across a range of scenarios, including string theory constructions with a dilaton stabilized below the string scale.

The complexity of problems attacked in topology optimization has increased dramatically during the past decade. Examples include fully coupled multiphysics problems in thermo-elasticity, fluid-structure interaction, Micro-Electro Mechanical System (MEMS) design and large-scale three dimensional problems. The only feasible way to obtain a solution within a reasonable amount of time is to use parallel computations in order to speed up the solution process. The focus of this article is on a fully parallel topology optimization framework implemented in C++, with emphasis on utilizing well tested and simple to implement linear solvers and optimization algorithms. However, to ensure generality, the code is developed to be easily extendable in terms of physical models as well as in terms of solution methods, without compromising the parallel scalability. The widely used Method of Moving Asymptotes optimization algorithm is parallelized and included as a fundamental part of the code. The capabilities of the presented approaches are demonstrated on topology optimization of a Stokes flow problem with target outflow constraints as well as the minimum compliance problem with a volume constraint from linear elasticity.

The Dyson index, β, plays an essential role in random matrix theory, as it labels the so-called “three-fold way” that refers to the symmetries satisfied by ensembles under unitary transformations. As is known, its 1, 2, and 4 values denote the orthogonal, unitary, and symplectic classes, whose matrix elements are real, complex, and quaternion numbers, respectively. It functions, therefore, as a measure of the number of independent non-diagonal variables. On the other hand, in the case of β ensembles, which represent the tridiagonal form of the theory, it can assume any real positive value, thus losing that function. Our purpose, however, is to show that, when the Hermitian condition of the real matrices generated with a given value of β is removed, and, as a consequence, the number of non-diagonal independent variables doubles, non-Hermitian matrices exist that asymptotically behave as if they had been generated with a value 2β. Therefore, it is as if the β index were, in this way, again operative. It is shown that this effect happens for the three tridiagonal ensembles, namely, the β–Hermite, the β–Laguerre, and the β–Jacobi ensembles.

A bstract We study scenarios where a scalar field has a spatially varying vacuum expectation value such that the total field variation is super-Planckian. We focus on the case where the scalar field controls the coupling of a U(1) gauge field, which allows us to apply the Weak Gravity Conjecture to such configurations. We show that this leads to evidence for a conjectured property of quantum gravity that as a scalar field variation in field space asymptotes to infinity there must exist an infinite tower of states whose mass decreases as an exponential function of the scalar field variation. We determine the rate at which the mass of the states reaches this exponential behaviour showing that it occurs quickly after the field variation passes the Planck scale.

Aim: We conducted the most extensive quantitative analysis yet undertaken of the form taken by the island species-area relationship (ISAR), among 20 models, to determine: (1) the best-fit model, (2) the best-fit model family, (3) the best-fit ISAR shape (and presence of an asymptote), (4) system properties that may explain ISAR form, and (5) parameter values and interpretation of the logarithmic implementation of the power model. Location: World-wide. Methods: We amassed 601 data sets from terrestrial islands and employed an information-theoretic framework to test for the best-fit ISAR model, family, and shape, and for the presence/absence of an asymptote. Two main criteria were applied: generality (the proportion of cases for which the model provided an adequate fit) and efficiency (the overall probability of a model, when adequate, being the best at explaining ISARs; evaluated using the mean overall AIC c weight). Multivariate analyses were used to explore the potential of island system properties to explain trends in ISAR form, and to describe variation in the parameters of the logarithmic power model. Results: Adequate fits were obtained for 465 data sets. The simpler models performed best, with the power model ranked first. Similar results were obtained at model family level. The ISAR form is most commonly convex upwards, without an asymptote. Island system traits had low descriptive power in relation to variation in ISAR form. However, the æ and c parameters of the logarithmic power model show significant pattern in relation to island system type and taxon. Main conclusions: Over most scales of space, ISARs are best represented by the power model and other simple models. More complex, sigmoid models may be applicable when the spatial range exceeds three orders of magnitude. With respect to the log power model, z-values are indicative of the process(es) establishing species richness and composition patterns, while c-values are indicative of the realized carrying capacity of the system per unit area. Variation in ISAR form is biologically meaningful, but the signal is noisy, as multiple processes constrain the ecological space available within island systems and the relative importance of these processes varies with the spatial scale of the system.

Recent studies of quantum field theory in FLRW spacetime suggest that the cause of the speeding up of the universe is the running vacuum (RV), see Moreno-Pulido and Solà Peracaula (Eur Phys J C 82(6):551, 2022; Eur Phys J C 80(8):692, 2020). Appropriate renormalization of the energy-momentum tensor shows that the vacuum energy density is a smooth function of the Hubble rate and its derivatives: ρvac=ρvac(H,H˙,H¨,…). This is because in QFT the quantum scaling of ρvac with the renormalization point turns into cosmic evolution with H. As a result, any two nearby points of the cosmic expansion during the standard FLRW epoch are smoothly related through δρvac∼O(H2). In our approach, what we call the ‘cosmological constant’ Λ is just the nearly sustained value of 8πG(H)ρvac(H) around (any) given epoch, where G(H) is the running gravitational coupling. In the present study, after summarizing the main QFT calculations supporting the RV approach, we focus on the calculation of the equation of state (EoS) of the RV for the entire cosmic history within such a QFT framework. In particular, in the very early universe, where higher (even) powers ρvac∼O(HN) (N=4,6,⋯) triggered inflation during a short period in which H=const, the vacuum EoS is very close to wvac=-1. This ceases to be true during the FLRW era, where it adopts the EoS of matter during the relativistic (wvac=1/3) and non-relativistic (wvac=0) epochs. Interestingly enough, we find that in the late universe the EoS becomes mildly dynamical and mimics quintessence, wvac≳-1. It finally asymptotes to -1 in the remote future, but in the transit the RV helps alleviating the H0 and σ8 tensions.

Quantum measurement remains a puzzle through its stormy history from the birth of quantum mechanics to state-of-the-art quantum technologies. Two complementary measurement schemes have been widely investigated in a variety of quantum systems: von Neumann’s projective ‘strong’ measurement and Aharonov’s weak measurement. Here, we report the observation of a weak-to-strong measurement transition in a single trapped 40 Ca + ion system. The transition is realized by tuning the interaction strength between the ion’s internal electronic state and its vibrational motion, which play the roles of the measured system and the measuring pointer, respectively. By pre- and post-selecting the internal state, a pointer state composed of two of the ion’s motional wavepackets is obtained, and its central-position shift, which corresponds to the measurement outcome, demonstrates the transition from the weak-value asymptotes to the expectation-value asymptotes. Quantitatively, the weak-to-strong measurement transition is characterized by a universal transition factor e − Γ 2 / 2 , where Γ is a dimensionless parameter related to the system–apparatus coupling. This transition, which continuously connects weak measurements and strong measurements, may open new experimental possibilities to test quantum foundations and prompt us to re-examine and improve the measurement schemes of related quantum technologies. A weak-to-strong quantum measurement transition has been observed in a single-trapped-ion system, where the ion’s internal electronic state and its vibrational motion play the roles of the measured system and the measuring pointer.

This paper presents a flexible framework for parallel and easy-to-implement topology optimization using the Portable and Extendable Toolkit for Scientific Computing (PETSc). The presented framework is based on a standardized, and freely available library and in the published form it solves the minimum compliance problem on structured grids, using standard FEM and filtering techniques. For completeness a parallel implementation of the Method of Moving Asymptotes is included as well. The capabilities are exemplified by minimum compliance and homogenization problems. In both cases the unprecedented fine discretization reveals new design features, providing novel insight. The code can be downloaded from www.topopt.dtu.dk/PETSc .

A bstract We derive a novel four-dimensional black hole with planar horizon that asymptotes to the linear dilaton background. The usual growth of its entanglement entropy before Page’s time is established. After that, emergent islands modify to a large extent the entropy, which becomes finite and is saturated by its Bekenstein-Hawking value in accordance with the finiteness of the von Neumann entropy of eternal black holes. We demonstrate that viewed from the string frame, our solution is the two-dimensional Witten black hole with two additional free bosons. We generalize our findings by considering a general class of linear dilaton black hole solutions at a generic point along the σ -model renormalization group (RG) equations. For those, we observe that the entanglement entropy is “running” i.e. it is changing along the RG flow with respect to the two-dimensional worldsheet length scale. At any fixed moment before Page’s time the aforementioned entropy increases towards the infrared (IR) domain, whereas the presence of islands leads the running entropy to decrease towards the IR at later times. Finally, we present a four-dimensional charged black hole that asymptotes to the linear dilaton background as well. We compute the associated entanglement entropy for the extremal case and we find that an island is needed in order for it to follow the Page curve.

A bstract Using spread complexity and spread entropy, we study non-unitary quantum dynamics. For non-hermitian Hamiltonians, we extend the bi-Lanczos construction for the Krylov basis to the Schrödinger picture. Moreover, we implement an algorithm adapted to complex symmetric Hamiltonians. This reduces the computational memory requirements by half compared to the bi-Lanczos construction. We apply this construction to the one-dimensional tight-binding Hamiltonian subject to repeated measurements at fixed small time intervals, resulting in effective non-unitary dynamics. We find that the spread complexity initially grows with time, followed by an extended decay period and saturation. The choice of initial state determines the saturation value of complexity and entropy. In analogy to measurement-induced phase transitions, we consider a quench between hermitian and non-hermitian Hamiltonian evolution induced by turning on regular measurements at different frequencies. We find that as a function of the measurement frequency, the time at which the spread complexity starts growing increases. This time asymptotes to infinity when the time gap between measurements is taken to zero, indicating the onset of the quantum Zeno effect, according to which measurements impede time evolution.