Quadratic growth of Out-of-time ordered correlators in quantum kicked rotor model

We investigate both theoretically and numerically the dynamics of Out-of-Time-Ordered Correlators (OTOCs) in quantum resonance condition for a kicked rotor model. We employ various operators to construct OTOCs in order to thoroughly quantify their commutation relation at different time, therefore unveiling the process of quantum scrambling. With the help of quantum resonance condition, we have deduced the exact expressions of quantum states during both forward evolution and time reversal, which enables us to establish the laws governing OTOCs' time dependence. We find interestingly that the OTOCs of different types increase in a quadratic function of time, breaking the freezing of quantum scrambling induced by the dynamical localization under non-resonance condition. The underlying mechanism is discovered and the possible applications in quantum entanglement are discussed.Comment: 6 pages, 1 figur

Characterisation of FG-type stars with an improved transport of chemical elements

Context. The modelling of chemical transport mechanisms is crucial for accurate stellar characterizations. Atomic diffusion is one of these processes and it is commonly included in stellar models. However, it is usually neglected for F-type or more massive stars because it produces surface abundance variations that are unrealistic. Additional mechanisms to counteract atomic diffusion must therefore be considered. It has been demonstrated that turbulent mixing can prevent the surface abundance over-variations, and can also be calibrated to mimic the effects of radiative accelerations on iron. Aims. We aim to evaluate the effect of a calibrated turbulent mixing on the characterisation of a sample of F-type stars, and how the estimates compare with those obtained when the chemical transport mechanisms are neglected. Methods. We selected stars from two samples - one from the Kepler LEGACY sample and the other from a sample of Kepler planet-hosting stars. We inferred their stellar properties using two grids. The first grid considers atomic diffusion only in models that do not show chemical over-variations at the stellar surface. The second grid includes atomic diffusion in all the stellar models and the calibrated turbulent mixing to avoid unrealistic surface abundances. Results. Comparing the derived results from the two grids, we found that the results for the more massive stars in our sample will have higher dispersion in the inferred values of mass, radius and age, due to the absence of atomic diffusion in one of the grids. This can lead to relative uncertainties for individual stars of up to 5% for masses, 2% for radii and 20% for ages. Conclusions. This work shows that a proper modelling of the microscopic transport processes is key for an accurate estimation of their fundamental properties not only for G-type stars, but also for F-type stars.Comment: 19 pages, 13 figures, accepted for publication in A&

Polynomials as terms and the Boolean Independence Theorem

We develop a theory of formal multivariate polynomials over commutative rings by treating them as ring terms. Our main result is that two ring terms are s-equivalent (when expanded they yield the same standard polynomial) iff they are f-equivalent (one can be transformed in the other by a series of elementary transformations). We consider in a similar way Boolean terms (formulas) and prove a theorem that two events $a$ and $b$ in a probability space, which are built by two Boolean terms from respective tuples $A$ and $B$ of elementary events, are independent if the events in $A$ are independent of the events in $B$. This theorem rigorizes arguments in the Probabilistic Method in Combinatorics.Comment: 37 pages, minor change

Pole skipping in holographic theories with gauge and fermionic fields

Using covariant expansions, recent work showed that pole skipping happens in general holographic theories with bosonic fields at frequencies $\mathrm{i}(l_b-s) 2\pi T$, where $l_b$ is the highest integer spin in the theory and $s$ takes all positive integer values. We revisit this formalism in theories with gauge symmetry and upgrade the pole-skipping condition so that it works without having to remove the gauge redundancy. We also extend the formalism by incorporating fermions with general spins and interactions and show that their presence generally leads to a separate tower of pole-skipping points at frequencies $\mathrm{i}(l_f-s)2\pi T$, $l_f$ being the highest half-integer spin in the theory and $s$ again taking all positive integer values. We also demonstrate the practical value of this formalism using a selection of examples with spins $0,\frac{1}{2},1,\frac{3}{2},2$.Comment: 42 pages; v2: matches published versio

Computationally Enhanced Approach for Chance-Constrained OPF Considering Voltage Stability

The effective management of stochastic characteristics of renewable power generations is vital for ensuring the stable and secure operation of power systems. This paper addresses the task of optimizing the chance-constrained voltage-stability-constrained optimal power flow (CC-VSC-OPF) problem, which is hindered by the implicit voltage stability index and intractable chance constraints Leveraging a neural network (NN)-based surrogate model, the stability constraint is explicitly formulated and directly integrated into the model. To perform uncertainty propagation without relying on presumptions or complicated transformations, an advanced data-driven method known as adaptive polynomial chaos expansion (APCE) is developed. To extend the scalability of the proposed algorithm, a partial least squares (PLS)-NN framework is designed, which enables the establishment of a parsimonious surrogate model and efficient computation of large-scale Hessian matrices. In addition, a dimensionally decomposed APCE (DD-APCE) is proposed to alleviate the "curse of dimensionality" by restricting the interaction order among random variables. Finally, the above techniques are merged into an iterative scheme to update the operation point. Simulation results reveal the cost-effective performances of the proposed method in several test systems

LLM Augmented LLMs: Expanding Capabilities through Composition

Foundational models with billions of parameters which have been trained on large corpora of data have demonstrated non-trivial skills in a variety of domains. However, due to their monolithic structure, it is challenging and expensive to augment them or impart new skills. On the other hand, due to their adaptation abilities, several new instances of these models are being trained towards new domains and tasks. In this work, we study the problem of efficient and practical composition of existing foundation models with more specific models to enable newer capabilities. To this end, we propose CALM -- Composition to Augment Language Models -- which introduces cross-attention between models to compose their representations and enable new capabilities. Salient features of CALM are: (i) Scales up LLMs on new tasks by 're-using' existing LLMs along with a few additional parameters and data, (ii) Existing model weights are kept intact, and hence preserves existing capabilities, and (iii) Applies to diverse domains and settings. We illustrate that augmenting PaLM2-S with a smaller model trained on low-resource languages results in an absolute improvement of up to 13\% on tasks like translation into English and arithmetic reasoning for low-resource languages. Similarly, when PaLM2-S is augmented with a code-specific model, we see a relative improvement of 40\% over the base model for code generation and explanation tasks -- on-par with fully fine-tuned counterparts.Comment: 17 pages, 2 figures, 8 table

Real-Time 2D Temperature Field Prediction in Metal Additive Manufacturing Using Physics-Informed Neural Networks

Accurately predicting the temperature field in metal additive manufacturing (AM) processes is critical to preventing overheating, adjusting process parameters, and ensuring process stability. While physics-based computational models offer precision, they are often time-consuming and unsuitable for real-time predictions and online control in iterative design scenarios. Conversely, machine learning models rely heavily on high-quality datasets, which can be costly and challenging to obtain within the metal AM domain. Our work addresses this by introducing a physics-informed neural network framework specifically designed for temperature field prediction in metal AM. This framework incorporates a physics-informed input, physics-informed loss function, and a Convolutional Long Short-Term Memory (ConvLSTM) architecture. Utilizing real-time temperature data from the process, our model predicts 2D temperature fields for future timestamps across diverse geometries, deposition patterns, and process parameters. We validate the proposed framework in two scenarios: full-field temperature prediction for a thin wall and 2D temperature field prediction for cylinder and cubic parts, demonstrating errors below 3% and 1%, respectively. Our proposed framework exhibits the flexibility to be applied across diverse scenarios with varying process parameters, geometries, and deposition patterns.Comment: 42 pages, 13 Figure

A dynamical measure of the black hole mass in a quasar 11 billion years ago

Tight relationships exist in the local universe between the central stellar properties of galaxies and the mass of their supermassive black hole. These suggest galaxies and black holes co-evolve, with the main regulation mechanism being energetic feedback from accretion onto the black hole during its quasar phase. A crucial question is how the relationship between black holes and galaxies evolves with time; a key epoch to probe this relationship is at the peaks of star formation and black hole growth 8-12 billion years ago (redshifts 1-3). Here we report a dynamical measurement of the mass of the black hole in a luminous quasar at a redshift of 2, with a look back time of 11 billion years, by spatially resolving the broad line region. We detect a 40 micro-arcsecond (0.31 pc) spatial offset between the red and blue photocenters of the H$\alpha$ line that traces the velocity gradient of a rotating broad line region. The flux and differential phase spectra are well reproduced by a thick, moderately inclined disk of gas clouds within the sphere of influence of a central black hole with a mass of 3.2x10$^{8}$ solar masses. Molecular gas data reveal a dynamical mass for the host galaxy of 6x10$^{11}$ solar masses, which indicates an under-massive black hole accreting at a super-Eddington rate. This suggests a host galaxy that grew faster than the supermassive black hole, indicating a delay between galaxy and black hole formation for some systems.Comment: 5 pages Main text, 8 figures, 2 tables, to be published in Nature, under embargo until 29 January 2024 16:00 (London

Assessing the Potential of Space-Time-Coding Metasurfaces for Sensing and Localization

Intelligent metasurfaces are one of the favorite technologies for integrating sixth-generation (6G) networks, especially the reconfigurable intelligent surface (RIS) that has been extensively researched in various applications. In this context, a feature that deserves further exploration is the frequency scattering that occurs when the elements are periodically switched, referred to as Space-Time-Coding metasurface (STCM) topology. This type of topology causes impairments to the established communication methods by generating undesirable interference both in frequency and space, which is worsened when using wideband signals. Nevertheless, it has the potential to bring forward useful features for sensing and localization. This work exploits STCM sensing capabilities in target detection, localization, and classification using narrowband downlink pilot signals at the base station (BS). The results of this novel approach reveal the ability to retrieve a scattering point (SP) localization within the sub-centimeter and sub-decimeter accuracy depending on the SP position in space. We also analyze the associated detection and classification probabilities, which show reliable detection performance in the whole analyzed environment. In contrast, the classification is bounded by physical constraints, and we conclude that this method presents a promising approach for future integrated sensing and communications (ISAC) protocols by providing a tool to perform sensing and localization services using legacy communication signals.Comment: 13 pages, 9 figures, 1 table. Manuscript submitted to IEEE-TWC on January 6th, 202

Inversion Ring in Chromonic Twisted Hedgehogs: Theory and Experiment

Twisted hedgehogs are defects in spherical cavities with homeotropic anchoring for the nematic director that arise when twist distortions are sufficiently less energetic than splay (and bend) distortions. They bear a characteristic inversion ring, where the director texture changes the sense it spirals about the center of the cavity. This paper applies a quartic twist theory recently proposed to describe the elasticity of chromonics to explain a series of inversion rings observed in aqueous solutions of SSY at two different concentrations. The theory features a phenomenological length a, whose measure is extracted from the data and shown to be fairly independent of the cavity radius, as expected for a material constant