Classical Field Research Articles

Geometric flavors of Quantum Field theory on a Cauchy hypersurface. Part I: Gaussian analysis and other mathematical aspects

In this series of papers we aim to provide a mathematically comprehensive framework to the hamiltonian pictures of quantum field theory in curved spacetimes. Our final goal is to study the kinematics and the dynamics of the theory from the point of differential geometry in infinite dimensions. In this first part we introduce the tools of Gaussian analysis in infinite dimensional spaces of distributions. These spaces will serve the basis to understand the Schrödinger and Holomorphic pictures, over arbitrary Cauchy hypersurfaces, using tools of Hida-Malliavin calculus. Here the Wiener-Ito decomposition theorem provides the QFT particle interpretation. Special emphasis is done in the applications to quantization of these tools in the second part of this paper. We devote a section to introduce Hida test functions as a notion of second quantized test functions. We also analyze of the ingredients of classical field theory modeled as distributions paving the way for quantization procedures that will be analyzed in [3].

Superoscillations in high energy physics and gravity

We explore superoscillations within the context of classical and quantum field theories, presenting novel solutions to Klein–Gordon’s, Dirac’s, Maxwell’s and Einstein’s equations. In particular, we illustrate a procedure of second quantization of fields and how to construct a Fock space which encompasses Superoscillating states. Furthermore, we extend the application of superoscillations to quantum tunnelings, scatterings and mixings of particles, squeezed states and potential advancements in laser interferometry, which could open new avenues for experimental tests of quantum gravity effects. By delving into the relationship among superoscillations and phenomena such as Hawking radiation, the black hole (BH) information and the Firewall paradox, we propose an alternative mechanism for information transfer across the BH event horizon.

Hydrogeological parameterisation of the Daruvar thermal aquifer: integration of fracture network analysis and well testing

Highly fractured Mesozoic carbonate rocks are the main reservoir of many geothermal resources in northern Croatia, being of environmental, cultural, and economic value for the local and regional communities. The Daruvar thermal springs (temperatures < 50°C) represent the outflow area of an intermediate scale, tectonically controlled, hydrothermal system hosted in Triassic carbonate rocks. Several investigations have been conducted in the Daruvar area detailing the architecture of regional and local fracture networks and quantifying the hydrogeological parameters of the thermal aquifer. In this work, an integrated approach based on structural and hydrogeological investigations was employed to model the network of fractures in the reservoir and quantify its impact on the hydraulic properties. Structural investigations were conducted in the Batinjska Rijeka quarry, considered as an outcrop analogue of the thermal aquifer, employing both a classical field approach and the virtual quantitative analysis of a 3D digital outcrop model. Structural analysis of the digital outcrop model allowed identification of two sub-vertical systems of discontinuities, dipping to the NW and the WSW respectively, in accordance with the data collected through direct field measurements. The main geometric features of the discontinuity network and their statistical distributions were employed to construct discrete fracture network models at both the outcrop scale (approximately 100 m) and the aquifer scale in Daruvar (approximately 700 m). Calibration of the input parameters allowed modelling of porosity and permeability values that reproduce the field values assessed through pumping tests, well tests, and well logging. This work highlights the importance of integrating geological and hydrogeological investigations to obtain a more reliable reconstruction and quantification of the processes driving the fluid flow in fractured aquifers and affecting the spatial distribution of their hydraulic properties.

On Darboux theorems for geometric structures induced by closed forms

This work reviews the classical Darboux theorem for symplectic, presymplectic, and cosymplectic manifolds (which are used to describe mechanical systems), as well as certain cases of multisymplectic manifolds, while extends the Darboux theorem in new ways to k-symplectic and k-cosymplectic manifolds (all these structures appear in the geometric formulation of first-order classical field theories). Moreover, we discuss the existence of Darboux theorems for classes of precosymplectic, k-presymplectic, k-precosymplectic, and premultisymplectic manifolds, which are the geometrical structures underlying some kinds of singular field theories, i.e. with locally non-invertible Legendre maps. Approaches to Darboux theorems based on flat connections associated with geometric structures are given, while new results on polarisations for (k-)(pre)(co)symplectic structures arise.

An extended gradient damage model for anisotropic fracture

This paper combines energy decomposition and an extended gradient damage (EGD) model to develop an anisotropic fracture framework with decoupling of tensile and shear cohesive laws. By introducing the shear-normal decomposition in the energy form, the driving force of the damage variable is established within the framework of the EGD model, which is then capable of capturing the traction-separation of potential crack surfaces in both shear and normal directions. The intrinsic correspondence between the cohesive law and the damage evolution enables the accurate prediction of anisotropic fracture behavior in the mixed form of Mode I and Mode II. Furthermore, the proposed model also addresses the damage unloading issue, which still remains a challenge in classic phase field theory or non-local damage theory. A number of numerical examples are presented as validation. Some cutting-edge benchmarks, such as complex mixed-mode fracture and perfect shear fracture, are well reproduced.

Phase field modeling of ductile fracture with isotropic hardening and radius return method

Phase field model has been investigated for brittle fracture in many static and dynamic scenarios, but its applications to ductile fracture is not as common as brittle fracture, especially implementing in software LS-DYNA with explicit scheme. In this study, an efficient LS-DYNA implementation of the phase field modeling of ductile fracture is presented and both with and without the split of elastic strain energy have been considered for the damage evolution. In more detail, plasticity formulation of ductile material with isotropic hardening is briefly presented first and then the governing equations of the classical phase field model are derived, which gives the displacement-phase coupled problem. For with the split of elastic strain energy, the shear component of elastic strain energy is considered for the damage evolution. The influence of degradation function on stress–strain curve is also investigated by using three kinds of function (polynomial function, algebraic fraction function and sigmoid function), which leads to linear and nonlinear finite element method (FEM) formulation of the phase field model and Newton–Raphson method is used to solve the nonlinear FEM formulation of the phase field model. A tensile bar test shows the influence of critical energy release rate and degradation function on stress–strain curve. Mode Ⅰ failure of three-point bending test, Mode Ⅱ failure of single-edge notched plate and mixed-mode failure of asymmetrical double-notched plate verify the proposed model in this study. From these simulations, with the split of elastic strain energy shows improvements on plastic deformation than without the split of elastic strain energy.

Well-Posedness and Regularity of Solutions to Neural Field Problems with Dendritic Processing

We study solutions to a recently proposed neural field model in which dendrites are modelled as a continuum of vertical fibres stemming from a somatic layer. Since voltage propagates along the dendritic direction via a cable equation with nonlocal sources, the model features an anisotropic diffusion operator, as well as an integral term for synaptic coupling. The corresponding Cauchy problem is thus markedly different from classical neural field equations. We prove that the weak formulation of the problem admits a unique solution, with embedding estimates similar to the ones of nonlinear local reaction–diffusion equations. Our analysis relies on perturbing weak solutions to the diffusion-less problem, that is, a standard neural field, for which weak problems have not been studied to date. We find rigorous asymptotic estimates for the problem with and without diffusion, and prove that the solutions of the two models stay close, in a suitable norm, on finite time intervals. We provide numerical evidence of our perturbative results.

Linear and Nonlinear Formulation of Phase Field Model with Generalized Polynomial Degradation Functions for Brittle Fractures

The classical phase field model has wide applications for brittle materials, but nonlinearity and inelasticity are found in its stress–strain curve. The degradation function in the classical phase field model makes it a linear formulation of phase field and computationally attractive, but stiffness reduction happens even at low strain. In this paper, generalized polynomial degradation functions are investigated to solve this problem. The first derivative of degradation function at zero phase is added as an extra constraint, which renders higher-order polynomial degradation function and nonlinear formulation of phase field. Compared with other degradation functions (like algebraic fraction function, exponential function, and trigonometric function), this polynomial degradation function enables phase in [0, 1] (should still avoid the first derivative of degradation function at zero phase to be 0), so there is no Γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma $$\\end{document} convergence problem. The good and meaningful finding is that, under the same fracture strength, the proposed phase field model has a larger length scale, which means larger element size and better computational efficiency. This proposed phase field model is implemented in LS-DYNA user-defined element and user-defined material and solved by the Newton–Raphson method. A tensile test shows that the first derivative of degradation function at zero phase does impact stress–strain curve. Mode I, mode II, and mixed-mode examples show the feasibility of the proposed phase field model in simulating brittle fracture.

Studying phonon coherence with a quantum sensor

Nanomechanical oscillators offer numerous advantages for quantum technologies. Their integration with superconducting qubits shows promise for hardware-efficient quantum error-correction protocols involving superpositions of mechanical coherent states. Limitations of this approach include mechanical decoherence processes, particularly two-level system (TLS) defects, which have been widely studied using classical fields and detectors. In this manuscript, we use a superconducting qubit as a quantum sensor to perform phonon number-resolved measurements on a piezoelectrically coupled phononic crystal cavity. This enables a high-resolution study of mechanical dissipation and dephasing in coherent states of variable size (n¯≃1−10\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\bar{n}\\simeq 1-10$$\\end{document} phonons). We observe nonexponential relaxation and state size-dependent reduction of the dephasing rate, which we attribute to TLS. Using a numerical model, we reproduce the dissipation signatures (and to a lesser extent, the dephasing signatures) via emission into a small ensemble (N = 5) of rapidly dephasing TLS. Our findings comprise a detailed examination of TLS-induced phonon decoherence in the quantum regime.

Sodium Triflate Water-in-Salt Electrolytes in Advanced Battery Applications: A First-Principles-Based Molecular Dynamics Study.

Offering a compelling combination of safety and cost-effectiveness, water-in-salt (WiS) electrolytes have emerged as promising frontiers in energy storage technology. Still, there is a strong demand for research and development efforts to make these electrolytes ripe for commercialization. Here, we present a first-principles-based molecular dynamics (MD) study addressing in detail the properties of a sodium triflate WiS electrolyte for Na-ion batteries. We have developed a workflow based on a machine learning (ML) potential derived from ab initio MD simulations. As ML potentials are typically restricted to the interpolation of the data points of the training set and have hardly any predictive properties, we subsequently optimize a classical force field based on physics principles to ensure broad applicability and high performance. Performing and analyzing detailed MD simulations, we identify several very promising properties of the sodium triflate as a WiS electrolyte but also indicate some potential stability challenges associated with its use as a battery electrolyte.

Computational Screening of Hydrophobic Zeolites for the Removal of Emerging Organic Contaminants from Water.

The pollution of water resources by pharmaceuticals and agents of personal care products (PPCPs) poses an increasingly pressing issue that has received considerable attention from scientists and government agencies alike. Hydrophobic zeolites can serve as selective adsorbents to remove these contaminants from aqueous solution. So far, the adsorption of PPCPs in zeolites has often been investigated in case studies focusing on a small number of contaminants and one or a few zeolites. We present a computational screening approach to investigate the interaction of 53 PPCPs with 14 all-silica zeolites, aiming at a more comprehensive understanding of factors that are beneficial for a strong host-guest interaction and thus an efficient adsorption. The systems are modelled on the classical force field level of theory, allowing for the efficient computational treatment of a large number of PPCP-zeolite combinations and evaluated in terms of the interaction energy between PPCP and zeolite framework. For selected PPCP-zeolite combinations additional Free Energy Perturbation simulations are employed to compute Free Energies of Transfer between the aqueous phase and the adsorbed state. These results can serve as a starting point for experimental studies of relevant PPCP-zeolite combination or more in-depth theoretical investigations.

Wave turbulence and the kinetic equationbeyond leading order.

We derive a scheme by which to solve the Liouville equationperturbatively in the nonlinearity, which we apply to weakly nonlinear classical field theories. Our solution is a variant of the Prigogine diagrammatic method and is based on an analogy between the Liouville equationin infinite volume and scattering in quantum mechanics, described by the Lippmann-Schwinger equation. The motivation for our work is wave turbulence: A broad class of nonlinear classical field theories are believed to have a stationary turbulent state-a far-from-equilibrium state, even at weak coupling. Our method provides an efficient way to derive properties of the weak wave turbulent state. A central object in these studies, which is a reduction of the Liouville equation, is the kinetic equation, which governs the occupation numbers of the modes. All properties of wave turbulence to date are based on the kinetic equationfound at leading order in the weak nonlinearity. We explicitly obtain the kinetic equationto next-to-leading order.

Modeling Water Interactions with Graphene and Graphite via Force Fields Consistent with Experimental Contact Angles.

Accurate simulation models for water interactions with graphene and graphite are important for nanofluidic applications, but existing force fields produce widely varying contact angles. Our extensive review of the experimental literature reveals extreme variation among reported values of graphene-water contact angles and a clustering of graphite-water contact angles into groups of freshly exfoliated (60° ± 13°) and not-freshly exfoliated graphite surfaces. The carbon-oxygen dispersion energy for a classical force field is optimized with respect to this 60° graphite-water contact angle in the infinite-force-cutoff limit, which in turn yields a contact angle for unsupported graphene of 80°, in agreement with the mean of the experimental results. Interaction force fields for finite cutoffs are also derived. A method for calculating contact angles from pressure tensors of planar equilibrium simulations that is ideally suited to graphite and graphene surfaces is introduced. Our methodology is widely applicable to any liquid-surface combination.

Abrupt Change from Ionic to Covalent Bonding in Nickel Halides Accompanied by Ligand Field Inversion.

The electronic configuration of transition metal centers and their ligands is crucial for redox reactions in metal catalysis and electrochemistry. We characterize the electronic structure of gas-phase nickel monohalide cations via nickel L2,3-edge X-ray absorption spectroscopy. Comparison with multiplet charge-transfer simulations and experimental spectra of selectively prepared nickel monocations in both ground- and excited-state configurations are used to facilitate our analysis. Only for [NiF]+ with an assigned ground state of 3Π can the bonding be described as predominantly ionic, while the heavier halides with assigned ground states of 3Π or 3Δ exhibit a predominantly covalent contribution. The increase in covalency is accompanied by a transition from a classical ligand field for [NiF]+ to an inverted ligand field for [NiCl]+, [NiBr]+, and [NiI]+, resulting in a leading 3d9 L̲ configuration with a ligand hole (L̲) and a 3d occupation indicative of nickel(I) compounds. Hence, the absence of a ligand hole in [NiF]+ precludes any ligand-based redox reactions. Additionally, we demonstrate that the shift in energy of the L3 resonance is reduced compared to that of isolated atoms upon the formation of covalent compounds.

Classical gravitational anomalies of Liouville theory

We show that for classical Liouville field theory, diffeomorphism invariance, Weyl invariance and locality cannot hold together. This is due to a genuine Virasoro center, present in the theory, that leads to an energy-momentum tensor with non-tensorial conformal transformations, in flat space, and with a non-vanishing trace, in curved space. Our focus is on a field-independent term, proportional to the square of the Weyl gauge field, WμWμ, that makes the action Weyl-invariant and was disregarded in previous investigations of Weyl and conformal symmetry. We show this term to be related to the classical center of the Virasoro algebra. The mechanism uncovered here is a classical version of the quantum anomalous phenomenon: the generalization to curved space only allows to keep one of the two symmetries enjoyed by the flat space theory, either Lorentz (diffeomorphism) or conformal invariance.

The entropic uncertainty preservation in non-Markovian environment via classical driving fields

Uncertainty relations in terms of entropies were initially proposed to deal with conceptual shortcomings in the original formulation of the uncertainty principle and, hence, play an important role in quantum foundations. In quantum information theory, the preferred mathematical quantity to express the entropic uncertainty relation is the Shannon’s entropy. In this work, we investigate the effect of a classical driving field on entropic uncertainty lower bound (EULB). In this regard, we consider a particle as the quantum memory correlated with a measured particle, where during the interaction with the environment, the quantum memory is driven by the external classical field. Our result reveals that in the presence of the classical driving fields, the EULB is reduced and consequently, the measurement accuracy is increased.

Raman Spectra of Amino Acids and Peptides from Machine Learning Polarizabilities.

Raman spectroscopy is an important tool in the study of vibrational properties and composition of molecules, peptides, and even proteins. Raman spectra can be simulated based on the change of the electronic polarizability with vibrations, which can nowadays be efficiently obtained via machine learning models trained on first-principles data. However, the transferability of the models trained on small molecules to larger structures is unclear, and direct training on large structures is prohibitively expensive. In this work, we first train two machine learning models to predict the polarizabilities of all 20 amino acids. Both models are carefully benchmarked and compared to density functional theory (DFT) calculations, with the neural network method being found to offer better transferability. By combination of machine learning models with classical force field molecular dynamics, Raman spectra of all amino acids are also obtained and investigated, showing good agreement with experiments. The models are further extended to small peptides. We find that adding structures containing peptide bonds to the training set greatly improves predictions, even for peptides not included in training sets.

Distribution of the built-in field extracted from switching dynamics in HfO2-based ferroelectric capacitor

In this work, we proposed a method to extract the distribution of the built-in field (Eb) from the switching dynamics of the TiN/HfZrO/TiN capacitor. The relationship between reversal polarization and the distribution of Eb is established based on the classic inhomogeneous field mechanism model. Both positive and negative write pulses with different amplitudes and durations are applied to obtain the distribution parameters of Eb. The distribution of Eb is fitted by a Gaussian-type distribution, and the mean value and standard deviation are about −0.02 MV/cm and 0.28 MV/cm, respectively. This work provides an effective approach to analyze Eb directly from the electrical measurement and helps optimize the device design from the polarization switching point of view.

Frequency beating and damping of breathing oscillations of a harmonically trapped one-dimensional quasicondensate

We study the breathing (monopole) oscillations and their damping in a harmonically trapped one-dimensional (1D) Bose gas in the quasicondensate regime using a finite-temperature classical field approach. By characterising the oscillations via the dynamics of the density profile's rms width over long time, we find that the rms width displays beating of two distinct frequencies. This means that 1D Bose gas oscillates not at a single breathing mode frequency, as found in previous studies, but as a superposition of two distinct breathing modes, one oscillating at frequency close to $\simeq\!\sqrt{3}\omega$ and the other at $\simeq\!2\omega$, where $\omega$ is the trap frequency. The breathing mode at $\sim\!\sqrt{3}\omega$ dominates the beating at lower temperatures, deep in the quasicondensate regime, and can be attributed to the oscillations of the bulk of the density distribution comprised of particles populating low-energy, highly-occupied states. The breathing mode at $\simeq\!2\omega$, on the other hand, dominates the beating at higher temperatures, close to the nearly ideal, degenerate Bose gas regime, and is attributed to the oscillations of the tails of the density distribution comprised of thermal particles in higher energy states. The two breathing modes have distinct damping rates, with the damping rate of the bulk component being approximately four times larger than that of the tails component.

Uncertainty in Automated Ontology Matching: Lessons from an Empirical Evaluation

Data integration is considered a classic research field and a pressing need within the information science community. Ontologies play a critical role in such processes by providing well-consolidated support to link and semantically integrate datasets via interoperability. This paper approaches data integration from an application perspective by looking at ontology matching techniques. As the manual matching of different sources of information becomes unrealistic once the system scales up, the automation of the matching process becomes a compelling need. Therefore, we have conducted experiments on actual non-semantically enriched relational data with the support of existing tools (pre-LLM technology) for automatic ontology matching from the scientific community. Even considering a relatively simple case study—i.e., the spatio–temporal alignment of macro indicators—outcomes clearly show significant uncertainty resulting from errors and inaccuracies along the automated matching process. More concretely, this paper aims to test on real-world data a bottom-up knowledge-building approach, discuss the lessons learned from the experimental results of the case study, and draw conclusions about uncertainty and uncertainty management in an automated ontology matching process. While the most common evaluation metrics clearly demonstrate the unreliability of fully automated matching solutions, properly designed semi-supervised approaches seem to be mature for more generalized application.