Scalar Theory Research Articles

The Fock-space landscape of many-body localisation.

This article reviews recent progress in understanding the physics of many-body localisation (MBL)in disordered and interacting quantum
many-body systems, from the perspective of ergodicity breaking on the associated Fock space. This approach to MBL is underpinned by mapping the dynamics of the many-body system onto that of a fictitious single particle on the high-dimensional, correlated and disordered Fock-space 
graph; yet, as we elaborate, the problem is fundamentally different from that of conventional Anderson localisation on high-dimensional or hierarchical graphs. We discuss in detail the nature of eigenstate correlations on the Fock space, both static and dynamic, and in the
ergodic and many-body localised phases as well as in the vicinity of the MBL transition. The latter in turn sheds light on the nature of the transition, and motivates a scaling theory for it in terms of Fock-space based quantities. We also illustrate how these quantities can be concretely connected
to real-space observables. An overview is given of several analytical and numerical techniques which have proven important in developing a comprehensive picture. Finally, we comment on some open questions in the field of MBL where the Fock-space approach is likely to prove 
insightful.

Magnetothermal effect and first-principles calculations of Zn-doped Mn5Ge3-based alloys

This study investigates the compound system Mn5−xZnxGe3 (x = 0.1, 0.2, and 0.3) through experimental investigations and theoretical calculations. Zn doping lowers the Curie temperature and magnetic entropy change of Mn5−xZnxGe3 alloys. Analysis of phenomenological curves, including Landau theories, normalized curves, and Arrott curves during the study of isothermal magnetization curves, reveals a second-order phase transition in this system. Through an extensive investigation of critical behavior using critical isotherm curves and the Kouvel–Fisher (KF) method, the consistency and reliability of these critical indices are validated by the prediction of the scaling theory in the critical region. By scaling the dependence of |ΔSM| on M and applying crucial exponen21t values, an efficient new approach is utilized to calculate the spontaneous magnetization that agrees well with the values deduced from the KF method. Additionally, first-principles calculations reveal that the Mn atoms' 3d orbitals are more significantly close to the Fermi energy level, with Zn doping generally reducing both the electronic density of states and the total magnetic moment of the Mn 3d orbitals. Consequently, the introduction of Zn leads to a decrease in the Mn–Mn atom exchange coupling, resulting in a deterioration of the total exchange interaction. This phenomenon also explains the decrease in the Curie temperature TC due to Zn doping, aligning with experimental observations.

Determination of Optical and Structural Parameters of Thin Films with Differently Rough Boundaries

The optical characterization of non-absorbing, homogeneous, isotropic polymer-like thin films with correlated, differently rough boundaries is essential in optimizing their performance in various applications. A central aim of this study is to derive the general formulae necessary for the characterization of such films. The applicability of this theory is illustrated through the characterization of a polymer-like thin film deposited by plasma-enhanced chemical vapor deposition onto a silicon substrate with a randomly rough surface, focusing on the analysis of its rough boundaries over a wide range of spatial frequencies. The method is based on processing experimental data obtained using variable-angle spectroscopic ellipsometry and spectroscopic reflectometry. The transition layer is considered at the lower boundary of the polymer-like thin film. The spectral dependencies of the optical constants of the polymer-like thin film and the transition layer are determined using the Campi–Coriasso dispersion model. The reflectance data are processed using a combination of Rayleigh–Rice theory and scalar diffraction theory in the near-infrared and visible spectral ranges, while scalar diffraction theory is used for the processing of reflectance data within the ultraviolet range. Rayleigh–Rice theory alone is sufficient for the processing of the ellipsometric data across the entire spectral range. We accurately determine the thicknesses of the polymer-like thin film and the transition layer, as well as the roughness parameters of both boundaries, with the root mean square (rms) values cross-validated using atomic force microscopy. Notably, the rms values derived from optical measurements and atomic force microscopy show excellent agreement. These findings confirm the reliability of the optical method for the detailed characterization of thin films with differently rough boundaries, supporting the applicability of the proposed method in high-precision film analysis.

Trace anomalies and the graviton-dilaton amplitude

We consider 3+1 dimensional Quantum Field Theories (QFTs) coupled to the dilaton and the graviton. We show that the graviton-dilaton scattering amplitude receives a universal contribution which is helicity flipping and is proportional to ∆c − ∆a along any RG flow, where ∆c and ∆a are the differences of the UV and IR c- and a-trace anomalies respectively. This allows us to relate ∆c − ∆a to spinning massive states in the spectrum of the QFT. We test our predictions in two simple examples: in the theory of a massive free scalar and in the theory of a massive Dirac fermion (a more complicated example is provided in a companion paper [1]). We discuss possible applications.

Some Exact Green Function Solutions for Non-Linear Classical Field Theories

We consider some non-linear non-homogeneous partial differential equations (PDEs) and derive their exact Green function solution as a functional Taylor expansion in powers of the source. The kind of PDEs we consider are dispersive ones where the exact solution of the corresponding homogeneous equations can have some known shape. The technique has a formal similarity with the Dyson–Schwinger set of equations to solve quantum field theories. However, there are no physical constraints. Indeed, we show that a complete coincidence with the statistical field model of a quartic scalar theory can be achieved in the Gaussian expansion of the cumulants of the partition function.

Relativistic BEC extracted from a complex FRG flow equation

Abstract Based on the functional renormalization group (FRG) under the local potential approximation, we analyze the Bose-Einstein condensation (BEC) in the relativistic complex scalar theory. This framework leads to a complex flow equation of the effective potential, even with the well-known Litim regulator. In order to evaluate the condensate from such a complex effective potential, we impose a condition between chemical potential and mass, analogously to those in the free theory or the mean field theory. We elucidate that for the strongly (weakly) coupled theory, the phase diagrams computed from the FRG are more (less) deviated from that under the mean field approximation. This result implies that quantum fluctuations strongly affect the nonperturbative formation of the BEC.

Topological recursion for hyperbolic string field theory

We derive an analog of Mirzakhani’s recursion relation for hyperbolic string vertices and investigate its implications for closed string field theory. Central to our construction are systolic volumes: the Weil-Petersson volumes of regions in moduli spaces of Riemann surfaces whose elements have systoles L ≥ 0. These volumes can be shown to satisfy a recursion relation through a modification of Mirzakhani’s recursion as long as L ≤ 2 sinh−1 1. Applying the pants decomposition of Riemann surfaces to off-shell string amplitudes, we promote this recursion to hyperbolic string field theory and demonstrate the higher order vertices are determined by the cubic vertex iteratively for any background. Such structure implies the solutions of closed string field theory obey a quadratic integral equation. We illustrate the utility of our approach in an example of a stubbed scalar theory.

A concrete construction of a topological operator in factorization algebras

Abstract Factorization algebras play a central role in the formulation of quantum field theories given by Kevin Costello and Owen Gwilliam. In this paper, we propose a concrete construction of a topological operator in their formulation. We focus on a shift symmetry of a one-dimensional massless scalar theory. And we give some discussions of $\mathbb {Z}$-gauging of it, i.e., compact scalar theory and its θ-vacuum.

Inter-city firm connections and the scaling of urban economic indicators.

Cities exhibit consistent returns to scale in economic outputs, and urban scaling analysis is widely adopted to uncover common mechanisms in cities' socioeconomic productivity. Leading theories view cities as closed systems, with returns to scale arising from intra-city social interactions. Here, we argue that the interactions between cities, particularly via shared organizations such as firms, significantly influence a city's economic output. By examining global data on city connectivity through multinational firms alongside urban scaling Gross Domestic Product (GDP) statistics from the United States, EU, and China, we establish that global connectivity notably enhances GDP, while controlling for population. After accounting for global connectivity, the effect of population on GDP is no longer distinguishable from linear. To differentiate between local and global mechanisms, we analyzed homicide case data, anticipating dominant local effects. As expected, inter-city connectivity showed no significant impact. Our research highlights that inter-city effects affect some urban outputs more than others. This empirical analysis lays the groundwork for incorporating inter-city organizational connections into urban scaling theories and could inform future model development.

Analysis of Hyers–Ulam stability and controllability of non-linear switched impulsive systems with delays on time scales

In this article, we have used the concepts of time scales theory to discuss nonlinear switched impulsive systems with delay. Our main objective is to determine the Hyers–Ulam stability and controllability of nonlinear switched impulsive systems with delay on non-uniform time domains. To obtain the necessary and sufficient conditions for existence, Hyers–Ulam stability, and controllability, we utilize the Banach fixed-point theorem and Krasnoselskii’s fixed-point theorem. In order to demonstrate our conclusions, we have discussed some simulation-based examples along with the three tank liquid control problem and a potential practical situation related to the infectious disease with switching rules. The results of this manuscript provide all the necessary and sufficient conditions for Hyers–Ulam stability and controllability that are true for discrete, continuous as well as unified time domains simultaneously.

Optimizing Business Processes: Harnessing Robotic Process Automation in Chinese Enterprises

Abstract: With the continuous development of science and technology, the study of digital technology in China has become increasingly in-depth. As an effective means for enterprises to achieve automated management and standardized operations, Robotic Process Automation (RPA) has attracted widespread attention. RPA process automation technology can improve the efficiency of financial management and ensure the quality of work while meeting enterprise development needs. This study explores the multifaceted applications and impact of RPA in the financial shared services sector. By utilizing RPA, companies can streamline processes, reduce costs and increase overall operational flexibility. The study delves into the theoretical underpinnings of RPA adoption, drawing on concepts such as economies of scale, process reengineering and information processing theory. In addition, the paper illuminates the transformative impact of RPA on business operations through field case studies, including the pioneering efforts of Sinochem International. By providing a comprehensive analysis of the pros and cons of RPA implementation, this paper provides valuable insights for Chinese companies seeking to optimize their business processes and embrace the era of intelligent automation.

Self-dual cosmology

We construct cosmological spacetimes with a self-dual Weyl tensor whose dynamics are described by conformally coupled scalars with only cubic self-interactions. Similar to the previously discovered cases in flat and (Anti) de Sitter backgrounds, the interactions are characterized by a bracket that encodes a kinematic algebra. We discuss how the color-kinematics duality and double copy are realized in these cosmological backgrounds. If we further impose that the Ricci scalar is that of an FLRW spacetime, we find two new self-dual metrics corresponding to radiation-dominated and coasting (non-accelerating) FLRW backgrounds. Relaxing this requirement, we find an infinite family of solutions given by three different conformal classes of cosmological self-dual metrics. These solutions approximate those of FLRW as long as we impose a simple additional constraint on the scalar theory.

Periodic Bonding Behaviors of Actinide Atoms (An = Th-Cm) with Negatively Curved Nanographene.

The nanographene with negative curvature has been extensively studied due to its interesting properties and potential applications. In the present work, we have performed all-electron scalar relativistic density functional theory (DFT) calculations to understand the periodic interaction mechanisms of actinide atoms (An = Th, Cm) with the TB8C nanographene. The encapsulated complexes (An@TB8C) were formed due to the octagonal vacancy in the TB8C nanographene. TB8C shows fairly high affinity toward An atoms, especially for Th and Pa. AIMD simulations further confirmed the effective trapping of An atom with TB8C. The partial covalent characters of An-C bonds in An@TB8C were revealed through various bond analysis methods. The 6d electrons of An play an important role in the participation of chemical bonds. The delocalization index (DI) is proposed as a useful descriptor in the study of bond strength involving the actinides. Electronic absorption spectra were simulated for further identification in the experiments. The current work has expanded the potential molecular properties and applications of nanographene.

Evolution of [formula omitted]-spacing in clay with PEG bulk volume fraction and molecular weight: Theoretical and experimental study

In the pursuit of ensuring the sustainability of the construction sector and fortifying its resilience against climate change, scientists have dedicated significant efforts to explore new classes of innovative, affordable, and technologically advanced materials that exhibit high efficiency, thereby securing the future for generations to come. In this context, we have opted to produce clay-polymer ecosystems through the direct insertion process. The PEG2000/clay and PEG6000/clay composites underwent analysis using X-ray diffraction (XRD) techniques, revealing the evolution of dhklconcerning the PEG bulk volume fraction. The results indicate the presence of two adsorption cycles, each comprising three stages (dilute, two-dimensional semi-dilute, and plateau). Each cycle delineates the incorporation of a polymer layer into the interlayer spaces of clay minerals. To elucidate this adsorption process, we have proposed a model depicting PEG chain conformation in confined spaces, represented as both monolayer and bilayer configurations. The influence of PEG molecular weight is distinctly evident in the dhklevolution across various clay categories. Ultimately, the application of scaling theory to model the experimental results proves to be robust, offering a precise description of the three discussed regimes.

Influence of the acceptance angle on the evaluation of reflectance data of randomly rough surfaces using scalar diffraction theory

Apart from coherent reflectance, which corresponds to specular reflection, the values obtained by real spectrophotometers also include contribution from incoherent reflectance, which represents light scattered by the samples and registered by the detector due to its finite acceptance angle. This work aims to investigate the influence of this second part on reflectance spectra measured for samples with randomly rough surfaces. Three silicon samples with roughened surfaces are investigated. The reflectance is measured using a commercial spectrophotometer with acceptance angles restricted by apertures placed in the incident and reflected beam. The proposed method is based on the simultaneous processing of spectral dependencies of reflectance measured with differently-sized apertures. The utilized theoretical approach is based on the scalar diffraction theory. Because the dependencies on both wavelength and acceptance angle are considered, a model providing correct predictions for these dependencies should also correctly describe how is the total reflectance separated into its coherent and incoherent parts. It is shown that the theoretical predictions for incoherent reflectance are consistent with the changes in the diameter of the apertures. It was possible to determine the RMS value of the heights as well as the estimate for the autocorrelation length and additional parameter controlling the course of the autocorrelation function. A short discussion comparing our results with those achieved using methods employed in earlier works is also provided.

Analyzing the spectrum characteristics of a double-grating transmission scheme

In this paper, the spectral characteristics formed by a double-grating transmission scheme are discussed based on the scalar diffraction theory. First, considering two different grating periods, the angular spectrum at the back of the second grating is obtained. Then, the spectral characteristics are discussed with three different periodic conditions, while it is proved that the spatial distribution and spacing of the spectrum are absolutely determined by the grating constants and angles. The theoretical results manifest that the spatial distribution range of the spectrum becomes larger as the angle increases, unlike the spectral points, which are distributed on a single line when the grating lines of the two gratings are parallel. Finally, for the sake of proving that our theoretical analysis is correct and reasonable, three sets of experiments are conducted with three different combinations of Ronchi gratings. As expected, the experimental and theoretical results are in perfect agreement. In a word, the involved results could be useful for expanding the application of moiré deflectometry.

Calibration of discrete meta-parameters of bamboo flour based on magnitude analysis and BP neural network.

In the research and development of technology and equipment for bamboo products deep processing, such as filling, drying, and medicinal use of bamboo flour (BF), the poor compaction and fluidity of BF materials entails the need for accurate discrete element model (DEM) and BF parameters to provide a reference for the simulation of BF processing operationsand the development of related equipment. The average particle size of the 5 types of BFs ranges from 0.136 mm to 0.293 mm, and the small particle size of BF particles causes to the number of BF particles in bamboo processing equipment to reach tens of millions or even billions. When conventional methods are used for simulation, ordinary computers cannot provide the required computing power. To address the aforementioned challenges, this paper proposes a calibration method for the discrete element contact parameters of BFs based on dimensional analysis and a back propagation (BP) neural network. Using particle scaling theory and dimensional analysis methods, the average particle size of the BF was increased to 1 mm, and the main discrete element contact parameters of the five types of BF to be tested were used as input layers. The injection method and sidewall collapse method were used to obtain the angle of repose (AR) as the output layer. Fifty groups were randomly selected using MATLAB for EDEM simulation, and the simulation results were trained using the BP neural network algorithm; an ideal neural network model was obtained, the discrete element parameters of different BFs were predicted, and physical experiments were performed to verify two types of AR and mold hole compression under calibrated parameters. The relative error between the simulated AR obtained through calibration parameters and the physical experimental values is less than 2.3%. Through BF parameter validity verification, the simulated maximum compression displacement and compression ratio after stabilization were 34.81 mm and 0.477, which were close to the actual experimental results of 34.77 mm and 0.461, respectively, verifying the accuracy of the neural network prediction model. The research results provide a reference for the simulation of BF processing operations and the development of related equipment.

Critical behavior and tunable magnetocaloric effect in (Gd1-xErx)3Al2 alloys

The magnetic properties, magnetocaloric effect, and the critical behavior near Curie temperature (TC) were systematically studied in a series of (Gd1-xErx)3Al2 (x = 0, 0.1, 0.2, 0.3) alloys. As the Er content increases, both the TC and lattice constant gradually decrease. The maximum magnetic entropy change and refrigerant capacity remain relatively high, ranging from −5.8 to −8.5J/kg K and 209.0 to 290.8 J/kg respectively, for a field change of 5 T. The critical exponents, derived from the field dependence of magnetic entropy change, conform to scaling theory and are consistent with those obtained using the Kouvel–Fisher method. These findings suggest that the reliability of the obtained critical exponents and imply the presence of long-range exchange interactions in (Gd1-xErx)3Al2 alloys.

Scaling study of diffusion in dynamic crowded spaces

Abstract We formulate a scaling theory for the long-time diffusive motion
in a space occluded by a high density of moving obstacles in
dimensions 1, 2 and 3. Our tracers diffuse anomalously over many decades in
time, before reaching a diffusive steady state with an effective diffusion
constant D eff, which depends on the obstacle diffusivity and density.
The scaling of D eff, above and below a critical regime,
is characterized by two independent critical
parameters: the conductivity exponent μ, also found in models with frozen
obstacles, and an exponent ψ, which quantifies the effect of obstacle
diffusivity.

Linking Thermal Conductivity to Equations of State Using the Residual Entropy Scaling Theory.

In recent years, the application of the residual entropy scaling (RES) method for modeling transport properties has become increasingly prominent. Based on Yang et al. (Ind. Eng. Chem. Res. 2021, 60, 13052) in modeling the thermal conductivity of refrigerants, we present here an RES model that extends Yang et al.'s approach to a wider range of pure fluids and their mixtures. All fluids available in the REFPROP 10.0 software, i.e., those with reference equations of state (EoS), were studied. A total of 71,554 experimental data of 125 pure fluids and 16,702 experimental data of 164 mixtures were collected from approximately 647 references, mainly based on the NIST ThermoData Engine (TDE) database 10.1. As a result, over 68.2% (corresponding to the standard deviation of a normal distribution) of the well-screened experimental data agree with the developed RES model within 3.1% and 4.6% for pure fluids and mixtures, respectively. Comparative analysis against the various models implemented in the REFPROP 10.0 (one of the state-of-the-art software packages for thermophysical property calculations) reveals that our RES model demonstrates analogous statistical agreement with experimental data yet with much fewer parameters. Regarding the average absolute value of the relative deviation (AARD) from experimental values to model predictions, the developed RES model shows a smaller or equal AARD for 74 pure fluids out of 125 and 76 mixtures out of 164. Besides, a detailed examination of the impact of the critical enhancement term on mixture calculations was conducted. To use our model easily, a software package written in Python is provided in the Supporting Information.