Noninteracting Model Research Articles

RKFD Scheme for Quantum Reflection Model of Bose-Einstein Condensates (BEC) from Silicon Surface

We applied the numerical combination of Runge-Kutta and Finite Difference (RKFD) scheme for a quantum reflection model of Bose-Einstein condensate (BEC) from a silicon surface. It is by the time-dependent Gross-Pitaevskii equation (GPE), a non-linear Schrödinger equation (NLSE) in the context of quantum mechanics. The role of cut-off potential δ and negative imaginary potential Vim is essential to estimating non-interacting BEC reflection models. Relying on these features, we performed a numerical simulation of the BEC quantum reflection model and calculated the effect of reflection probability R versus incident speed vx. The model is based on the three rapid potential variations: positive-step potential +Vstep, negative-step potential -Vstep, and Casimir-Polder potential VCP. As a result, the RKFP numerical scheme was successfully set up and applied to the quantum reflection model of BEC from the silicon surface. The numerical simulations results show that the reflection probability R decays exponentially to the incident speed vx.

Non-interactive Private Multivariate Function Evaluation using Homomorphic Table Lookup

To address security issues in cloud computing, fully homomorphic encryption (FHE) enables a third party to evaluate functions using ciphertexts that do not leak information to the cloud server. The remaining problems of FHE include high computational costs and limited arithmetic operations, only evaluating additions and multiplications. Arbitrary functions can be evaluated using a precomputed lookup table (LUT), which is one of the solutions for those problems. Previous studies proposed LUT-enabled computation methods 1) with bit-wise FHE and 2) with word-wise FHE. The performance of LUT-enabled computation with bit-wise FHE drops quickly when evaluating BigNum functions because of the complexity being O(s·2^d·m), where m represents the number of inputs, d and s represent the bit lengths of the inputs and outputs, respectively. Thus, LUT-enabled computation with word-wise FHE, which handles a set of bits with one operation, has also been proposed; however, previous studies are limited in evaluating multivariate functions within two inputs and cannot speed up the evaluation when the domain size of the integer exceeds 2N, where N is the number of elements packed into a single ciphertext. In this study, we propose a non-interactive model, in which no decryption is required, to evaluate arbitrary multivariate functions using homomorphic table lookup with word-wise FHE. The proposed LUT-enabled computation method 1) decreases the complexity to O(2^d·m/l), where l is the element size of FHE packing; 2) extends the input and output domain sizes to evaluate multivariate functions over two inputs; and 3) adopts a multidimensional table for enabling multithreading to reduce latency. The experimental results demonstrate that evaluating a 10-bit two-input function and a 5-bit three-input function takes approximately 90.5 and 105.5 s with 16-thread, respectively. Our proposed method achieves 3.2x and 23.1x speedup to evaluate two-bit and three-bit 3-input functions compared with naive LUT-enabled computation with bit-wise FHE.

Evaluating the Role of Institutional Quality in the Relationship Between Education Expenditure and Manufacturing Growth: Insights from Quantile Regression Models

This study aims to provide empirical insight into the role of institutional quality and its impact on the relationship between expenditure on education and the growth of manufacturing in Malaysia. The study employed time series data from 1984 to 2020, using a quantile regression model for three quantiles: 25%, 50%, and 75%. The results showed that government spending on education (GXE) had a negative and statistically significant effect on manufacturing sector growth (MSG) on all quantiles in both interaction and non-interaction models. This may indicate a lack of quality, allocation, and efficiency in government expenditure and its targeting. However, the interaction effect between government spending on education and institutional quality (INTC GXE&IQI) on manufacturing sector growth (MSG) provided a consistently positive effect across all quantiles. This positive interaction means that the effect of education spending on manufacturing sector growth is conditional on the quality of institutions. The positive coefficients indicate that when government spending aligns with robust institutional frameworks, it effectively stimulates growth within the manufacturing sector. This phenomenon may be attributed to effective institutions amplifying the impact of government expenditure by ensuring efficient fund utilization for intended purposes. Policies aimed at strengthening institutions' quality —such as improving bureaucracy, enhancing transparency, and combating corruption—can enhance the efficacy of education expenditure, which supports the long-term and sustainable growth of the manufacturing sector.

Phase space analysis of interacting and non-interacting models in f(Q, C) gravity

Abstract Using a dynamical system method, we have studied a Friedmann-Robertson-Walker (FRW) cosmological model within the context of $f(Q,C)$ gravity, where $Q$ is the non-metricity scalar and $C$ represents the boundary term, considering both interacting and non-interacting models. A set of autonomous equations is derived, and solutions are calculated accordingly. We assessed the critical points obtained from these equations, identified their characteristic values, and explored the physical interpretation of the phase space for this system. Two types of $f(Q,C)$ are assumed to be $(i)$ $f(Q,C)=Q+\alpha Q+\beta C logC$ and $(ii)$ $f(Q,C)=Q+\alpha Q+\frac{\beta}{C}$, where $\alpha$ and $\beta$ are the parameters. In Model I, we obtain two stable critical points, while in Model II, we identified three stable critical points for both interacting and non-interacting models. We look into how the phase space trajectories behave at every critical points. We calculate the values of the physical parameters for both systems at each critical point, indicating the Universe's accelerated expansion.

Mathematical modelling of decision making: the case of motor insurance choices

This paper employs a statistical mechanical model as a framework to investigate how socioeconomic factors of individuals such as gender and place of residence influence their decision when deciding between comprehensive and third-party motor insurance policies in Ghana. Data from a general insurance firm was used for this investigation taking five years’ worth of transactions into account. The methods of partial least squares and the ordinary least squares are, respectively, used to estimate the parameters of the interacting and the non-interacting models in the Multipopulation Currie-Weiss model in a discrete choice framework. The findings showed that both location and gender have discernible influences on how people choose their motor insurance. We encourage insurance companies to intensify their campaign on the importance of motor insurance to all vehicle/car owners, especially those in rural areas in order to reduce the risk and associated losses in vehicular accidents on Ghanaian roads.

On the influence of ion interactions on the predictions of a non-interacting model applied to evaluate lithium-ion battery materials

On the influence of ion interactions on the predictions of a non-interacting model applied to evaluate lithium-ion battery materials

Exact counterdiabatic driving in finite topological lattice models

Adiabatic protocols are often employed in state preparation schemes but require the system to be driven by a slowly varying Hamiltonian so that transitions between instantaneous eigenstates are exponentially suppressed. Counterdiabatic driving is a technique to speed up adiabatic protocols by including additional terms calculated from the instantaneous eigenstates that counter diabatic excitations. However, this approach requires knowledge of the full eigenspectrum meaning that the exact analytical form of counterdiabatic driving is only known for a subset of problems, e.g., the harmonic oscillator and transverse field Ising model. We extend this subset of problems to include the general family of one-dimensional noninteracting lattice models with open boundary conditions and arbitrary onsite potential, tunneling terms, and lattice size. We will derive a general analytical form for the counterdiabatic term for all states of lattice models, including bound and in-gap states which appear, e.g., in topological insulators. We also derive the general analytical form of targeted counterdiabatic driving terms which are tailored to enforce the dynamical state to remain in a specific state. As an example of the use of the derived analytical forms, we consider state transfer using the topological edge states of the Su-Schrieffer-Heeger model. The derived analytical counterdiabatic driving Hamiltonian can be utilized to inform control protocols in many-body lattice models or to probe the nonequilibrium properties of lattice models. Published by the American Physical Society 2024

From Liouville to Landauer: Electron transport and the bath assumptions made along the way

A generalized quantum master equation approach is introduced to describe electron transfer in molecular junctions that spans both the off-resonant (tunneling) and resonant (hopping) transport regimes. The model builds on prior insights from scattering theory but is not limited to a certain parameter range with regard to the strength of the molecule–electrode coupling. The framework is used to study the simplest case of energy and charge transfer between the molecule and the electrodes for a single site noninteracting Anderson model in the limit of symmetric and asymmetric coupling between the molecule and the electrodes. In the limit of elastic transport, the Landauer result is recovered for the current by invoking a single active electron Ansatz and a binary collision approximation for the memory kernel. Inelastic transport is considered by allowing the excitation of electron–hole pairs in the electrodes in tandem with charge transport. In the case of low bias voltages where the Fermi levels of the electrodes remain below the molecular state, it is shown that the current arises from tunneling and the molecule remains neutral. However, once the threshold is reached for aligning the fermi level of one electrode with the molecular orbital, a small amount of charge transfer occurs with a negligible amount of hopping current. While inelasticity in the current has a minimal impact on the shape of the current–voltage curve in the case of symmetric electrode coupling, the results for a slight asymmetry in coupling demonstrate complete charge transfer and a significant drop in current. These results provide encouraging confirmation that the framework can describe charge transport across a wide range of electrode–molecule coupling and provide a unique perspective for developing new master equation treatments for energy and charge transport in molecular junctions. An extension of this work to account for inelastic scattering from electron–vibrational coupling at the molecule is straightforward and will be the subject of subsequent work.

Stepwise Multidimensional Climate Envelop Modeling of Pitch Pine (Pinus rigida)

Understanding the intricate relationships between climate and vegetation remains a fundamental challenge in contemporary ecology. The ability to anticipate the specific climatic factors affecting different tree species and understand how they respond is crucial for mitigating the impacts of climate change on forested ecosystems. Additionally, quantitatively assessing habitat loss resulting from anthropogenic activities is essential for informed conservation efforts. Our objective is to evaluate the potential distribution of pitch pine (Pinus rigida) in North America and assess the associated habitat loss. To achieve this, we employ a stepwise multidimensional climate envelope modeling approach, comparing two data-intensive models—the Variable Interaction Model (VIM) and the Variable Non-Interaction Model (VNM). These models discern the influence of diverse combinations of climatic characteristics on the distribution of the species. Both VNM and VIM employ Shapley values for factor ranking during construction. VNM assumes independent effects, resulting in a hyperrectangle-shaped climate envelope, while VIM considers interactions, yielding a complex, data-driven multidimensional envelope. Data integration involves mining the US Forest Inventories and climatic data, encompassing 19 parameters. The results unequivocally highlight the superior predictive accuracy of VIM compared to the Variable Non-Interaction Model, VNM. The modeling approach developed in this study has the potential to enhance species distribution models for various tree species in the context of evolving climatic conditions.

Genetic risk accentuates dietary effects on hepatic steatosis, inflammation and fibrosis in a population-based cohort

Steatotic liver disease (SLD), characterized by elevated liver fat content (LFC), is influenced by genetics and diet. However, whether diet has a differential effect based on genetic risk is not well-characterized. We aimed to determine how genetic factors interact with diet to affect SLD in a large national biobank. We included UK Biobank participants with dietary intake measured by 24-hour recall and genotyping. The primary predictors were dietary pattern, PNPLA3-rs738409-G, TM6SF2-rs58542926-T, a 16-variant hepatic steatosis polygenic risk score (PRS), and gene-environment interactions. The primary outcome was LFC, and secondary outcomes were iron-controlled T1 time (cT1, a measure of liver inflammation and fibrosis) and liver-related events/mortality. A total of 21,619 participants met inclusion criteria. In non-interaction models, Mediterranean diet and intake of fruit/vegetables/legumes and fish associated with lower LFC, while higher red/processed meat intake and all genetic predictors associated with higher LFC. In interaction models, all genetic predictors interacted with Mediterranean diet and fruit/vegetable/legume intake, while the steatosis PRS interacted with fish intake and the TM6SF2 genotype interacted with red/processed meat intake, to affect LFC. Dietary effects on LFC were up to 3.8-fold higher in PNPLA3-rs738409-GG vs. -CC individuals, and 1.4-3.0-fold higher in the top vs. bottom quartile of the steatosis PRS. Gene-diet interactions were stronger in participants with vs. without overweight. The steatosis PRS interacted with Mediterranean diet and fruit/vegetable/legume intake to affect cT1 and most dietary and genetic predictors associated with risk of liver-related events or mortality by age70. Effects of diet on LFC and cT1 were markedly accentuated in patients at increased genetic risk for SLD, implying dietary interventions may be more impactful in these populations. Genetic variants and diet both influence risk of hepatic steatosis, inflammation/fibrosis, and hepatic decompensation; however, how gene-diet interactions influence these outcomes has previously not been comprehensively characterized. We investigated this topic in the community-based UK Biobank and found that genetic risk and dietary quality interacted to influence hepatic steatosis and inflammation/fibrosis on liver MRI, so that the effects of diet were greater in people at elevated genetic risk. These results are relevant for patients and medical providers because they show that genetic risk is not fixed (i.e. modifiable factors can mitigate or exacerbate this risk) and realistic dietary changes may result in meaningful improvement in liver steatosis and inflammation/fibrosis. As genotyping becomes more routinely used in clinical practice, patients identified to be at high baseline genetic risk may benefit even more from intensive dietary counseling than those at lower risk, though future prospective studies are required.

Study of dark energy models in [formula omitted] theory

This paper investigates the quantum chromodynamics ghost model of dark energy in the framework of f(R,T2) theory. The investigation centers on the non-interacting ghost dark energy model in a Friedmann–Robertson–Walker universe. Various cosmic parameters such as the Hubble parameter, equation of state and deceleration parameter are computed to examine the implications of the ghost dark energy model. Further, it is discovered that the equation of state parameter of ghost dark energy traverses the phantom regime. The stability analysis of this model is conducted using the squared sound speed. This study serves to reconstruct the model of gravity by incorporating dark matter and the ghost dark energy model. Special emphasis is placed on the scenario where the function is defined as f(R,T2)=f1(R)+f2(T2). In this context, our attention is focused on a specific model that allows for the use of the standard continuity equation in this modified theory. The conclusion drawn is that the reconstructed ghost dark energy model in the framework of f(R,T2) gravity exhibit phantom or quintessence eras of the cosmos, describing the accelerated expansion of the universe. This exploration sheds light on the complex interplay between quantum chromodynamics, dark energy and modified theories of gravity, offering valuable insights into the dynamics of the cosmos at large scales.

Toward a universal description of hadronic phase of QCD

Mean-field model quantum field theories of hadrons were traditionally developed to describe cold and dense nuclear matter and are by now very well constrained from the recent neutron star merger observations. We show that when augmented with additional known hadrons and resonances but not included earlier, these mean-field models can be extended beyond its regime of applicability. Calculating some specific ratios of baryon number susceptibilities for finite temperature and moderate values of baryon densities within mean-field approximation, we show that these match consistently with the lattice QCD data available at lower densities, unlike the results obtained from a noninteracting hadron resonance gas model. We also estimate the curvature of the line of constant energy density, fixed at its corresponding value at the chiral crossover transition in QCD, in the temperature-density plane. The number density at low temperatures and high density is found to be about twice the nuclear saturation density. Moreover from this line we can indirectly constrain the critical endpoint of QCD to be beyond μB=596 MeV for temperature ∼125 MeV. Published by the American Physical Society 2024

PAC learning halfspaces in non-interactive local differential privacy model with public unlabeled data

In this paper, we study the problem of PAC learning halfspaces in the non-interactive local differential privacy model (NLDP). To breach the barrier of exponential sample complexity, previous results studied a relaxed setting where the server has access to some additional public but unlabeled data. We continue in this direction. Specifically, we consider the problem under the standard setting instead of the large margin setting studied before. Under different mild assumptions on the underlying data distribution, we propose two approaches that are based on the Massart noise model and self-supervised learning and show that it is possible to achieve sample complexities that are only linear in the dimension and polynomial in other terms for both private and public data, which significantly improve the previous results. Our methods could also be used for other private PAC learning problems.

Genome-wide analysis identifies non-reference transposable element polymorphisms associated with Parkinson’s disease

Parkinson’s disease (PD) is a common neurodegenerative disease that primarily affects the elderly, significantly impacting patients’ health and quality of life. While most genetic studies on PD have focused on single nucleotide polymorphisms, the effects of other forms of genomic variation in PD are yet to be fully elucidated. Transposable elements (TEs) are one of the main sources of human genome structural variation, with known associations with many human diseases. However, their potential connection to PD remains unclear. In this study, we investigated non-reference TE polymorphisms in three independent PD cohorts and explored their associations with both PD risk and progression. Our findings revealed that one non-reference TE is associated with the risk of PD, while two TEs are associated with disease progression. Furthermore, through expression quantitative trait locus (eQTL) analysis, we identified 18 cis TE-eQTLs in an interaction model and 290 cis TE-eQTLs in a non-interaction model. Several non-reference TE polymorphisms are correlated with specific PD-gene expression patterns in trans. These results indicate the feasibility of delving into the genetics of PD through the study of complex genomic variations. Advances in genomics research have the potential to deepen our understanding of this disease and pave the way for further translational medicine research in PD.

Smart contract-based integrity audit method for IoT

With the widespread adoption of Internet of Things (IoT) technology, a large amount of private data has been generated. Due to the limited computing and storage resources of IoT devices, enterprises and individuals choose to use a cloud storage provider (CSP) to manage their data. However, they lose the actual control of the data, and hence users need to verify the integrity of the data in the cloud. As a result, reducing the computational overhead of integrity auditing tasks for massive amounts of data and optimizing the distribution of benefits among the participants have become the key to the healthy development of IoT technologies. This paper proposes an integrity auditing method based on smart contracts. First, we construct a noninteractive auditing model based on a chaotic system so that the third-party auditor (TPA) can complete the auditing task without challenging the CSP. Second, we proposed a new construction method for audit trees that can quickly generate the verification tag of the root node. Finally, we design a smart contract-based auditing algorithm on the blockchain, which can simultaneously verify the behaviour of the CSP and the TPA to achieve fair payments. The theoretical analysis shows that our scheme can effectively prevent the TPA from falsifying audit results and prevent collusion between the TPA and the CSP. The experimental results show that our scheme has higher audit efficiency.

Monte Carlo simulation of a magnetic nanoparticles system under an external rotating magnetic field

The magnetic response of an identical magnetic nanoparticles (MNP) system to a rotating external field (RMF) is studied via Monte Carlo simulations. The field of amplitude H0 and frequency ω, was applied in the y−z plane rotating clockwise. The energy was modeled by the Stoner–Wohlfarth scheme for fixed or random orientations of the anisotropy, and is in contact with a thermal bath at a temperature T. Interparticle dipolar interactions were also considered.In the non-interacting system and for low temperature, hysteresis is observed in the z magnetization component Mz for both orientations of the anisotropy axis and only in the y component (My) for the random case. Furthermore, the loop areas were estimated, and increased with ω for all orientations and (My,Mz) components. At higher temperatures the superparamagnetic state is observed, so both the blocking temperatures TB and loop areas were estimated. The values of TB were close from the room temperature TR=300K for all components, and the areas decreased with T but they are practically not zero at TB.When dipolar interactions are included a new scenario is revealed. In the low temperature regime, the blocked state is present for both My and Mz for all anisotropy orientations, and extends beyond the interval of amplitudes H0 estimated theoretically for the model without interactions and fixed anisotropy. The loops are displaced with respect to the origin of the magnetization-external field plane. When the temperature is raised, the blocked state extends for a larger range than the model without interactions, and the loop displacement decreases with T. These behaviors could be explained by observing that the average dipolar field per particle produces an effective field – the sum of both dipolar and external field – that is asymmetric with respect to the zero field line at low temperatures, becomes half-wave symmetric at higher temperatures, so the the centered character of the loops is restored . In addition, the loop areas show a peak for all orientations of the anisotropy axes in an intermediate range of temperatures. This result can be associated with a dominance of the anisotropy induced by the dipolar field.Finally, by comparing the areas of the loops of the models with and without interactions, it was found that the non-interacting model have larger areas at low temperatures that vanish near the room temperature, unlike the areas of the model with interactions due to the extension of the blocked state.

Spin transport in non-Hermitian quantum systems

Transport in non-Hermitian quantum systems is studied. The goal is a better understanding of transport in non-Hermitian systems like the Lieb lattice due to its flat bands and the integrability of the Ising chain which allows transport in that model to be computed analytically. This is a very special feature that is not present in a generic non-Hermitian system. We obtain the behaviour of the spin conductivity as a function of the non-Hermitian parameters of each system with aim to verify the influence of variation them on conductivity. For all models analyzed: Ising model as well as noninteracting fermion models, we obtain a little influence of the non-Hermitian parameters on conductivity and thus, a small effect over transport coefficients. Furthermore, we obtain an influence of opening of the gap in the spectrum in these models on longitudinal conductivity as well.

Dynamical system approach of interacting dark energy models with minimally coupled scalar field

We investigated the stability condition of [Formula: see text] gravity theory with interacting and noninteracting models by using dynamical system. We assume the [Formula: see text] function as [Formula: see text], where [Formula: see text] is the free parameter. We evaluated the critical points for this model and examined the stability behavior. We found two stable critical points for interacting model. The phase plots for this system are examined and the physical interpretation is discussed. We illustrate all the cosmological parameters such as [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] at each fixed point and compare the parameters with observational values. Further, we assume hybrid scale factor and the equation of redshift and time is [Formula: see text]. We transform all the parameters in terms of redshift by using this equation and examine the behavior of these parameters. Our model represents the accelerated expansion of the universe. The energy conditions are examined in terms of redshift and strong energy conditions are not satisfied for the model. We also find the statefinder parameters [Formula: see text] in terms of z and discuss the nature of r–s and r–q plane. For both pairs [Formula: see text] and [Formula: see text] our model represents the [Formula: see text]CDM model. Hence, we determine that our [Formula: see text] model is stable and it satisfies all the observational values.

Collision-sticking rates of acid–base clusters in the gas phase determined from atomistic simulation and a novel analytical interacting hard-sphere model

Abstract. Kinetics of collision-sticking processes between vapor molecules and clusters of low-volatility compounds govern the initial steps of atmospheric new particle formation. Conventional non-interacting hard-sphere models underestimate the collision rate by neglecting long-range attractive forces, and the commonly adopted assumption that every collision leads to the formation of a stable cluster (unit mass accommodation coefficient) is questionable for small clusters, especially at elevated temperatures. Here, we present a generally applicable analytical interacting hard-sphere model for evaluating collision rates between molecules and clusters, accounting for long-range attractive forces. In the model, the collision cross section is calculated based on an effective molecule–cluster potential, derived using Hamaker's approach. Applied to collisions of sulfuric acid or dimethylamine with neutral bisulfate–dimethylammonium clusters composed of 1–32 dimers, our new model predicts collision rates 2–3 times higher than the non-interacting model for small clusters, while decaying asymptotically to the non-interacting limit as cluster size increases, in excellent agreement with a collision-rate-theory atomistic molecular dynamics simulation approach. Additionally, we calculated sticking rates and mass accommodation coefficients (MACs) using atomistic molecular dynamics collision simulations. For sulfuric acid, a MAC ≈1 is observed for collisions with all cluster sizes at temperatures between 200 and 400 K. For dimethylamine, we find that MACs decrease with increasing temperature and decreasing cluster size. At low temperatures, the MAC ≈1 assumption is generally valid, but at elevated temperatures MACs can drop below 0.2 for small clusters.

Catalog of noninteracting tight-binding models with two energy bands in one dimension

We classify Hermitian tight-binding models describing noninteracting electrons on a one-dimensional periodic lattice with two energy bands. To do this, we write a generalized Rice-Mele model with two orbitals per unit cell, including all possible complex-valued long-range hoppings consistent with Hermicity. We then apply different forms of time-reversal, charge-conjugation and chiral symmetry in order to constrain the parameters, resulting in an array of possible models in different symmetry classes. For each symmetry class, we define a single, canonical form of the Hamiltonian and identify models that are related to the canonical form by an off-diagonal unitary transformation in the atomic basis. The models have either symmorphic or nonsymmorphic nonspatial symmetries (time $T$, chiral and charge-conjugation). The nonsymmorphic category separates into two types of state of matter: an insulator with a $\mathbb{Z}_2$ topological index in the absence of nonsymmorphic time-reversal symmetry or, in the presence of nonsymmorphic time-reversal symmetry, a metallic state. The latter is an instance of Kramer's degeneracy with one degeneracy point in the Brillouin zone as opposed to no degeneracy points in symmorphic systems with $T^2 = 1$ and two in symmorphic systems with $T^2 = - 1$.