Quantum Mechanics Research Articles

Non-Hermitian Extension of Q Uncertainty Relation

In quantum mechanics it is well known that observables are represented by hermitian matrices (or operators). Uncertainty relations are represented as some kinds of trace inequalities satisfied by two observables and one density matrix (or operator). By releasing the hermitian restriction on observables, we obtained non-hermite uncertainty relations. In this paper we give several non-hermitian extensions of Heisenberg or Schrödinger type q uncertainty relations for generalized skew information under some conditions.

Gas turbine energy yield prediction framework using neural network based on quantum mechanics

Gas turbine energy yield prediction framework using neural network based on quantum mechanics

A COMPARATIVE STUDY OF A CLASS OF LINEAR AND NONLINEAR PANTOGRAPH DIFFERENTIAL EQUATIONS VIA DIFFERENT ORTHOGONAL POLYNOMIAL WAVELETS

We propose a wavelet approach on different orthogonal polynomials for solving linear and nonlinear pantograph equations with stretch kind. The pantograph differential equation is a unique proportional delay functional differential equation class. It has been used to deal with numerous physics, mathematics, and engineering applications, such as quantum mechanics, control systems, electrodynamics, and number theory. This scheme is based on constructing the operational matrix for integration via different wavelets with their collocation nodes. This study aims to examine the numerical dynamics of the pantograph equation under stretch kind through different orthogonal polynomial wavelets. Illustrative examples are presented to highlight the flexibility of this scheme, and comparisons are made between the mentioned scheme and other existing schemes using tables and graphs. These numerical results correctly predict the applicability and effectiveness of the mentioned scheme.

Quantum mechanics principle and other physics principles involved in light and laser therapy

Quantum mechanics principle and other physics principles involved in light and laser therapy

Quantum AI in Healthcare : Revolutionizing Diagnosis, Treatment and Drug Discovery

This paper explores the convergence of synthetic intelligence (AI) and quantum computing, unveiling its potential to revolutionize healthcare. By leveraging quantum mechanics' standards, the paper examines how AI may be amplified to gain breakthroughs in clinical diagnoses, personalized treatment plans, and accelerated drug discovery. The exploration delves into how quantum simulations can model complex organic methods at a molecular level, permitting the prediction of remedy interactions and the layout of medicine with unequalled precision. Additionally, the paper discusses the combination of quantum sensors with AI for more suitable clinical imaging, capable of detecting diffused abnormalities. The transformative ability of this synergy is addressed, emphasizing its function in ushering in a brand new technology of personalised medicinal drug and efficient drug improvement.

Complementarity of subjective and objective realities: An experimental investigation of variations of subjective self-reported intelligence data when objective data are erased or not-erased

The Complementarity Principle (CP), introduced by Nils Bohr, described the wave-particle duality of quantum phenomena and its dependence on the measurement setup exploring the quantum states. In general, this principle summarized the fact that two mutually exclusive and contradictory states of quantum events can be reconciled as a measurement-dependent occurrence of these states. Originally, the CP was postulated only for the realm of quantum mechanics, but recently the Generalized Quantum Theory (GQT) extended its area of applicability to the macroscopic domain. According to GQT complementarity relations are also hypothesized to exist between macroscopic objective and subjective measurements of the same concept. This implies objective measurement-dependent variations of subjective experience. To test this hypothesis, seven studies were conducted in which individual variations in subjective intelligence ratings were tested in relation to the availability or non-availability of corresponding objective individual intelligence data. Only one pre-registered study (Study 2) showed strong Bayesian evidence for H1 (BF10 > 10), indicating, as predicted, higher subjective intelligence ratings when objective data were erased compared to a condition in which objective data were available within a male sample. This effect could not be replicated in direct replication attempts, nor did a moderator search in subsequent studies find any robust systematic variation in the data. The results seem to question the validity of the macroscopic complementarity conjecture derived from the GQT. On the other hand, they could also be interpreted as the “effect and decline” data pattern that the Model of Pragmatic Information would predict when conducting empirical confirmations of macroscopic complementarity relations. Possible future research strategies to clarify these different interpretations are discussed.

Pell Collocation Approach for the Nonlinear Pantograph Differential Equations

Pantograph equations, which we encounter in the branches of pure and applied mathematics such as electrodynamics, control systems and quantum mechanics, are essentially a particular form of the functional differential equations characterized with proportional delays. This study focuses on exploring the approximate solution to the Pantograph differential equation. Since there is no analytic solutions for this equation class, only the approximate solutions can be obtain. For this purpose, Pell Collocation Method which is one of the numerical solution methods is chosen. As the result of applying the method to the equation, an algebraic equation system has been gained and then the approximate solution has been found by using MATHEMATICA via the given initial conditions. The method is applied to the some test examples and then the results are presented by both graphically and by table. The error estimations show that the method works accurately and efficiently.

Quantum Machine Learning: The Superhero That Classical Machine Learning Never Knew It Needed

Quantum Machine Learning (QML) is an emerging interdisciplinary field that combines the principles of quantum mechanics and machine learning to develop algorithms that can potentially outperform classical algorithms in certain tasks. QML leverages the unique properties of quantum systems, such as superposition and entanglement, to process information in ways that are not possible with classical computers. This paper provides a comprehensive overview of QML, including its principles, algorithms, and applications. We focus particularly on supervised learning methods, which involve training a quantum model on labeled data to make predictions on new, unseen data. We discuss the potential of QML to revolutionize various domains, such as finance, chemistry, and materials science, and highlight the challenges associated with the development and implementation of QML algorithms, including the need for more advanced quantum hardware and software. This paper aims to provide a clear understanding of the current state of QML research and its potential impact on future computational capabilities.

Broadening access to small-molecule parameterization with the force field toolkit.

Access to accurate force-field parameters for small molecules is crucial for computational studies of their interactions with proteins. Although a number of general force fields for small molecules exist, e.g., CGenFF, GAFF, and OPLS, they do not cover all common chemical groups and their combinations. The Force Field Toolkit (ffTK) provides a comprehensive graphical interface that streamlines the development of classical parameters for small molecules directly from quantum mechanical (QM) calculations, allowing for force-field generation for almost any chemical group and validation of the fit relative to the target data. ffTK relies on supported external software for the QM calculations, but it can generate the necessary QM input files and parse and analyze the QM output. In previous ffTK versions, support for Gaussian and ORCA QM packages was implemented. Here, we add support for Psi4, an open-source QM package free for all users, thereby broadening user access to ffTK. We also compare the parameter sets obtained with the new ffTK version using Gaussian, ORCA, and Psi4 for three molecules: pyrrolidine, n-propylammonium cation, and chlorobenzene. Despite minor differences between the resulting parameter sets for each compound, most prominently in the dihedral and improper terms, we show that conformational distributions sampled in molecular dynamics simulations using these parameter sets are quite comparable.

Emergent universality of free fall from quantum mechanics

Emergent universality of free fall from quantum mechanics

EReaxFF force field development for BaZr0.8Y0.2O3-δ solid oxide electrolysis cells applications

The use of solid-oxide materials in electrocatalysis applications, especially in hydrogen-evolution reactions, is promising. However, further improvements are warranted to overcome the fundamental bottlenecks to enhancing the performance of solid-oxide electrolysis cells (SOECs), which is directly linked to the more-refined fundamental understanding of complex physical and chemical phenomena and mass exchanges that take place at the surfaces and in the bulk of electrocatalysis materials. Here, we developed an eReaxFF force field for barium zirconate doped with 20 mol% of yttrium, BaZr0.8Y0.2O3-δ (BZY20) to enable a systematic, large-length-scale, and longer-timescale atomistic simulation of solid-oxide electrocatalysis for hydrogen generation. All parameters for the eReaxFF were optimized to reproduce quantum-mechanical (QM) calculations on relevant condensed phase and cluster systems describing oxygen vacancies, vacancy migrations, electron localization, water adsorption, water splitting, and hydrogen generation on the surfaces of the BZY20 solid oxide. Using the developed force field, we performed both zero-voltage (excess electrons absent) and non-zero-voltage (excess electrons present) molecular dynamics simulations to observe water adsorption, water splitting, proton migration, oxygen-vacancy migrations, and eventual hydrogen-production reactions. Based on investigations offered in the present study, we conclude that the eReaxFF force field-based approach can enable computationally efficient simulations for electron conductivity, electron leakage, and other non-zero-voltage effects on the solid oxide materials using the explicit-electron concept. Moreover, we demonstrate how the eReaxFF force field-based atomistic-simulation approach can enhance our understanding of processes in SOEC applications and potentially other renewable-energy applications.

Quantum Mechanics-Based Fast and Reliable Prediction of Binding Pose Structures.

Predicting the binding poses of docking with an accurate estimation of binding energies is highly important but very challenging in computational drug design. A quantum mechanics (QM) calculation-based docking approach considering multiple conformations and orientations of the ligand is introduced here to tackle the problem. This QM docking consists of three steps: generating an ensemble of binding poses with a conventional docking simulation, computing the binding energies with self-consistent charge density functional theory tightly binding with dispersion correction (DFTB-D) to selecting the 10 top binding modes, and optimizing the selected binding mode structures using the ONIOM(DFTB:PM7) technique to determine the binding poses. The ONIOM(DFTB-D:PM6) docking approach is tested on 121 ligand-receptor biocomplexes with the crystal structures obtained from the Research Collaboratory for Structural Bioinformatics Protein Data Bank (RCSB PDB). The result shows that the new method is highly satisfactory for the accurate prediction of the binding poses. The new docking method should be beneficial to structure-based drug design.

A New Method for Low Density Distribution Modeling and Near Threatened Species: The Study Case of Plectrohyla Guatemalensis

We introduce a model that can be used for the description of the distribution of species when there is scarcity of data, based on our previous work (Ballesteros et al. J Math Biol 85(4):31, 2022). We address challenges in modeling species that are seldom observed in nature, for example species included in The International Union for Conservation of Nature’s Red List of Threatened Species (IUCN 2023). We introduce a general method and test it using a case study of a near threatened species of amphibians called Plectrohyla Guatemalensis (see IUCN 2023) in a region of the UNESCO natural reserve “Tacaná Volcano”, in the border between Mexico and Guatemala. Since threatened species are difficult to find in nature, collected data can be extremely reduced. This produces a mathematical problem in the sense that the usual modeling in terms of Markov random fields representing individuals associated to locations in a grid generates artificial clusters around the observations, which are unreasonable. We propose a different approach in which our random variables describe yearly averages of expectation values of the number of individuals instead of individuals (and they take values on a compact interval). Our approach takes advantage of intuitive insights from environmental properties: in nature individuals are attracted or repulsed by specific features (Ballesteros et al. J Math Biol 85(4):31, 2022). Drawing inspiration from quantum mechanics, we incorporate quantum Hamiltonians into classical statistical mechanics (i.e. Gibbs measures or Markov random fields). The equilibrium between spreading and attractive/repulsive forces governs the behavior of the species, expressed through a global control problem involving an energy operator.

Innovative Use of an Injectable, Self-Healing Drug-Loaded Pectin-Based Hydrogel for Micro- and Supermicro-Vascular Anastomoses.

Microvascular surgery plays a crucial role in reconnecting micrometer-scale vessel ends. Suturing remains the gold standard technique for small vessels; however, suturing the collapsed lumen of microvessels is challenging and time-consuming, with the risk of misplaced sutures leading to failure. Although multiple solutions have been reported, the emphasis has predominantly been on resolving challenges related to arteries rather than veins, and none has proven superior. In this study, we introduce an innovative solution to address these challenges through the development of an injectable lidocaine-loaded pectin hydrogel by using computational and experimental methods. To understand the extent of interactions between the drug and the pectin chain, molecular dynamics (MD) simulations and quantum mechanics (QM) calculations were conducted in the first step of the research. Then, a series of experimental studies were designed to prepare lidocaine-loaded injectable pectin-based hydrogels, and their characterization was performed by using Fourier transform infrared spectroscopy (FT-IR), scanning electron microscopy (SEM), and rheological analysis. After all the results were evaluated, the drug-loaded pectin-based hydrogel exhibiting self-healing properties was selected as a potential candidate for in vivo studies to determine its performance during operation. In this context, the hydrogel was injected into the divided vessel ends and perivascular area, allowing for direct suturing through the gel matrix. While our hydrogel effectively prevented vasospasm and facilitated micro- and supermicro-vascular anastomoses, it was noted that it did not cause significant changes in late-stage imaging and histopathological analysis up to 6 months. We strongly believe that pectin-based hydrogel potentially enhanced microlevel arterial, lymphatic, and particularly venous anastomoses.

Evaluation of Point Group Symmetry in Lanthanide(III) Complexes: A New Implementation of a Continuous Symmetry Operation Measure with Autonomous Assignment of the Principal Axis.

The structure of molecular systems dictates the physical properties, and symmetry is the determining factor for all electronic properties. This makes group theory a powerful tool in quantum mechanics to compute molecular properties. For inorganic compounds, the coordination geometry has been estimated as idealized polyhedra with high symmetry, which, through ligand field theory, provides predictive capabilities. However, real samples rarely have ideal symmetry, and although continuous shape measures (CShM) can be used to evaluate deviation from an ideal reference structure σideal, this often fails for lanthanide(III) complexes with high coordination numbers, no obvious choice of principal axes, and no obvious reference structure. In lanthanide complexes, the unique electronic structures and associated properties are intricately tied to the symmetry around the lanthanide center. Therefore, robust methodologies to evaluate and estimate point group symmetry are instrumental for building structure-property relationships. Here, we have demonstrated an algorithmic approach that orients a molecular structure Q in the best possible way to the symmetry axis of any given point group G and computes a deviation from the ideal symmetry σsym(G,Q). This approach does not compute the deviation from an ideal reference system, but the intrinsic deviation in the structure induced by symmetry operations. If the structure contains the symmetry operation, there is no deviation and σsym(G,Q) = 0. The σsym deviation is generated from all of the symmetry operation ÔS in a point group G using the most correct orientation of the sample structure in each group G. The best orientation is found by an algorithm that minimizes the orientation of the structure with respect to G. To demonstrate the methodology, we have investigated the structure and symmetry of 8- and 9-coordinated lanthanide(III) aqua complexes and correlated the luminescence from 3 europium(III) crystals to their actual symmetry. To document the methodology, the approach has been tested on 26 molecules with different symmetries. It was concluded that the method is robust and fully autonomous.

Testing Multi-Subroutine Quantum Programs: From Unit Testing to Integration Testing

Quantum computing has emerged as a promising field with the potential to revolutionize various domains by harnessing the principles of quantum mechanics. As quantum hardware and algorithms continue to advance, developing high-quality quantum software has become crucial. However, testing quantum programs poses unique challenges due to the distinctive characteristics of quantum systems and the complexity of multi-subroutine programs. This article addresses the specific testing requirements of multi-subroutine quantum programs. We begin by investigating critical properties by surveying existing quantum libraries and providing insights into the challenges of testing these programs. Building upon this understanding, we focus on testing criteria and techniques based on the whole testing process perspective, spanning from unit testing to integration testing. We delve into various aspects, including IO analysis, quantum relation checking, structural testing, behavior testing, integration of subroutine pairs, and test case generation. We also introduce novel testing principles and criteria to guide the testing process. We conduct comprehensive testing on typical quantum subroutines, including diverse mutants and randomized inputs, to evaluate our proposed approach. The analysis of failures provides valuable insights into the effectiveness of our testing methodology. Additionally, we present case studies on representative multi-subroutine quantum programs, demonstrating the practical application and effectiveness of our proposed testing principles and criteria.

A numerical approach for solving nonlinear fractional Klein–Gordon equation with applications in quantum mechanics

Abstract In this paper, we propose a numerical approach for solving the nonlinear fractional Klein–Gordon equation (FKGE), a model of significant importance in simulating nonlinear waves in quantum mechanics. Our method combines the Bernoulli wavelet collocation scheme with a functional integration matrix to obtain approximate solutions for the proposed model. Initially, we transform the main problem into a system of algebraic equations, which we solve using the Newton–Raphson method to extract the unknown coefficients and achieve the desired approximate solution. To theoretically validate our method, we conduct a comprehensive convergence analysis, demonstrating its uniform convergence. We perform numerical experiments on various examples with different parameters, presenting the results through tables and figures. Our findings indicate that employing more terms in the utilized techniques enhances accuracy. Furthermore, we compare our approach with existing methods from the literature, showcasing its performance in terms of computational cost, convergence rate, and solution accuracy. These examples illustrate how our techniques yield better approximate solutions for the nonlinear model at a low computational cost, as evidenced by the calculated CPU time and absolute error. Additionally, our method consistently provides better accuracy than other methods from the literature, suggesting its potential for solving more complex problems in physics and other scientific disciplines.

Implementation of Small Term Reduction in Taylor Series in Analytical Physics Problem

This research is motivated by the low ability of students to apply mathematical solving methods to analytic physics. The purpose of this research is to show the implementation of small term reduction in Taylor series on analytic physics problems. The analytical physics material described in this study is the pendulum oscillation material, heat conduction and the perturbation quantum state function. This research method involves a mathematical derivation of the Taylor series formation. The epicenter of the idea of reducing the Taylor series in this study is the use of very small terms in the Taylor series to reduce terms with values reaching towards zero, namely the third term and the fourth term. This small term reduction method is spread into problems of mechanics, oscillations, heat, electricity, magnetism and quantum mechanics. The results of this study show that after using the small term reduction principle, the equations to be solved are like first-order and second-order differential equations. By solving these equations we get a variable physical quantity.

Bartender: Martini 3 Bonded Terms via Quantum Mechanics-Based Molecular Dynamics.

Coarse-grained (CG) molecular dynamics (MD) simulations have grown in applicability over the years. The recently released version of the Martini CG force field (Martini 3) has been successfully applied to simulate many processes, including protein-ligand binding. However, the current ligand parametrization scheme is manual and requires an a priori reference all-atom (AA) simulation for benchmarking. For systems with suboptimal AA parameters, which are often unknown, this translates into a CG model that does not reproduce the true dynamical behavior of the underlying molecule. Here, we present Bartender, a quantum mechanics (QM)/MD-based parametrization tool written in Go. Bartender harnesses the power of QM simulations and produces reasonable bonded terms for Martini 3 CG models of small molecules in an efficient and user-friendly manner. For small, ring-like molecules, Bartender generates models whose properties are indistinguishable from the human-made models. For more complex, drug-like ligands, it is able to fit functional forms beyond simple harmonic dihedrals and thus better captures their dynamical behavior. Bartender has the power to both increase the efficiency and the accuracy of Martini 3-based high-throughput applications by producing numerically stable and physically realistic CG models.

Immobilization of gaseous As2O3 on γ-Fe2O3 (001) surface by forming monodentate and bidentate complexes: Insight from DFT study

Coal combustion is one primary anthropogenic emission source of atmospheric arsenic. Ferromagnetic γ-Fe2O3 has been regarded as an effective and promising immobilization sorbent for As2O3(g) in flue gas with good magnetic properties. The reported mechanism explorations about gaseous arsenic capture in flue gas by density functional theory (DFT) are mainly based on forming one chemical bond between arsenic and sorbent. Recent studies demonstrated that multidentate arsenic complexes could be formed with iron oxides in solution. However, the possible formation pathway of multidentate complexes between gaseous As2O3 and γ-Fe2O3 was not been reported yet. This is the first study to investigate the thermodynamics and quantum mechanics of bidentate complexes between As2O3(g) and γ-Fe2O3 (001) by DFT. Three kinds of arsenic bidentate complexes were discovered at γ-Fe2O3 (001) surface, including “2 O to 2 Feoct”, “2 O to Fetet & Feoct,” and “As & O to 2 Feoct,” which were named as configuration A, B and C, respectively. Configuration B, “2 O to Fetet & Feoct”, showed the lowest adsorption energy (Eads) among the three kinds of bidentate complexes. The Mulliken population analysis further confirmed the electron transfer between the atoms of newly formed chemical bonds in bidentate configurations. In addition, the projected density of states (PDOS) analysis exhibiting resonance peaks also showed the formation of hybrid orbitals. The criteria for the determination of bidentate complexes were also proposed. The results evidence a convincing conclusion that monodentate and bidentate complexes with stable chemical bonds can be formed when As2O3(g) is immobilized by γ-Fe2O3 (001).