Quantum Mechanics Research Articles

Exploring the potential of quinacridone-porphyrin-based materials for nitrogen oxides sensing: quantum chemical design, mechanism and future prospects

Exploring the potential of quinacridone-porphyrin-based materials for nitrogen oxides sensing: quantum chemical design, mechanism and future prospects

A novel partition function for elementary particles

Three different partition functions are well-known and described in statistical physics. Here, a novel partition function for the description of intra-particular interactions and with this for the mass of particles is presented below. In statistical physics, three different partition functions are already well-established. These are the microcanonical, the canonical, and the macro-canonical partition functions. Here a fourth, novel partition function is added to these already well-established three. Thereby due to the properties of quantum mechanics and superposition, this novel partition function is of fundamental different nature. According to this concept, the new partition function for particles is first defined. The masses and energies of the elementary particles are then calculated using this novel partition function. The energy of an elementary particle is proportional to the mass on the one hand and to the novel partition function on the other. The constant of proportionality with respect to the new partition function is found to be identical with Rydberg constant and Rydberg energy. The relationships found for the proton, the electron, and the sigma particle are then generalized to all elementary particles.

Phase-space representation of coherent states generated through SUSY QM for tilted anisotropic Dirac materials

In this paper, we examine the electron interaction within tilted anisotropic Dirac materials when subjected to external electric and magnetic fields possessing translational symmetry. Specifically, we focus on a distinct non-zero electric field magnitude, enabling the decoupling of the differential equation system inherent in the eigenvalue problem. Subsequently, employing supersymmetric quantum mechanics facilitates the determination of eigenstates and eigenvalues corresponding to the Hamiltonian operator. To delve into a semi-classical analysis of the system, we identify a set of coherent states. Finally, we assess the characteristics of these states using fidelity and the phase-space representation through the Wigner function.

On testimony in scenarios with Wigner and Friend

The paper constructs a semi-formal language suited to the analysis of Wigner’s Friend scenarios: it represents an epistemic notion of rational beliefs and perspectives, to accommodate the insights of perspectival interpretations of quantum mechanics. The language is then used to analyze a paradox put forward by Frauchiger and Renner (Nat Commun, 9(1):3711, 2018). Their argument is presented as a semi-formal derivation with specified rules of reasoning. These rules bear an affinity to some of the cherished tenets of epistemology and we argue that they are valid (one universally, and the other in experimental contexts). Since our proof is a reductio, it leaves a choice which premises are responsible for a contradiction. Our first choice is a step that appears incorrect from the point of view of the universal unitary evolution as well as the view that every measurement induces a collapse of a measured system’s state. Our second choice, brought to view by the paper’s attention to perspectives and epistemology, points to a step reporting the transmission of beliefs (testimony) about measurement results. We argue that testimony is not licensed by quantum mechanical formalism; we discuss some recent attempts to save the cogency of testimony in the context of quantum measurements.

Review Research Paper of Feasibility study on Anti-Gravity Effect for Advance Propulsion system and technologies

The concept of anti-gravity, often portrayed in science fiction as a means to counteract or negate the effects of gravitational force, has intrigued scientists and enthusiasts alike for decades. This paper explores the feasibility of achieving anti-gravity effects through various theoretical and experimental perspectives. Firstly, theoretical frameworks such as general relativity and quantum mechanics are reviewed to understand gravity and its potential manipulation. While these theories provide foundational insights, they also highlight the immense challenges involved in directly counteracting gravitational forces due to their fundamental nature. Next, experimental efforts and hypothetical technologies proposed in scientific literature are examined. Concepts such as negative mass, exotic matter, and gravitational shielding are discussed in terms of their theoretical underpinnings and practical limitations. Experimental evidence, including anomalies in gravitational measurements and speculative engineering proposals, are scrutinized to evaluate their relevance to achieving anti-gravity effects. Furthermore, the paper addresses the technological and ethical implications of developing anti-gravity technology. Considerations such as energy requirements, environmental impact, and societal readiness are explored to provide a holistic perspective on the feasibility and desirability of pursuing anti-gravity research. Ultimately, while the idea of anti-gravity remains a captivating subject of scientific inquiry and fiction, current understanding and technological capabilities suggest significant hurdles that must be overcome before practical anti-gravity effects can be realized. This paper concludes by outlining potential avenues for future research and highlighting the interdisciplinary nature of addressing such a complex phenomenon.

Quasiprobabilities in Quantum Thermodynamics and Many-Body Systems

In this tutorial, we present the definition, interpretation, and properties of some of the main quasiprobabilities that can describe the statistics of measurement outcomes evaluated at two or more times. Such statistics incorporate the incompatibility of the measurement observables and the state of the measured quantum system. We particularly focus on Kirkwood-Dirac quasiprobabilities and related distributions. We also discuss techniques to experimentally access a quasiprobability distribution, ranging from the weak two-point measurement scheme, to a Ramsey-like interferometric scheme and procedures assisted by an external detector. Once defined the fundamental concepts following the standpoint of joint measurability in quantum mechanics, we illustrate the use of quasiprobabilities in quantum thermodynamics to describe the quantum statistics of work and heat, and to explain anomalies in the energy exchanges entailed by a given thermodynamic transformation. On the one hand, in work protocols, we show how absorbed energy can be converted to extractable work and vice versa due to Hamiltonian incompatibility at distinct times. On the other hand, in exchange processes between two quantum systems initially at different temperatures, we explain how quantum correlations in their initial state may induce cold-to-hot energy exchanges, which are unnatural between any pair of equilibrium nondriven systems. We conclude the tutorial by giving simple examples where quasiprobabilities are applied to many-body systems: scrambling of quantum information, sensitivity to local perturbations, and quantum work statistics in the quenched dynamics of models that can be mapped onto systems of free fermions, for instance, the Ising model with a transverse field. Throughout the tutorial, we meticulously present derivations of essential concepts alongside straightforward examples, aiming to enhance comprehension and facilitate learning. Published by the American Physical Society 2024

Observation of quantum entanglement with top quarks at the ATLAS detector

Entanglement is a key feature of quantum mechanics1–3, with applications in fields such as metrology, cryptography, quantum information and quantum computation4–8. It has been observed in a wide variety of systems and length scales, ranging from the microscopic9–13 to the macroscopic14–16. However, entanglement remains largely unexplored at the highest accessible energy scales. Here we report the highest-energy observation of entanglement, in top–antitop quark events produced at the Large Hadron Collider, using a proton–proton collision dataset with a centre-of-mass energy of √s = 13 TeV and an integrated luminosity of 140 inverse femtobarns (fb)−1 recorded with the ATLAS experiment. Spin entanglement is detected from the measurement of a single observable D, inferred from the angle between the charged leptons in their parent top- and antitop-quark rest frames. The observable is measured in a narrow interval around the top–antitop quark production threshold, at which the entanglement detection is expected to be significant. It is reported in a fiducial phase space defined with stable particles to minimize the uncertainties that stem from the limitations of the Monte Carlo event generators and the parton shower model in modelling top-quark pair production. The entanglement marker is measured to be D = −0.537 ± 0.002 (stat.) ± 0.019 (syst.) for 340GeV<mtt¯<380GeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$340\\,{\\rm{GeV}} < {m}_{t\\bar{t}} < 380\\,{\\rm{GeV}}$$\\end{document}. The observed result is more than five standard deviations from a scenario without entanglement and hence constitutes the first observation of entanglement in a pair of quarks and the highest-energy observation of entanglement so far.

Energy spectra with the Dirac equation of the q-deformed generalized Pöschl-Teller potential via the Feynman approach for .

The diatomic molecules of potassium is widely used in industrial chemicals and alternative energy. Besides that, is very useful for researching molecular interactions and energy states, especially in the context of quantum chemistry and spectroscopy. In the present work, a newly proposed diatomic potential model within relativistic and non-relativistic quantum mechanics has been considered, to obtain corresponding energy eigenvalues and related normalized eigenfunctions. The Dirac equation has been solved for an arbitrary spin-orbit quantum number using the path integral technique with the -deformed generalized Pöschl-Teller potential . By including a Pekeris-type approximation to handle the centrifugal factor, it was possible to obtain the spin and pseudospin-symmetric solution of the relativistic energy eigenvalues and wave equation. To assess the correctness of this work, Maple software was used to present some numerical findings for various values of and . With the constraint , it was shown that in the situation of pseudospin symmetry, only bound states exist with negative energy. In the non-relativistic limits, the non-relativistic ro-vibrational energy expression of the diatomic molecule is derived from the relativistic energy equation under spin symmetry. Under Varshni conditions, both vibrational and ro-vibrational energies of the molecule were computed and compared with the data. The average absolute percentage deviations from the data obtained for the potassium molecule are . This demonstrates that the model is a very consistent model to study and characterize diatomic molecules.

Quantum embedding method with transformer neural network quantum states for strongly correlated materials

The neural-network quantum states (NNQS) method is rapidly emerging as a powerful tool in quantum mechanisms. While significant advancements have been achieved in simulating simple molecules using NNQS, the ab initio simulation of complex solid-state materials remains challenging. Here in this work, we have adopted the periodic density matrix embedding theory to extend the NNQS method to deal with complex solid-state systems. Our approach notably reduces the computational problem size while maintaining high accuracy. We have validated the accuracy and efficiency of our method against traditional methodologies and experimental data in extended systems, and have investigated the magnetic ordering and charge density wave state in transition metal compounds. The findings from our research indicate that the integration of quantum embedding with intuitive chemical fragmentation can significantly enhance the NNQS simulation of realistic materials.

Steady-state magnon entanglement and backaction-evading of a weak magnetic signal via two-tone modulated cavity electromagnonics

Cavity electromagnonics explore the coupling between microwave cavity fields and magnons in micromagnets. This field has emerged as a promising platform for probing fundamental aspects of quantum mechanics and advancing quantum technologies. This paper investigates a scheme involving two-tone frequency modulation to engineer simultaneous magnon-photon two-mode squeezing and beam-splitter-like interactions. We demonstrate that this scheme enables the direct generation of macroscopic magnonic squeezed and entangled states. Moreover, it facilitates ultra-sensitive magnon-based magnetic field sensing through quantum non-demolition (QND) interactions between magnons and photons. The present scheme provides promising opportunities for generating macroscopic nonclassical quantum states in solid magnetic materials and developing spintronics-related quantum devices.

Force Fields, Quantum-Mechanical- and Molecular-Dynamics-Based Descriptors of Radiometal–Chelator Complexes

Radiopharmaceuticals are currently a key tool in cancer diagnosis and therapy. Metal-based radiopharmaceuticals are characterized by a radiometal–chelator moiety linked to a bio-vector that binds the biological target (e.g., a protein overexpressed in a particular tumor). The right match between radiometal and chelator influences the stability of the complex and the drug’s efficacy. Therefore, the coupling of the radioactive element to the correct chelator requires consideration of several features of the radiometal, such as its oxidation state, ionic radius, and coordination geometry. In this work, we systematically investigated about 120 radiometal–chelator complexes taken from the Cambridge Structural Database. We considered 25 radiometals and about 30 chelators, featuring both cyclic and acyclic geometries. We used quantum mechanics methods at the density functional theoretical level to generate the general AMBER force field parameters and to perform 1 µs-long all-atom molecular dynamics simulations in explicit water solution. From these calculations, we extracted several key molecular descriptors accounting for both electronic- and dynamical-based properties. The whole workflow was carefully validated, and selected test-cases were investigated in detail. Molecular descriptors and force field parameters for the complexes considered in this study are made freely available, thus enabling their use in predictive models, molecular modelling, and molecular dynamics investigations of the interaction of compounds with macromolecular targets. Our work provides new insights in understanding the properties of radiometal–chelator complexes, with a direct impact for rational drug design of this important class of drugs.

The role of encodings and distance metrics for the quantum nearest neighbor

Over the past few years, we observed a rethinking of classical artificial intelligence algorithms from a quantum computing perspective. This trend is driven by the peculiar properties of quantum mechanics, which offer the potential to enhance artificial intelligence capabilities, enabling it to surpass the constraints of classical computing. However, redesigning classical algorithms into their quantum equivalents is not straightforward and poses numerous challenges. In this study, we analyze in-depth two orthogonal designs of the quantum K-nearest neighbor classifier. In particular, we show two solutions based on amplitude encoding and basis encoding of data, respectively. These two types of encoding impact the overall structure of the respective algorithms, which employ different distance metrics and show different performances. By breaking down each quantum algorithm, we clarify and compare implementation aspects ranging from data preparation to classification. Eventually, we discuss the difficulties associated with data preparation, the theoretical advantage of quantum algorithms, and their impact on performance with respect to the classical counterpart.

Fundamental Laws and Quantum Dynamics

Background: Recently, we obtained a unitary theory of quantum mechanics and general relativity, where a quantum particle is a continuous distribution of matter in the two conjugate spaces of the coordinates and momentum, quantized by the equality of the mass parameter describing the relativistic dynamics of the matter, with the mass as an integral of the matter density. However, in this framework, we have not explicitly revealed the connection between our new theory and the fundamental laws of quantum mechanics. Methods: We analyzed in detail the three fundamental laws of quantum mechanics, explicitly describing experimental data: 1) Planck’s law of the blackbody electromagnetic radiation of a system of electrically charged harmonic oscillators, 2) Einstein’s law of the photon energy proportionality with the photon frequency, and 3) de Broglie’s law of the quantum particle as an oscillator in space. Results: We reobtained the two dynamical equations, in the conjugate spaces of the coordinates and momentum, as functions of the Lagrangian system, unlike the Schrödinger equation, depending on the Hamiltonian. Conclusion: According to the fundamental laws of quantum mechanics, a quantum particle is a continuous distribution of matter with an intrinsic mass, unlike the conventional quantum mechanics for the state occupation probabilities of punctual entities moving with the light velocity and getting an apparent mass only by collisions with some bosons pervading the whole universe. According to these laws, we obtained a quantum theory in agreement with common sense, classical logic, and general relativity.

Mourre Theory and Asymptotic Observables in Local Relativistic Quantum Field Theory

We prove the convergence of Araki–Haag detectors in any Haag–Kastler quantum field theory with an upper and lower mass gap. We cover the case of a single Araki–Haag detector on states of bounded energy, which are selected from the absolutely continuous part of the energy-momentum spectrum sufficiently close to the lower boundary of the multi-particle spectrum. These states essentially encompass those states in the multi-particle spectrum lying below the three-particle threshold. In our proof, we draw on insights from proofs of asymptotic completeness in quantum mechanics. Notably, we apply Mourre’s conjugate operator method for the first time within the framework of Haag–Kastler quantum field theory. Furthermore, we discuss applications of our findings for the problem of asymptotic completeness in local relativistic quantum field theory.

Quantum mechanics emerging from complex Brownian motions

The connection between the Schrödinger equation and Einstein's diffusion theory based on the Brownian motion of independent particles is well known. However, in contrast to diffusion theory, quantum mechanics theory has suffered controversial interpretations due to the counterintuitive concept of wavefunction. Here, while we confirm there is no difference in the mathematical form of these two equations, we derive the imaginary version of displacement. Using the diffusion theory of particles in a medium, as simple as it is, we describe that quantum mechanics is just an elegant and subtle equation to describe the probability of all the trajectories that a particle can take to propagate in time by a predictive wavefunction. Therefore, information on the position of particles through time in quantum theory is embedded in the wavefunction, which predicts the evolution of an ensemble of individual Brownian particles.

Relative entropy based uncertainty principles for graph signals

In physical quantum mechanics, the uncertainty principle in presence of quantum memory [Berta M, Christandl M, Colbeck R,et al., Nature Physics] can reach much lower bound, which has resulted in a huge breakthrough in quantum mechanics. Inspired by this idea, this paper would propose some novel uncertainty relations in terms of relative entropy for signal representation and time-frequency resolution analysis. On one hand, the relative entropy measures the distinguishability between the known (priori) basis and the client basis, which implies that we have partial “memory” of the client basis so that the uncertainty bounds become sharper in some cases. On the other hand, in some cases, if the reference basis along with nearly the same energy distribution could be given, then the uncertainty bound would tend to zero, as shows that there is no uncertainty any longer. These novel uncertainty relationships with sharper bounds would give us the potential advantages over the classical counterpart. In addition, the detailed comparison with classical Shannon entropy based uncertainty principle has been addressed as well via combined uncertainty relations. Finally, the theoretical analysis and numerical experiments on certain application over graph signals have been demonstrated to show the efficiency of these proposed relations.

Preparation of red mud derived eggshell coupling adsorbent and study on carbon dioxide capture performance based on experiment and density functional theory simulation

Preparing advanced CO2 capture materials is crucial for mitigating carbon emissions and alleviating global warming. Calcium-based adsorbents have attracted much attention due to their excellent environmental performance and high theoretical CO2 adsorption capacity. However, its poor cycling stability limits its widespread application. In this study, a red mud derived eggshell coupled CO2 adsorbent (RM/CaO) was prepared using solid waste RM and eggshell. The structure, CO2 capture performance, and micro-mechanism of the adsorbent were evaluated through macro micro-experiments combined with quantum mechanics simulations, to improve the adsorption performance of calcium-based adsorbents and achieve waste resource utilisation—an active, open area of research. The 1-1RM/CaO adsorbent had a specific surface area of 10.62 m2/g and a spatial structure with fused cross-linking layers. Its CO2 saturation adsorption capacity was 0.481 g/g; 171.43 % that of pure CaO. High level cycling stability can still be maintained after 15 cycles of CO2 adsorption desorption. Quantum mechanics simulations revealed that the CO2 adsorption energy on the RM/CaO (200) crystal plane can be enhanced to −8.25 eV. This indicates that the interaction between RM/CaO atoms is stronger, which is enhances the CO2 adsorption. This study optimized environmental and economic benefits by utilizing waste resources, deepened understanding of the interaction mechanism between CO2 adsorbents, and provided theoretical guidance for designing as well as optimizing future adsorbents.

Assessing the Accuracy of Quantum Dynamics Performed in the Time-Dependent Basis Representation.

A full quantum-mechanical (QM) description of large amplitude nuclear motion, associated with chemical reactions or isomerization of high-dimensional molecular systems, is inherently challenging due to the exponential scaling of the QM complexity with system size. To ameliorate the scaling bottleneck in studies of realistic systems, typically modeled in the configuration space, the nuclear wave functions are represented in terms of time-dependent basis functions. Such bases are expected to give an accurate description with a modest number of basis functions employed, by adapting them to the wave function solving the time-dependent Schrödinger equation. It is not, however, straightforward to estimate the accuracy of the resulting solution: in QM the energy conservation, a convenient such measure for a classical trajectory evolving in a time-independent potential, is not a sufficient criterion of the dynamics' accuracy. In this work, we argue that the expectation value of the Hamiltonian's "variance", quantifying the basis completeness, is a suitable practical measure of the quantum dynamics' accuracy. Illustrations are given for several chemistry-relevant test systems, modeled employing time-independent as well as time-dependent bases, including the coupled and variational coherent states methods and the quantum-trajectory guided adaptable Gaussians (QTAG) as the latter basis type. A novel semilocal definition of the QTAG basis time-evolution for placing the basis functions "in the right place at the right time" is also presented.

Non-equilibrium thermodynamics in NMR: understanding quadrupolar spin-1 systems.

In this study, we explore the non-equilibrium thermodynamics of a quantum system,&#xD;specifically focusing on spin-1 quadrupole nuclei. By employing fundamental principles&#xD;from quantum mechanics and statistical mechanics, we aim to understand the behavior&#xD;of the quadrupole spin-1 nuclei when subjected to external perturbations. Our analysis&#xD;involves the investigation of the system's dynamic response to non-equilibrium conditions through the manipulation of a work parameter. By treating work as a random&#xD;variable, we gather data from multiple cycles of finite duration, enabling us to compute&#xD;the complete distribution of the work generated during this process. Through these&#xD;finite-time non-equilibrium process data, we are able to determine equilibrium values&#xD;for important quantities such as the difference in free energy between the initial and&#xD;final states of the system. Additionally, we explore various properties of the system's&#xD;work distribution.

Quantum Machine Learning: Leveraging Quantum Computing for Enhanced Learning Algorithms

The paper "Quantum Machine Learning: Leveraging Quantum Computing for Enhanced Learning Algorithms" explores the integration of quantum computing principles into classical machine learning techniques, aiming to address limitations such as scalability and computational inefficiency. It presents the foundational concepts of quantum computing, including superposition and entanglement, and their application in accelerating machine learning processes. The study emphasizes the potential for quantum algorithms to significantly improve the performance of machine learning tasks by processing large datasets more efficiently and exploring larger hypothesis spaces. Key quantum machine learning algorithms discussed include Quantum Support Vector Machines (QSVM), Quantum Principal Component Analysis (QPCA), and Quantum Neural Networks (QNN), each of which leverages quantum mechanics to overcome the computational barriers faced by classical algorithms. The Quantum Approximate Optimization Algorithm (QAOA) is also highlighted for its ability to optimize machine learning models more effectively. While the theoretical benefits of Quantum Machine Learning (QML) are promising, the practical application of these techniques is currently limited by the constraints of existing quantum hardware. This research contributes to the emerging field of QML by examining its potential advantages and future implications in addressing complex data processing challenges.