Aspects Of Quantum Mechanics Research Articles

Scalar Metrics Tensor Gradation Rank-n Quantum Gravity Physics

In this paper, logical and novel approach in quantifying and scalarizing tensor metrics quantum gravity with rank gradation process of interactively coupled phenomena of gravity, time, space-time, quanta, and fields domains have been thoroughly analyzed mathematically. The author advances the theory of quantum gravity by integrating gravity and tensor time metrics, building on emergent theories such as Loop Quantum Gravity (LQG). LQG suggests that spacetime is quantized at the smallest scales, with gravity and spacetime geometry emerging from the quantum states of the gravitational field. This study proposes a method to quantize the gravitational field, focusing on the implications of tensor gradation and its impact on the metric structure of spacetime, explores the gradation of time tensors from rank-6 to rank-1 vectors in spacetime, bridging General Relativity (GR) and Quantum Relativity (QR). This study shows how metrics affects the time wavefunctions via Hamiltonian action differ from that those of influencing the gravitational gradients. By separating these metrics, we propose a method for the prediction of future time events on purely empirical basis. The results indicate that our approach can be enabled to reconcile the various aspects of general relativity and quantum mechanics, and finally offer a new insights into the nature of spacetime at the quantum level.

Investigation of splitting of a beam of potassium atoms in the classical Stern-Gerlach experiment at varying inhomogeneity of the magnetic field

The splitting of a beam of potassium atoms in the classical Stern-Gerlach scheme under varying inhomogeneity of the magnetic field is experimentally investigated in this work. First, the basic shape of the beam in the absence of an effective field is recorded, which makes it possible to introduce and calibrate the geometrical parameters of the channel. Then, when the current in the magnet windings increases and the field gradient grows, a systematic shift of the beam density maxima is observed, described by the model function F(u), which includes the parameter q, which characterizes the strength of interaction of atoms with the field. Theoretical calculations based on this function showed good agreement with the experimental results, including the asymmetry of the distribution due to the nonideal symmetry of the magnetic system. The obtained dependences of the position of the intensity maxima on ∇B confirmed the validity of both linear and asymptotic approximation for different modes of magnet operation. These conclusions have both fundamental importance for understanding the quantum mechanical aspects of beam splitting and applied significance in the development of methods for precise control of spin-polarized atomic beams in spectroscopy and spintronics.

Maximal steered coherence in accelerating Unruh–DeWitt detectors

Quantum coherence, a fundamental aspect of quantum mechanics, plays a crucial role in various quantum information tasks. However, preserving coherence under extreme conditions, such as relativistic acceleration, poses significant challenges. In this paper, we investigate the influence of Unruh temperature and energy levels on the evolution of maximal steered coherence (MSC) for different initial states. Our results reveal that MSC is strongly dependent on Unruh temperature, exhibiting behaviors ranging from monotonic decline to non-monotonic recovery, depending on the initial state parameter Δ0. Notably, when Δ0=1, MSC is generated as Unruh temperature increases. Additionally, we observe that higher energy levels help preserve or enhance MSC in the presence of Unruh effects. These findings offer valuable insights into the intricate relationship between relativistic effects and quantum coherence, with potential applications in developing robust quantum technologies for non-inertial environments.

Schrdinger equation for various quantum systems based on Heisenberg's uncertainty principle

This article establishes the proof of the Schrdinger equation for numerous quantum systems, utilizing Heisenberg's uncertainty principle. The Fourier transform connects functions in the time and frequency domains, resulting in the mathematical inequality that is the foundation of the uncertainty principle. In the part of Methods and Theory, the article derives the uncertainty principle through Fourier transforms by defining the mean and variance of angular frequency and time, and subsequently expanding the integral. This establishes the fundamental connection between time and frequency domains, illustrating the constraints imposed by quantum mechanics. In the part of Results and Application, the article applies the uncertainty principle to derive the Schrdinger equation under different conditions: free particle, particle in a box, harmonic oscillator, and hydrogen atom. For each case, the article assumes wave function solutions, uses the uncertainty in position and momentum to estimate kinetic and potential energies, and shows that the total energy matches the ground state energy derived from the Schrdinger equation. The results highlight the critical role of Heisenberg's uncertainty principle in understanding key aspects of quantum mechanics, providing a unified framework for these diverse systems.

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.

Pursuing Extreme Descriptive Power and Generality in Chemical Bond Theories: A Method to Decipher "Interatomic Genomes" from Interatomic Electron Structures.

The description and analysis of chemical bonds have been difficult following the popularization of electronic structure calculations. Although many attempts have been made from the perspective of electronic structure, the sheer volume of information in the electronic structure has left contemporary chemical bond analysis methods grappling with an inescapable "Trilemma" where the model briefness, generality, and descriptiveness (descriptive power) cannot be obtained simultaneously. To push the generality and descriptiveness to their extremes, herein a general machine learning-based framework is introduced to compact chemical bonds into a detailed residue-by-residue "genome" with matched encoding/decoding tools. The framework fuses the quantum mechanical aspects, auto feature extraction, nanostructures and/or simulations, and generative models. The encoded genomes are information-dense and decodable, where 100% generality is guaranteed. The descriptiveness of genomes appears to be broader than most known models. As a proof of concept, the realization presented in this work compacts the complete information regarding two critical chemical bonds in thiolate-protected gold nanoclusters, the S-Au and Au-Au bonds, from a Bosonic-Fermionic character perspective into 8-valued genomes. The machine learning component is trained based on 26,528 density functional theory simulated electron localization function images. With an exploration of the space span for the genome, bond polarization, hybridization, intrusion of other atoms, alignments, crystal orientation, atomic motions, and more details are observed. Furthermore, it has emerged from extensive generation tests that molecules and solids can be integrated in such a concise manner than is typically achieved with purely geometric representations. To showcase the intraclass complexity of S-Au and Au-Au bonds visually, a roadmap is plotted by summarizing and correlating the similarities of 8-value-genomes. Furthermore, genomes can be associated with realistic indices easily with a simple multilayer perception architecture as a simple calculating tool. Besides, there are 3 sets of applications, including a set of chemisorption, a set of molecular dynamical analysis, and a set of ultrafast processes, showcasing the interpretability potentials of interatomic genomes in the geometric structures, kinetic properties, and vibration characteristics of molecular systems. As the framework rose to the challenge of nanoclusters from a complicated mesoscopic family of material, the displayed generality and comprehensiveness indicate that the model may "understand" chemical bonds in a machine's way.

Efficient detection of multidimensional single-photon time-bin superpositions

The ability to detect quantum superpositions lies at the heart of fundamental and applied aspects of quantum mechanics. The time-frequency degree of freedom of light enables encoding and transmitting quantum information in a multidimensional fashion compatible with fiber and integrated platforms. However, the ability to efficiently detect high-dimensional time-bin superpositions, a subset of encodings in the wider time-frequency paradigm, is not yet available. Here we show that multidimensional time-bin superpositions can be detected using a single time-resolved photon detector. Our approach uses off-the-shelf components and is based on the temporal Talbot effect—a time-frequency counterpart of the well-known near field diffraction effect. We provide experimental results and highlight the possible applications in quantum communication, quantum information processing, and time-frequency quantum state tomography.

Accounting for quantum effects in atomistic spin dynamics

Atomistic spin dynamics (ASD) is a standard tool to model the magnetization dynamics of a variety of materials. The fundamental dynamical model underlying ASD is entirely classical. In this paper, we present two approaches to effectively incorporate quantum effects into ASD simulations, thus enhancing their low-temperature predictions. The first allows to simulate the magnetic behavior of a quantum spin system by solving the equations of motion of a classical spin system at an effective temperature relative to the critical temperature. This effective temperature is determined from the microscopic properties of the system. The second approach is based on a semiclassical model where classical spins interact with an environment with a quantumlike power spectrum. The parameters that characterize this model can be calculated or extracted from experiments. This semiclassical model quantitatively reproduces the absolute temperature behavior of a magnetic system, thus accounting for the quantum mechanical aspects of its dynamics, even at low temperature. The methods presented here can be readily implemented in current ASD simulations with no additional complexity cost. Published by the American Physical Society 2024

Some Aspects of Maxwell’s Equations, Klein-Gordon Equations, and Heat and Mass Transfer Equations in an n-Dimensional Maximally Symmetric Space-Time from the Classical and Quantum Mechanical Standpoints

This manuscript examines Maxwell’s equations, Klein-Gordon equations, and heat and mass transfer equations in n-dimensional maximally symmetric space-time. It investigates these equations in spherical and hyperbolic spaces embedded in higher-dimensional Euclidean and Minkowski spaces. The study focuses on the implications of these geometries and symmetries on the behaviour of the equations, highlighting how specific transformations and parametrizations impact their solutions. The findings reveal the underlying connections between geometric symmetries and physical laws, providing insights into their possible applications in theoretical physics. We touch upon both classical and quantum mechanical aspects of density and velocity evolutions with time in the universe. Quantum mechanical aspects of single and two-particle state evolution and statistical moments of the matter four-current are derived from the quantum Boltzmann equation and Feynman’s path integral method for fields applied to gravity interacting with electrons and positrons.

Atomic Quantum Technologies for Quantum Matter and Fundamental Physics Applications

Physics is living an era of unprecedented cross-fertilization among the different areas of science. In this perspective review, we discuss the manifold impact that state-of-the-art cold and ultracold-atomic platforms can have in fundamental and applied science through the development of platforms for quantum simulation, computation, metrology and sensing. We illustrate how the engineering of table-top experiments with atom technologies is engendering applications to understand problems in condensed matter and fundamental physics, cosmology and astrophysics, unveil foundational aspects of quantum mechanics, and advance quantum chemistry and the emerging field of quantum biology. In this journey, we take the perspective of two main approaches, i.e., creating quantum analogues and building quantum simulators, highlighting that independently of the ultimate goal of a universal quantum computer to be met, the remarkable transformative effects of these achievements remain unchanged. We wish to convey three main messages. First, this atom-based quantum technology enterprise is signing a new era in the way quantum technologies are used for fundamental science, even beyond the advancement of knowledge, which is characterised by truly cross-disciplinary research, extended interplay between theoretical and experimental thinking, and intersectoral approach. Second, quantum many-body physics is unavoidably taking center stage in frontier’s science. Third, quantum science and technology progress will have capillary impact on society, meaning this effect is not confined to isolated or highly specialized areas of knowledge, but is expected to reach and have a pervasive influence on a broad range of society aspects: while this happens, the adoption of a responsible research and innovation approach to quantum technologies is mandatory, to accompany citizens in building awareness and future scaffolding. Following on all the above reflections, this perspective review is thus aimed at scientists active or interested in interdisciplinary research, providing the reader with an overview of the current status of these wide fields of research where cold and ultracold-atomic platforms play a vital role in their description and simulation.

The Mind Travels on the Waves of Fantasy to Pursue Universal Evolution

A positive aspect of quantum mechanics has been that we have become familiar with wave sizes. Declined in the various forms that these can assume, we offer a probabilistic approach in the study of phenomena that occur in nature. Whether it is sound waves, electromagnetic waves or gravitational waves, whether they collapse when we measure phenomena, they present us with a completely different view than we have so far conceived of natural events. The maximum systems that have accompanied us to this day, and that have represented the foundation of our knowledge, have failed in favor of a philosophy that projects us into an evanescent abstract dimension, and not usable with the common senses of which we are endowed. In this work we present a synthesis of wave concepts, adopting them to a possible theoretical interpretation of how even our feeling and our knowledge can travel on the special waves of fantasy, and at the same time offer a personal reinterpretation of natural phenomena in harmony with the wave-like conception.

Neoclassical Theory of Atoms

The "Neoclassical Theory of Atoms" challenges the dominance of quantum mechanics in explaining certain atomic phenomena. This work argues that a classical approach, utilizing electromagnetic Coulomb forces and Newtonian mechanics, can potentially account for discrete energy levels and spectral lines observed in hydrogen and helium atoms. It questions the necessity of invoking the seemingly counterintuitive aspects of quantum mechanics for these specific phenomena. By demonstrating the potential of a classical framework, this research aims to stimulate debate and exploration of alternative explanations within physics. This could potentially lead to a deeper understanding of the nature of reality and the limitations (or potential for expansion) of current physical theories.

Consistent Treatment of Quantum Systems with a Time-Dependent Hilbert Space.

We consider some basic problems associated with quantum mechanics of systems having a time-dependent Hilbert space. We provide a consistent treatment of these systems and address the possibility of describing them in terms of a time-independent Hilbert space. We show that in general the Hamiltonian operator does not represent an observable of the system even if it is a self-adjoint operator. This is related to a hidden geometric aspect of quantum mechanics arising from the presence of an operator-valued gauge potential. We also offer a careful treatment of quantum systems whose Hilbert space is obtained by endowing a time-independent vector space with a time-dependent inner product.

Examples of atoms absorbing photon via Schrödinger equation and vacuum fluctuations

The absorption of photons by atoms encompasses fundamental quantum mechanical aspects, particularly the emergence of randomness to account for the inherent unpredictability in absorption outcomes. We demonstrate that vacuum fluctuations can be the origin of this randomness. An illustrative example of this is the absorption of a single photon by two symmetrically arranged atoms. In the absence of a mechanism to introduce randomness, the Schrödinger equation alone can govern the time evolution of the process initially. Then, it becomes stuck, and an entangled state of the two atoms emerges. This entangled state consists of two components: in one, the first atom is excited by the photon while the second is in the ground state, and in the other, the second atom is excited while the first remains in the ground state. These components form a superposition state characterized by an unbreakable symmetry in the absence of external influences. Consequently, the absorption process remains incomplete. When vacuum fluctuations come into play, they can induce fluctuations in the weights of these components, akin to Brownian motion. Over time, one component diminishes, thereby breaking the entanglement between the two atoms and allowing the photon absorption process to conclude. The remaining component shows which atom completes the photon absorption. Vacuum fluctuations not only introduce randomness but also have the potential to give rise to the Born rule in this context. Furthermore, the Casimir effect, which is closely tied to vacuum fluctuations, presents a promising experimental avenue for validating this mechanism. Similar studies can also be conducted with varying numbers of atoms.

Further Aspect of Quantum Mechanics and Particle Physics

Further Aspect of Quantum Mechanics and Particle Physics

Quantum Fisher information in moving reference frame

In the field of quantum metrology, an important application is quantum parameter estimation. As the fundamental theory of quantum parameter estimation, quantum Cramér-Rao inequality shows that the variance of parameter estimation is determined by the inverse of quantum Fisher information. Higher quantum Fisher information corresponds to a lower variance, thereby improving the precision of parameter estimation. Quantum Fisher information has been extensively investigated in many aspects of non-relativistic quantum mechanics, including entanglement structure detection, quantum teleportation, quantum phase transition, quantum chaos, and quantum computation. However, there are few researches considering the influence of relativistic effect on quantum Fisher information, and therefore, we attempt to investigate this topic in this work. The relativistic transformation of particle states is employed, and the quantum Fisher information about amplitude parameter <inline-formula><tex-math id="M3">\begin{document}$ \theta $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M3.png"/></alternatives></inline-formula> and phase parameter <inline-formula><tex-math id="M4">\begin{document}$\varphi $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M4.png"/></alternatives></inline-formula> are investigated in moving reference frame. In this work, the parameters to be estimated are encoded into the spin degree of freedom, and the pure single-qubit state and the pure two-qubit state are both considered. The quantum Fisher information about <inline-formula><tex-math id="M5">\begin{document}$ \theta $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M5.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M6">\begin{document}$\varphi $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M6.png"/></alternatives></inline-formula> of single-qubit state and two-qubit state in moving reference frame are numerically calculated, respectively. It can be observed that the quantum Fisher information is associated with rapidity, amplitude parameter, and the ratio of the width to the particle mass <inline-formula><tex-math id="M7">\begin{document}${{{\sigma _r}} \mathord{\left/ {\vphantom {{{\sigma _r}} m}} \right. } m}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M7.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M7.png"/></alternatives></inline-formula>. The quantum Fisher information of the estimated parameters decreases with rapidity increasing for both single-qubit state and two-qubit state. As rapidity approaches infinity, i.e. increases to the speed of light, the quantum Fisher information reaches to a constant which decreases as the ratio <inline-formula><tex-math id="M8">\begin{document}${{{\sigma _r}} \mathord{\left/ {\vphantom {{{\sigma _r}} m}} \right. } m}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M8.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M8.png"/></alternatives></inline-formula> increases. More importantly, for the phase parameter <inline-formula><tex-math id="M9">\begin{document}$ \varphi $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M9.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M9.png"/></alternatives></inline-formula>, it is observed that the quantum Fisher information of two-qubit state reduces more significantly than that of single-qubit state. While, for the amplitude parameter <inline-formula><tex-math id="M10">\begin{document}$\theta $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M10.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M10.png"/></alternatives></inline-formula>, the quantum Fisher information of two-qubit state is greater than that of single-qubit state. These results are useful and valuable for improving the precision of parameter estimation under the influence of relativistic effect.

Persistency of tripartite nonlocality sharing with noise

Recently, researchers have proven that an infinite number of Charlies and a pair of Alice and Bob can share standard tripartite nonlocality and genuinely nonsignal nonlocality by violating the Mermin and NS inequalities within tripartite systems. This discovery undoubtedly provides new perspectives and potential in quantum information science. However, it should be noted that the above-mentioned conclusion is derived on the highly idealized assumption that the quantum system is perfect and free from external disturbances. In reality, the realization of this ideal state is a challenging proposition. As a fundamental aspect of quantum mechanics, the phenomenon of quantum entanglement is susceptible to the influence of external factors, such as noise, during its practical implementation. Additionally, the process of quantum measurement can introduce potential errors, which may potentially diminish or even negate the observed quantum nonlocality. In light of the above situation, we investigate whether it is possible to share the corresponding quantum nonlocality, despite the inevitable occurrence of noise and error. This paper aims to study and discuss the persistency of nonlocality in noisy three-qubit systems. Firstly, the sufficient conditions are provided for Alice and Bob to share standard tripartite nonlocality with any number of Charlies, even when measurements are noisy and the initial three-qubit system is in a maximally entangled state with noise. This finding indicates that certain standard tripartite nonlocality can persist under non-ideal conditions as long as certain conditions are met. Moreover, this article elucidates the necessary conditions for multiple independent Charlies to share genuinely nonsignal nonlocality with a pair of Alice and Bob in a non-ideal state. This implies that despite the presence of noise and errors, this type of genuinely nonsignal nonlocality can still be securely shared among multiple parties as long as specific conditions are met. This research provides a new theoretical basis for the security and feasibility of quantum communication. The comprehensive analysis presented in this paper offers insights into the behavior of triple quantum nonlocality under noiseless conditions.

Jan Stochel, a stellar mathematician

The occasion for this survey article was the 70th birthday of Jan Stochel, professor at Jagiellonian University, former head of the Chair of Functional Analysis and a prominent member of the Krak�w school of operator theory. In the course of his mathematical career, he has dealt, among other things, with various aspects of functional analysis, single and multivariable operator theory, the theory of moments, the theory of orthogonal polynomials, the theory of reproducing kernel Hilbert spaces, and mathematical aspects of quantum mechanics.

Different Aspects of Spin in Quantum Mechanics and General Relativity

In this paper, different aspects of the concept of spin are studied. The most well-established one is, of course, the quantum mechanical aspect: spin is a broken symmetry in the sense that the solutions of the Dirac equation tend to have directional properties that cannot be seen in the equation itself. It has been clear since the early days of quantum mechanics that this has something to do with the indefinite metric in Lorentz geometry, but the mechanism behind this connection is elusive. Although spin is not the same as rotation in the usual sense, there must certainly be a close relationship between these concepts. And, a possible way to investigate this connection is to instead start from the underlying geometry in general relativity. Is there a reason why rotating motion in Lorentz geometry should be more natural than non-rotating motion? In a certain sense, the answer turns out to be yes. But, it is by no means easy to see what this should correspond to in the usual quantum mechanical picture. On the other hand, it seems very unlikely that the similarities should be just coincidental. The interpretation of the author is that this can be a golden opportunity to investigate the interplay between these two theories.

Preface: 2nd International Forum on Mathematical Statistics, Physical Sciences and Telecommunication System (IFMPT 2023)

We are glad to introduce you that the 2023 2nd International Forum on Mathematical Statistics, Physical Sciences and Telecommunication System (IFMPT 2023) was successfully held on June 24-25, 2023 in Guangzhou, China. This forum aims to bring together academic scientists, leading engineers, industry researchers, and scholar students to exchange and share their experiences and research results about all aspects of mathematical statistics, mathematical model, physical sciences, quantum mechanics, astrophysics, 5G networking, and telecommunication system. This forum also discusses the practical challenges encountered and the solutions adopted.
 This scientific event brings together more than 50 national and international researchers. During the conference, the conference model was divided into three sessions, including oral presentations, keynote speeches, and online Q&A discussion. In the first part, some scholars, whose submissions were selected as the excellent papers, were given about 8-10 minutes to perform their oral presentations one by one. Then in the second part, keynote speakers were each allocated 30-40 minutes to hold their speeches.
 Lastly, we would like to express our sincere gratitude to the distinguished keynote speakers, as well as all the participants. We also want to thank the publisher for publishing the proceedings. We are expecting more and more experts and scholars from all over the world to join this international event next year.
 The Committee of IFMPT 2023
 Guangzhou, China