Quantum Mechanical Theory Research Articles

Lok Purush Siddhant: Exploring the Reflection of the Universe in the Human Body

The Lok Purush Siddhant is a foundational concept in Ayurveda that elucidates the intrinsic connection between the individual (microcosm) and the universe (macrocosm). This ancient Ayurvedic philosophy underscores the principle that the human body mirrors the cosmos, with both governed by similar laws and elements. In the Ayurvedic worldview, the physical body, mind, and soul are seen as a reflection of the larger universe, consisting of the five elements (Panchamahabhutas) - earth, water, fire, air, and ether. By understanding the balance and interaction of these elements within the human body, one can achieve optimal health, mirroring the harmony of the cosmos. This exploration of the Lok Purush Siddhant aims to highlight its relevance in modern health practices, particularly in holistic and integrative medicine. The paper discusses the parallels between Ayurvedic principles and contemporary scientific theories of biology, ecology, and quantum mechanics. It also delves into how this ancient wisdom informs various Ayurvedic therapeutic approaches such as diet, lifestyle, and treatment protocols, which seek to align the microcosm with the macrocosm to achieve balance and healing. Ultimately, this concept emphasizes that true well-being is achieved when the individual harmonizes with the greater cosmic order, making it a timeless and essential aspect of Ayurvedic philosophy.

QUANTUM MECHANICS – DETERMINISTIC VS. PROBABILISTIC

A deterministic quantum mechanics theory is presented. The proposed theory is shown to be consistent with the current mainstream statistical quantum theory as well as with classical physics. It produces solutions that demonstrate that causality, physical reality, and determinism are restored and can explain in simple form concerns raised by results from the current mainstream statistical quantum theory. The meaning of particle-wave duality and complementarity, the possibility of a particle, like an electron, crossing through the nucleus as it does when the angular momentum of the electron is zero at the ground state of the hydrogen atom, the possibility of a point-size particle to have an “intrinsic spin,” the possibility of “quantum jumps” as the electron transitions instantaneously from one stable orbital to another without passing through the space in between the orbitals and does that at irregular time intervals. The natural collapse of the wave function as part of the solution is a result that emerges from the proposed deterministic quantum mechanics theory. The phenomenon of entanglement is also discussed in the context that information transfer between entangled “particles” does not occur in a superluminal fashion and is not a “spooky action at a distance” but rather the local measurement of global property. A linear stability method presents actual analytical solutions consistent with current mainstream quantum theory and classical physics. The Bohr-Schrödinger energy levels leading to the experimentally confirmed spectral lines and the fine structure constant emerge from an approximate solution to these equations.

Quasi-Classical Models of Nonlinear Relaxation Polarization and Conductivity in Electric, Optoelectric, and Fiber Optic Elements Based on Materials with Ionic–Molecular Chemical Bonds

A generalized scientific review with elements of additions and clarifications has been carried out on the methods of theoretical research on the electrophysical properties of crystals with ionic–molecular chemical bonds (CIMBs). The main theoretical tools adopted are the methods of quasi-classical kinetic theory as applied to ionic subsystems relaxing in layered dielectrics (natural silicates, crystal hydrates, various types of ceramics, and perovskites) in an electric field. A universal (applicable for any CIMBs class crystals) nonlinear quasi-classical kinetic equation of theoretical and practical importance has been constructed. This equation describes, in complex with the Poisson equation, the mechanism of ion-relaxation polarization and conductivity in a wide range of polarizing field parameters (0.1–1000 MV/m) and temperatures (1–1550 K). The physical model is based on a system of non-interacting ions (due to the low concentration in the crystal) moving in a one-dimensional, spatially periodic crystalline potential field, perturbed by an external electric field. The energy spectrum of ions is assumed to be continuous. Elements of quantum mechanical theory in a quasi-classical model are used to mathematically describe the influence of tunnel transitions of hydrogen ions (protons) during the interaction of proton and anion subsystems in hydrogen-bonded crystals (HBC) on the polarization of the dielectric in the region of nitrogen (50–100 K) and helium (1–10 K) temperatures. The mathematical model is based on the solution of a system of nonlinear Fokker-Planck and Poisson equations, solved by perturbation theory methods (via expanding solutions into infinite power series in a small dimensionless parameter). Theoretical frequency and temperature spectra of the dielectric loss tangent were constructed and analyzed, the molecular parameters of relaxers were calculated, and the physical nature of the maxima of the experimental temperature spectra of dielectric losses for a number of HBC crystals was discovered. The low-temperature maximum, which is caused by the quantum tunneling of protons and is absent in the experimental spectra, was theoretically calculated and investigated. The most effective areas of scientific and technical application of the theoretical results obtained were identified. The application of the equations and recurrent formulas of the constructed model to the study of nonlinear optical effects in elements of laser technologies and nonlinear radio wave effects in elements of microwave signal control systems is of the greatest interest.

Exploring alpha emissions in neutron induced reactions via QMFT based dynamical cluster-decay approach

Abstract This study theoretically investigates alpha emission from compound nuclei formed in neutron-induced reactions, inspired by the experiments of Yu M. Gledenov et al. at Peking University, China. The research focuses on the decay dynamics of even-mass compound nuclei 144Nd* and 148Sm*, formed with neutron beam energies of 4 to 6 MeV. Employing the Dynamical Cluster-decay Model (DCM) based on Quantum Mechanical Fragmentation Theory (QMFT), high Q-value alpha emission channels 144Nd*→ 140Ce+α and 148Sm*→ 144Nd+α are explored. Cross-sections for alpha emissions are calculated by optimizing the neck-length parameter “∆R”, showing agreement with experimental data. Given the highly asymmetric incoming channel, the beam energy approximates the centre of mass energy (E beam≈E c.m. ). The study evaluates the impact of deformations, considering spherical and quadrupole-deformed configurations of the decaying fragments, and examines the alterations in potential energy surfaces. For deformed fragmentation, orientations are optimized for hot configurations. A comparative analysis of fragmentation structures, preformation profiles, and barrier characteristics is conducted between spherical and quadrupole-deformed fragmentation. The DCM’s collective clusterization approach treats all exit channels equally, emphasizing the formation of the preferred decay channel over competing channels such as fission. Observed changes in fragmentation profiles underscore the influence of nuclear parameters like angular momentum and deformations, providing insights into the dynamics of compound nucleus decay and the pivotal role of these parameters in shaping reaction outcomes.

Strong Coupling between Moiré-Type Plasmons and Phonons in Suspended Monolayer Metallic Twisted Superlattices.

We demonstrate both experimentally and analytically a strong coupling phenomenon between moiré-type plasmons and phonons within moiré superlattices. We study the dependence of moiré wave vector and the twist angle and numerically simulate and experimentally fabricate metallic moiré superlattices on a suspended thin film SiO2 substrate at different twist angles. The results suggest that the coupling strength initially increases and then decreases with increasing twist angles. When the twist angle is at 16.26°, we achieve a moiré-type plasmon-phonon strong coupling with a Rabi splitting strength approaching 45 meV. We further analyze the coupling system by utilizing the coupled-harmonic-oscillators theory and quantum mechanical theory. The calculations and numerical simulations further agree with the experimental results. The proposed strong coupling system has the potential to contribute substantially to electromagnetic field controlling and coupling.

Classical Stochastic Representation of Quantum Mechanics

Classical Stochastic Representation of Quantum Mechanics

Challenges in sensemaking and reasoning in the context of degenerate perturbation theory in quantum mechanics

We discuss an investigation of student sensemaking and reasoning in the context of degenerate perturbation theory (DPT) in quantum mechanics. We find that advanced undergraduate and graduate students in quantum physics courses often struggled with expertlike sensemaking and reasoning to solve DPT problems. The sensemaking and reasoning were particularly challenging for students as they tried to integrate physical and mathematical concepts to solve DPT problems. Their sensemaking showed local coherence but lacked global consistency with different knowledge resources getting activated in different problem-solving tasks even if the same concepts were applicable. Depending upon the issues involved in the DPT problems, students were sometimes stuck in the “physics mode” or “math mode” and found it challenging to coordinate and integrate the physics and mathematics appropriately to solve quantum mechanics problems involving DPT. Their sensemaking shows the use of various reasoning primitives. It also shows that some advanced students struggled with self-monitoring and checking their answers to make sure they were consistent across different problems. Some also relied on memorized information, invoked authority, and did not make appropriate connections between their DPT problem solutions and the outcomes of experiments. Advanced students in quantum mechanics often displayed analogous patterns of challenges in sensemaking and reasoning as those that have been found in introductory physics. Student sensemaking and reasoning show that these advanced students are still developing expertise in this novel quantum physics domain as they learn to integrate physical and mathematical concepts. Published by the American Physical Society 2024

Sayed`s Theory in Quantum Mechanics: An Innovative Approach for Wave Function Equations Measurability, Efficacy and Universality

Allah (God) is ubiquitous and the only Creator of Everything. Quantum mechanics is the world of the microscopic scale of physics. The universe is a macroscopic manifestation of the quantum approach. In this revolutionary article, correctness and rectification of Schrodinger wave equations that has huge limitations and shortcomings, were proudly achieved. The Sayed quantum wave function (SQWF) was derived and defined (Ψs) for free electron and in Laplace coordinates as a function in wavelength and light speed. The SQWF was calculated and quantified for de Broglie moving electron; 0.4033x10-20 Second. Using SQWF equation, the speed of light was accurately calculated; ~3x108 m/s. respectively. An outstanding Sayed`s quantum wavelength (SQW) was proposed and elucidated. The Sayed time dependent wave function equations (STDWFE) were derived and given to be a generic alternative to deal with all atoms rather than the one electron atoms of Schrodinger. The crucial parameters; wavelength, Rydberg constant RH, atomic number, principle quantum number, and mc2 were introduced in the STDWFE. It is a quantized formula. The (Ψs) was calculated for H, He, B and found to be , ,The Sayed quantum constantRH mc2, was quantified to be 8.93x10-7 J/m.

Second-order dissociation and transition of heavy quarkonia in the quark-gluon plasma

We revisit the dissociation of heavy quarkonia by thermal partons at the next-to-leading order (NLO, also known as inelastic parton scattering dissociation) in the quark-gluon plasma (QGP). Utilizing the chromoelectric dipole coupling from quantum chromodynamics (QCD) multipole expansion as an effective Hamiltonian, this has been conducted in the approach of second-order quantum mechanical perturbation theory, which allows us to systematically incorporate the bound state wave functions. Employing the quarkonium wave functions and binding energies obtained from an in-medium potential model, we then numerically evaluate the dissociation cross sections and rates for various charmonia and bottomonia, where the infrared and collinear divergences are regularized by the thermal masses of medium partons. We demonstrate that distinct from the leading order (LO, also known as gluo-dissociation) counterparts peaking at relatively low gluon energy and falling off thereafter, the NLO cross sections first grow and then nearly saturate as the incident parton energy increases, as a result of the outgoing parton carrying away the excess energy. The resulting NLO dissociation rates increase with temperature and take over from the LO counterparts toward high temperatures, similar to pertinent findings from previous studies. We also evaluate the in-medium second-order transition between different bound states, which may contribute to the total thermal decay widths of heavy quarkonia in the QGP. Published by the American Physical Society 2024

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.

Superluminal matter waves

The Dirac equation has resided among the greatest successes of modern physics since its emergence as the first quantum mechanical theory fully compatible with special relativity. This compatibility ensures that the expectation value of the velocity is less than the vacuum speed of light. Here, we show that the Dirac equation admits free-particle solutions where the peak amplitude of the wave function can travel at any velocity, including those exceeding the vacuum speed of light, despite having a subluminal velocity expectation value. The solutions are constructed by superposing basis functions with correlations in momentum space. These arbitrary velocity wave functions feature a near-constant profile and may impact quantum mechanical processes that are sensitive to the local value of the probability density as opposed to expectation values. Published by the American Physical Society 2024

Stable-to-unstable transition in quantum friction

We investigate the frictional force arising from quantum fluctuations when two dissipative metallic plates are set in a shear motion. While early studies showed that the electromagnetic fields in the quantum friction setup reach nonequilibrium steady states, yielding a time-independent force, other works have demonstrated the failure to attain steady states, leading to instability and time-varying friction under sufficiently low-loss conditions. Here, we develop a fully quantum-mechanical theory without perturbative approximations, and we unveil the transition from stable to unstable regimes of the quantum friction setup. Due to the relative motion of the plates, their electromagnetic response may be active in some conditions, resulting in optical gain. We prove that the standard fluctuation-dissipation leads to inconsistent results when applied to our system, and, in particular, it predicts a vanishing frictional force. Using a modified fluctuation-dissipation relation tailored for gain media, we calculate the frictional force in terms of the system Green's function, thereby recovering early works on quantum friction. Remarkably, we also find that the frictional force diverges to infinity as the relative velocity of the plates approaches a threshold. This threshold is determined by the damping strength and the distance between the metal surfaces. Beyond this critical velocity, the system exhibits instability, akin to the behavior of a laser cavity, where no steady state exists. In such a scenario, the frictional force escalates exponentially. Our findings pave the way for experimental exploration of the frictional force in proximity to this critical regime. Published by the American Physical Society 2024

Effective modeling of open quantum systems by low-rank discretization of structured environments.

The accurate description of the interaction of a quantum system with its environment is a challenging problem ubiquitous across all areas of physics and lies at the foundation of quantum mechanics theory. Here, we pioneer a new strategy to create discrete low-rank models of the system-environment interaction, by exploiting the frequency and time domain information encoded in the fluctuation-dissipation relation connecting the system-bath correlation function and the spectral density. We demonstrate the effectiveness of our methodology by combining it with tensor-network methodologies and simulating the quantum dynamics of complex excitonic systems in a highly structured bosonic environment. The new modeling framework sets the basis for a leap in the analysis of open quantum systems, providing controlled accuracy at significantly reduced computational costs, with benefits in all connected research areas.

Investigation of Phosphazene Superbase Interactions with [PCl2N]3.

In this study, the reaction between phosphazene superbases and a chlorophosphazene trimer ([PCl2N]3) has been investigated. In this room temperature reaction, the phosphazene superbase (Me2N)3PN(Me2N)2P═NEt, commonly known as P2Et, was shown to behave as a nucleophile, displacing one of the chlorides from [PCl2N]3 and producing the tadpole-like structure 1. The reaction described herein is one of the few instances of a phosphazene superbase behaving as a nucleophile rather than a Brønsted base. Once formed, this structure contains contrasting reactivity, containing a weakly basic phosphazene head while maintaining a highly basic phosphazene tail of the tadpole. The mechanism of the reaction was explored by investigating the potential energy surface through density functional theory calculations at the B3LYP/6-311+G(d,p) level of quantum mechanical theory. It was determined that the reaction of P2Et with [PCl2N]3 followed a stepwise process beginning with the substitution of P2Et onto [PCl2N]3 with the concurrent loss of chloride. Subsequently, the chloride attacks the ethyl group of the P2Et moiety, and ethyl chloride is released, producing 1. Compound 1 was further characterized via 31P NMR spectroscopy, mass spectrometry, and X-ray crystallography.

PERSPECTIVES FOR THE DEVELOPMENT OF SCIENCE IN THE SOCIETY

The world has never been so open to scientific research and technological development as it is today, nor has human competence evolved so rapidly in directions not previously appreciated. The pace of discoveries is faster, although there are scientific fields in which goals are achieved more slowly and with considerable collective effort. However, we find that the successes achieved in the field of science have had an enormous impact on people's mentality and as a consequence have formed the belief that reflects science as a dominant factor in contemporary society. A philosophical reflection on the process of scientific development reveals that for a long time, the physical sciences have been dominant, and in recent years we are witnessing a fulminating development of biology (genetics), which has not only economic implications but also the ethical implications of a major importance. At the same time, the contemporary society of information and knowledge attests to obvious factors of a unique phenomenon called integrative science. It is projected at the integrative frontier of the astrophysics field that combines the processes of the universe constitution as a quantum system (processes that go beyond the theory of quantum mechanics, but also the theory of super lathes) and the processes of life, mind and consciousness. Integrative science proposes a new understanding of reality, even the one considered today purely structural. We hope that integrative science theories will reflect the reality that includes Consciousness as a fundamental factor of Existence.

FRACTALS IN QUANTUM MECHANICS: FROM THEORY TO PRACTICAL APPLICATIONS

This article examines the use of fractals to estimate the probability of classical events controlled by quantum processes. A hypothesis explaining the opposite charges of the positron and electron is discussed, as well as the relationship with the main modern theories of quantum mechanics, such as quantum electrodynamics (QED), string theory, etc. The relationship with the tunnel effect and the pulsed tunnel effect is considered. Examples of practical application of fractals are given, for example, in photocatalysts. The concepts of the effective mass of a photon and the quantum nature of elementary particles, the idea of their internal structure and the formation of matter from the point of view of quantum mechanics are touched upon. Particular attention is paid to the fractal structure of the quantum field as a probability associated with the formation of a positron or electron, and the mathematical connection with the Dirac equation, QED and the Schrödinger equation.

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.

Intrinsic squeezing of mechanical motion of a harmonically trapped atom with spin-orbit coupling

In this paper we investigated one-dimensional harmonically trapped atom with Raman-induced spin-orbit coupling by mapping to quantum-like model. Using displacement Fock states in quantum optics and variational methods we found the odd-parity superposition state of left- and right-displaced oscillator state is a good approximate solution to the ground state, which captures the essential physics of the system. The ground state wave function owes nodes which is remarkably different from the conventional no-node theory in quantum mechanics. The results show the atomic motion of center of mass exhibits intrinsic squeezing properties with relation to the Raman and spin-orbit coupling strength characterized by the variance in position and momentum, information entropy, as well as the Wigner function of the ground state. The dynamics of center of mass are also studied which demonstrates intuitive Zitterbewegung oscillations in momentum space and real space. Our results could be used for observing Zitterbewegung oscillations in neutral atomic gases and engineering nonclassic states.

Quantum geometric perspective on the origin of quantum-conditioned curvatures

Abstract The quantization of the gravitational field, which includes the metric field, has been investigated using various methods such as loop quantum gravity, quantum field theory, and string theory. Nevertheless, an alternative strategy to tackle the challenge of merging the fundamentally different theories of general relativity (GR) and quantum mechanics (QM) is through a quantum geometric approach. This particular approach entails extending QM to relativistic energies and finite gravitational fields, while also expanding the continuous Riemann to a discretized (quantized) Finsler-Hamilton geometry. By embracing this method, it may be feasible to bridge the gap between GR and QM or even achieve their unification. The resulting fundamental tensor appears to blend its original classical and quantum characteristics, effectively integrating quantum-mechanically induced revisions to the affine connections and spacetime curvatures. Our study primarily focuses on investigating the Ricci curvature tensor in the context of the Einstein-Gilbert-Straus metric. By employing both analytical and numerical methods, we have identified quantum-conditioned curvatures (QCC) that act as additional sources of gravitation. These QCC exhibit a fundamental difference from the traditional curvatures described by Einsteinian GR. While the Ricci curvatures are predominantly positive across most regions, the quantized Ricci curvatures display negativity. We conclude that the QCC a) possess an intrinsic, essential, and real character, b) should not be disregarded due to their significant magnitude, and c) are fundamentally different from the curvatures found in classical GR. Moreover, we conclude that the proposed quantum geometric approach may offer an alternative mathematical framework for understanding the emergence of quantum gravity.

Relativistic generalized uncertainty principle for a test particle in four-dimensional spacetime

The generalized uncertainty principle provides a promising phenomenological approach to reconciling the fundamentals of general relativity with quantum mechanics. As a result, noncommutativity, measurement uncertainty, and the fundamental theory of quantum mechanics are subject to finite gravitational fields. The generalized uncertainty principle (RGUP) on curved spacetime allows for the imposition of quantum-induced elements on general relativity (GR) in four dimensions. In the relativistic regimes, the determination of a test particle’s spacetime coordinates, [Formula: see text], becomes uncertain. There exists a specific range of coordinates where the accessibility to [Formula: see text] is notably limited. Consequently, the spacetime coordinates lack both smoothness and continuity. The quantum-mechanical calculations of the spacetime coordinates are directly linked to their measurement through the expectation value [Formula: see text]. This expectation value is dependent on [Formula: see text], which is itself limited by a minimum measurable length [Formula: see text]. A crucial finding presented in this script is the existence of a lower bound for the Hamiltonian, which implies the stability of the quantum nature of spacetime. The direct correlation between [Formula: see text] and [Formula: see text] is a significant discovery, suggesting a proportional relationship. The conjecture is made that the primary metric g carries all essential information regarding spacetime curvature and serves a role akin to the Jacobian determinant in general relativity. Moreover, the linear relationship between [Formula: see text] and the Planck length [Formula: see text] is established with a proportionality factor of [Formula: see text], where [Formula: see text] denotes the RGUP parameter. The discretization of spacetime coordinates results in the discontinuity of the test particle’s wavefunction [Formula: see text], leading to an unrealistic [Formula: see text]. It is also noted that the lower limit of [Formula: see text] is directly proportional to the fundamental tensor.