Quantum Mechanical Particle Research Articles

UMA TEORIA UNIFICADA DA FÍSICA: A INTERCONEXÃO ENTRE MASSA, ENERGIA, ENTROPIA E TEMPO COMO FUNDAMENTO PARA A REFORMULAÇÃO DA GRAVIDADE, DO CAMPO ELETROMAGNÉTICO E DAS INTERAÇÕES DAS PARTÍCULAS NA MECÂNICA QUÂNTICA

This scientific article explores the unification between the relationships between particles, in Quantum Mechanics, and large bodies, in the Theory of Relativity, as a conceptual path to reformulate the concepts of gravity and time, contributing to the development of a Theory of Everything. The proposal investigated six hypotheses for the results of experiments previously carried out by scientists, physicists and scholars, but which marked the history of Physics and Chemistry and which gave rise to current concepts about gravity, the electromagnetic field and interactions between particles in Quantum Mechanics. The hypotheses focused on commutability in the relationship between mass and energy, the dynamics of Time, the relationship between Gravity and the Ultraviolet Catastrophe, the relationship between Gravity and Time, the relationship between Time and the Atomic Model of Orbitals and the relationship between Time and the Electromagnetic Field of magnets. The methodology combined a theoretical review of the experiments, considering the conditions under which the experiment was carried out and the results found, and reanalysis of the results based on the relationship between entropy and time, providing a conceptual basis for the unification between Quantum Mechanics and the Theory of Relativity, through the prism of the foundation found between Time and Entropy. The results aim not only to validate the proposed hypotheses, but also to advance the understanding of fundamental concepts in physics, offering support for the construction of a broader theoretical structure, essential for the formulation of a Theory of Everything.

PT symmetric fermionic particle oscillations in even dimensional representations

We describe a novel class of quantum mechanical particle oscillations in both relativistic and nonrelativistic systems based on PT symmetry and T2=−1 (relevant for fermions), where P is parity and T is time reversal. The Hamiltonians are chosen at the outset to be self-adjoint with respect to a PT inner product. The quantum mechanical time evolution is based on a modified CPT inner product constructed in terms of a suitable C operator. The resulting quantum mechanical evolution is shown to be unitary and probability is conserved by the oscillations. Published by the American Physical Society 2024

Ballistic Photons, Justification of their Structure and Movement Patterns

Aim: The work relates to the fundamentals of quantum physics and photonics, in particular to the formation of photons in two states: elementary particles and electromagnetic radiation, and the parameters of their structure and motion processes. The study of these problems is a relevant and important task, has not been fully studied. In general case, a photon is considered an elementary particle and wave, quantum of energy emitted by its electromagnetic field, which does not exist without moving at the speed of light. However, the presence of the material part of a photon is not always manifested, so a photon is considered a wave of electromagnetic radiation and the photon has no internal structure and dimensions, except for its wave parameters. The process of photon movement is also problematic. It is believed that it exists as a particle at the moment of its origin, and then it is only the movement of a wave, which, when meeting a target, again turns into an elementary particle. Moreover, ballistic photons is not, and their flight occurs by absorption and re-emission of waves by the environment. However, all these factors have contradictions, the elimination of which is the main goal of the work performed. Its scientific novelty is a new justification for the presence and parameters of a ballistic photon and the processes of its movement on the basis of reliable laws of physics. Methodology: The research methodology is based on the general principles of scientific knowledge, on the application of the laws of dialectics and reliable laws of physics. The author's method was also used – this access to the initial level of the material world, which is formed by physical fields and particles on the basis of natural physical constants: the speed of light c, Planck's constant h, gravitational constant G. New Results of the Work: The possibility of the existence of ballistic photons in the dual form of substance and electromagnetic waves is shown, within the framework of the general physical principles of the existence of elementary particles and the real principles of their movement in the material world. It was found that the disappearance of ballistic photons in flight after their birth and their appearance when meeting a target can be explained by their quantum structure and the process of their movement by quantum jumps based on the Heseisenberg uncertainty principle. Conclusions: The presence of the proposed quantum structure of the photon and the process of its movement is ensured by the absence of contradictions with the real laws of the material world that have a strict physical basis. For to confirm the reality of the existence of ballistic photons in the form of a real quantum mechanical particle, having the shape of a regular hexagon with a side of 1/ 6 of the wavelength λ of their radiation, as well as their movement in quantum jumps at 1/ 6 of the length of this wave, an experiment has been proposed. All laboratories with metrological equipment are invited to conduct the experiment.

Quantum mechanics of particles constrained to spiral curves with application to polyene chains

ContextDue to advances in synthesizing lower-dimensional materials, there is the challenge of finding the wave equation that effectively describes quantum particles moving on 1D and 2D domains. Jensen and Koppe and Da Costa independently introduced a confining potential formalism showing that the effective constrained dynamics is subjected to a scalar geometry-induced potential; for the confinement to a curve, the potential depends on the curve’s curvature function.MethodTo characterize the π\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varvec{\\pi }$$\\end{document} electrons in polyenes, we follow two approaches. First, we utilize a weakened Coulomb potential associated with a spiral curve. The solution to the Schrödinger equation with Dirichlet boundary conditions yields Bessel functions, and the spectrum is obtained analytically. We employ the particle-in-a-box model in the second approach, incorporating effective mass corrections. The π\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varvec{\\pi }$$\\end{document}-π∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varvec{\\pi ^{*}}$$\\end{document} transitions of polyenes were calculated in good experimental agreement with both approaches, although with different wave functions.

Quantum physics and artificial intelligence: current challenges and opportunities in technical diagnostics and condition monitoring

The current pace of scientific and technological development is unprecedented. Globalisation ensures that these changes are felt almost immediately everywhere. This also applies to areas of application that overlap endlessly. Consequently, it is of great importance to observe these changes and developments, identify challenges and threats, and to recognise the opportunities that arise from them. The paper attempts to analyse how the development of knowledge in physics and the pace of technological evolution, with its latest achievements, namely artificial intelligence and quantum computers, affect the validity of the approach and methods in technical diagnostics and condition monitoring. Furthermore, it identifies several challenges and opportunities arising from these changes and initiates a discussion on the confrontation of the current foundations and methods used in technical diagnostics with the fundamentals of elementary particle physics and quantum mechanics. Nevertheless, the principal objective of this paper is to prompt scientists and researchers engaged in the field of diagnostics and condition monitoring to observe the evolving environment and embrace the challenge of implementing novel foundations for describing physical reality in diagnostic methodologies. Let us commence the process of revisiting assumptions and discussing new problems, and take up the challenge of expanding our knowledge and experimental practices.

Interaction of a quantum particle with gravitational wave in modified gravity theory

We present the formal solution for a quantum mechanical particle responding to gravitational wave (GW) in the framework of modified theories of gravity (MTG) where, apart from the two standard tensorial modes of polarization of GW, we have considered an additional scalar mode. The presence of this longitudinal scalar mode makes it necessary to extend the usual two-dimensional description of matter-GW interaction to a three-dimensional one. Naturally this requires non-trivial changes in the quantum mechanical treatment which we elaborate in this paper.

Anharmonic effects on the squeezing of axion perturbations

It is assumed in standard cosmology that the Universe underwent a period of inflation in its earliest phase, providing the seeds for structure formation through vacuum fluctuations of the inflaton scalar field. These fluctuations get stretched by the quasi-exponential expansion of the Universe and become squeezed. The aim of this paper is to deepen the understanding of the squeezing process, considering the effect of self-interactions. Axion-like particles can provide a useful setup to study this effect. Specifically we focus on the consequences that a non-trivial evolution of the background axion field has on the squeezing of the perturbations. We follow the evolution of the axion's fluctuation modes from the horizon exit during inflation to the radiation-dominated epoch. We compute Bogoliubov coefficients and squeezing parameters, which are linked to the axion particle number and isocurvature perturbation. We find that the quantum mechanical particle production and the squeezing of the perturbations are enhanced, if one accounts for anharmonic effects, i.e., the effect of higher order terms in the potential. This effect becomes particularly strong towards the hilltop of the potential.

Open quantum systems with Kadanoff-Baym equations

We study the temporal evolution of quantum mechanical fermionic particles exhibiting one bound state within a one-dimensional attractive square-well potential in a heat bath of bosonic particles. For this open quantum system we formulate the non-equilibrium Kadanoff-Baym equations for the system particles by taking the interactions to be elastic 2-2 scatterings with the heat-bath particles. The corresponding spatially inhomogeneous integro-differential equations for the one-particle Greens's function are solved numerically. We demonstrate how the system particles equilibrate and thermalize with the heat bath and how the off-diagonal elements of the density matrix, expressed in the one-particle energy eigenbasis, decohere, so that only the diagonal entries, i.e. the occupation numbers, survive. In addition, the time evolution of the (retarded) Green's function also determines the spectral properties of the various one-particle quantum states.

Quantum Leap: A Price Leap Mechanism in Financial Markets

This study explores the quantum leapfrog mechanism within the context of quantum finance and presents a new interpretation of established financial models through a quantum perspective. In quantum physics, the well-documented phenomenon of particles tunneling through energy barriers has a parallel in finance. We propose a quantum financial leapfrog model in which asset prices make quantum leaps, penetrating market “energy barriers” in non-sequential advances. By leveraging the Hamiltonian operator and the Schrödinger equation, our approach simulates the dynamics of asset prices in a manner akin to the trajectories of particles in quantum mechanics. We draw an analogy between financial markets and gravitational fields, and from this we derive energy equations for pricing orbits. Using path integration techniques, we map out potential price transitions between these orbits, which are guided by the calculation of minimal energy barriers. Furthermore, we introduce a market “propagator” that aligns with the uncertainty principle, identifying the optimal price pathways. Our findings provide new insights and methodologies for navigating the complexities of financial markets, underscoring the significant potential of quantum approaches in the field of finance. These findings have theoretical implications for a variety of market stakeholders, offering strategic guidance and a reference point. We expect that the advancement of the quantum financial leapfrog theory will refine analytical methods and enhance investment strategies in practical financial applications.

Non-Fock ground states in the translation-invariant Nelson model revisited non-perturbatively

The Nelson model, describing a quantum mechanical particle linearly coupled to a bosonic field, exhibits the infrared problem in the sense that no ground state exists at arbitrary total momentum. However, passing to a non-Fock representation, one can prove the existence of so-called dressed one-particle states. In this article, we give a simple non-perturbative proof for the existence of such one-particle states at arbitrary coupling strength and for almost all total momenta in a physically motivated momentum region. Our results hold both for the non- and the semi-relativistic Nelson model.

BRST invariant formulation of the Bell-CHSH inequality in gauge field theories

A study of the Bell-CHSH inequality in gauge field theories is presented. By using the Kugo-Ojima analysis of the BRST charge cohomology in Fock space, the Bell-CHSH inequality is formulated in a manifestly BRST invariant way. The examples of the free four-dimensional Maxwell theory and the Abelian Higgs model are scrutinized. The inequality is probed by using BRST invariant squeezed states, allowing for large Bell-CHSH inequality violations, close to Tsirelson’s bound. An illustrative comparison with the entangled state of two 1/21/2 spin particles in Quantum Mechanics is provided.

Exhaustive search for optimal molecular geometries using imaginary-time evolution on a quantum computer

This study proposes a nonvariational scheme for geometry optimization of molecules for the first-quantized eigensolver, which is a recently proposed framework for quantum chemistry using probabilistic imaginary-time evolution (PITE). In this scheme, the nuclei in a molecule are treated as classical point charges while the electrons are treated as quantum mechanical particles. The electronic states and candidate geometries are encoded as a superposition of many-qubit states, for which a histogram created from repeated measurements gives the global minimum of the energy surface. We demonstrate that the circuit depth per step scales as {{{mathcal{O}}}}({n}_{{rm {e}}}^{2}{{{rm{poly}}}}(log {n}_{{rm {e}}})) for the electron number ne, which can be reduced to {{{mathcal{O}}}}({n}_{{rm {e}}}{{{rm{poly}}}}(log {n}_{{rm {e}}})) if extra {{{mathcal{O}}}}({n}_{{rm {e}}}log {n}_{{rm {e}}}) qubits are available. Moreover, resource estimation implies that the total computational time of our scheme starting from a good initial guess may exhibit overall quantum advantage in molecule size and candidate number. The proposed scheme is corroborated using numerical simulations. Additionally, a scheme adapted to variational calculations is examined that prioritizes saving circuit depths for noisy intermediate-scale quantum (NISQ) devices. A classical system composed only of charged particles is considered as a special case of the scheme. The new efficient scheme will assist in achieving scalability in practical quantum chemistry on quantum computers.

A Schrödinger Equation for Evolutionary Dynamics

We establish an analogy between the Fokker–Planck equation describing evolutionary landscape dynamics and the Schrödinger equation which characterizes quantum mechanical particles, showing that a population with multiple genetic traits evolves analogously to a wavefunction under a multi-dimensional energy potential in imaginary time. Furthermore, we discover within this analogy that the stationary population distribution on the landscape corresponds exactly to the ground-state wavefunction. This mathematical equivalence grants entry to a wide range of analytical tools developed by the quantum mechanics community, such as the Rayleigh–Ritz variational method and the Rayleigh–Schrödinger perturbation theory, allowing us not only the conduct of reasonable quantitative assessments but also exploration of fundamental biological inquiries. We demonstrate the effectiveness of these tools by estimating the population success on landscapes where precise answers are elusive, and unveiling the ecological consequences of stress-induced mutagenesis—a prevalent evolutionary mechanism in pathogenic and neoplastic systems. We show that, even in an unchanging environment, a sharp mutational burst resulting from stress can always be advantageous, while a gradual increase only enhances population size when the number of relevant evolving traits is limited. Our interdisciplinary approach offers novel insights, opening up new avenues for deeper understanding and predictive capability regarding the complex dynamics of evolving populations.

Feynman–Kac Formula and Asymptotic Behavior of the Minimal Energy for the Relativistic Nelson Model in Two Spatial Dimensions

We consider the renormalized relativistic Nelson model in two spatial dimensions for a finite number of spinless, relativistic quantum mechanical matter particles in interaction with a massive scalar quantized radiation field. We find a Feynman–Kac formula for the corresponding semigroup and discuss some implications such as ergodicity and weighted Lp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^p$$\\end{document} to Lq\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^q$$\\end{document} bounds, for external potentials that are Kato decomposable in the suitable relativistic sense. Furthermore, our analysis entails upper and lower bounds on the minimal energy for all values of the involved physical parameters when the Pauli principle for the matter particles is ignored. In the translation invariant case (no external potential), these bounds permit to compute the leading asymptotics of the minimal energy in the three regimes where the number of matter particles goes to infinity, the coupling constant for the matter–radiation interaction goes to infinity and the boson mass goes to zero.

Bare-bones multi-scale quantum harmonic oscillator algorithm for global optimization

The Multi-scale Quantum Harmonic Oscillator Algorithm (MQHOA) is a novel heuristic optimization technique, underpinned by the quantum wave function as its theoretical foundation. In this study, we present a streamlined MQHOA framework, dubbed the Bare-Bones Multi-scale Quantum Harmonic Oscillator Algorithm (BBMQHOA). This minimalist paradigm employs the most rudimentary free particle in quantum mechanics to simulate particle movement. BBMQHOA leverages group stability over individual stability, enabling the algorithm to fully capitalize on population data, thereby enhancing exploration and exploitation. An extensive array of experiments is carried out on a collection of 24 benchmark functions and a pair of real-world applications to validate the efficacy of our suggested methodology. The outcomes reveal that its performance is both practical and competitive while simultaneously maintaining user-friendliness.

Quantum-enhanced sensing on optical transitions through finite-range interactions.

The control over quantum states in atomic systems has led to the most precise optical atomic clocks so far1-3. Their sensitivity is bounded at present by the standard quantum limit, a fundamental floor set by quantum mechanics for uncorrelated particles, which can-nevertheless-be overcome when operated with entangled particles. Yet demonstrating a quantum advantage in real-world sensors is extremely challenging. Here we illustrate a pathway for harnessing large-scale entanglement in an optical transition using 1D chains of up to 51 ions with interactions that decay as a power-law function of the ion separation. We show that our sensor can emulate many features of the one-axis-twisting (OAT) model, an iconic, fully connected model known to generate scalable squeezing4 and Greenberger-Horne-Zeilinger-like states5-8. The collective nature of the state manifests itself in the preservation of the total transverse magnetization, the reduced growth of the structure factor, that is, spin-wave excitations (SWE), at finite momenta, the generation of spin squeezing comparable with OAT (a Wineland parameter9,10 of -3.9 ± 0.3 dB for only N = 12 ions) and the development of non-Gaussian states in the form of multi-headed cat states in the Q-distribution. We demonstrate the metrological utility of the states in a Ramsey-type interferometer, in which we reduce the measurement uncertainty by -3.2 ± 0.5 dB below the standard quantum limit for N = 51 ions.

Dynamical Coupling between Particle and Antiparticle in Relativistic Quantum Mechanics: A Multistate Perspective on the Energy–Momentum Relation

A molecular formalism based on a decomposed energy space constructed by a modular basis of matter and radiation is proposed for relativistic quantum mechanics. In the proposed formalism, matter radiation interactions are incorporated via the dynamical transformation of the coupled particle/antiparticle pair in a multistate quantum mechanical framework. This picture generalizes relativistic quantum mechanics at minimal cost, unlike quantum field theories, and the relativistic energy–momentum relation is interpreted as energy transformations among different modules through a multistate Schrödinger equation. The application of two-state and four-state systems using a time-dependent Schrödinger equation with pair states as a basis leads to well-defined solutions equivalent to those obtained from the Klein–Gordon equation and the Dirac equation. In addition, the particle–antiparticle relationship is well manifested through a particle conjugation group. This work provides new insights into the underlying molecular mechanism of relativistic dynamics and the rational design of new pathways for energy transformation.

Thermomagnetic properties and its effects on Fisher entropy with Schioberg plus Manning-Rosen potential (SPMRP) using Nikiforov-Uvarov functional analysis (NUFA) and supersymmetric quantum mechanics (SUSYQM) methods

Thermomagnetic properties, and its effects on Fisher information entropy with Schioberg plus Manning-Rosen potential are studied using NUFA and SUSYQM methods in the presence of the Greene-Aldrich approximation scheme to the centrifugal term. The wave function obtained was used to study Fisher information both in position and momentum spaces for different quantum states by the gamma function and digamma polynomials. The energy equation obtained in a closed form was used to deduce numerical energy spectra, partition function, and other thermomagnetic properties. The results show that with an application of AB and magnetic fields, the numerical energy eigenvalues for different magnetic quantum spins decrease as the quantum state increases and completely removes the degeneracy of the energy spectra. Also, the numerical computation of Fisher information satisfies Fisher information inequality products, indicating that the particles are more localized in the presence of external fields than in their absence, and the trend shows complete localization of quantum mechanical particles in all quantum states. Our potential reduces to Schioberg and Manning-Rosen potentials as special cases. Our potential reduces to Schioberg and Manning-Rosen potentials as special cases. The energy equations obtained from the NUFA and SUSYQM were the same, demonstrating a high level of mathematical precision.

The balance In the six dimensions of space-time description of quantum mechanics phenomena and nature of time

<p>This study presents a theory with a six-dimensional space-time structure, R^6, in order to describe quantum mechanic phenomena, the time arrow and quantum gravity. The interpretation of quantum world phenomena using four-dimensional space-time would be a very complicated and indescribable task. The dual wave-particle behavior, entanglement, quantum corridors, etc., represent the complex space-time structure. Previous studies indicate that complicated behaviors of particles in quantum mechanics are basically considered as the inherent behavior of those particles. The theoretical framework of the balance is the transformation of imaginary dimensions into geometric dimensions and the description of quantum mechanical phenomena using external Euclidean geometry. The six-dimensional space-time structure consists of three space and three time dimensions and the time arrow is the result of the impossibility of the existence of matter in six space-time dimensions, and the direction of the arrow is aligned with the expansion of the universe.</p>

A new approach to dominant motion pattern recognition at the macroscopic crowd level

Automatic analysis and the recognition and prediction of the behaviour of large-scale crowds in video-surveillance data is a research field of paramount importance for the security of modern societies. It serves to predict and help prevent disasters in public places where crowds of people gather. The paper proposes a novel method for generating meta-tracklets and recognition of dominant motion patterns as a basis for automatic crowd behaviour analysis at the macroscopic level, where a crowd is treated as an entity. The basic characteristic of macroscopic crowd scenes is that it is impossible to detect and track individuals in the scene. The idea of the method proposed in this paper is to recognize dominant crowd motion patterns, by avoiding time-consuming and error-sensitive crowd segmentation, crowd tracking and detection of regions of interest. Thus, the process of determining dominant motion patterns and recognizing crowd behaviour is accelerated. The method is inspired by a quantum mechanical approach. It combines a set of particles, which are considered as particles in quantum mechanics, tracklets of particles’ advection in a video clip, and the interaction of wave functions spread out from particle positions. A wave function is expressed in the form of an asymmetric potential function. Peaks of the wave field define the most probable particle flow, which defines a meta-tracklet. Dominant motion patterns are recognized by applying the functions of fuzzy predicates, which represent a combination of common-sense and human expert knowledge about crowd motions, to the meta-tracklets. The experimental results of the proposed method are presented for a subset of UCF dataset and AGORASET crowd simulation videos and have shown promising results in dominant motion pattern recognition.