Quantum Mechanical Point Of View Research Articles

Effects of nanocutting environments on the electronic structure of armchair-type graphene nanoribbons: the first-principles study

In order to investigate the effect of nanocutting environment on the electronic structure of armchair-type graphene nanoribbons, this paper adopts a first-principle computational approach to study the effect of different substrates and solutions, such as on the motion of electrons in the middle and outer orbitals of graphene nanoribbons, by observing the energy band structure, the value of the band gap, and the density of the split-wave states. The results show that the adsorption of Si and C atoms at the edge of the nanoribbon leads to a decrease in the band gap value. The adsorption of Al and O atoms at the edges of graphene nanoribbons leads to a decrease in the nanoribbon band gap value to 0 eV. Different substrate atoms mainly affect the p-orbital electron motion in the nanobelt. Bare-edge graphene nanoribbons are indirect bandgap structures, and graphene nanoribbons with H, O and OH atoms adsorbed at the edges of the nanoribbons are direct bandgap structures. Edge O-isation leads to a nanobelt band gap of 0, which exhibits metallic properties. The edge H-isation nanoribbon band gap is higher than the bare edge nanoribbon band gap. Nanoribbon edge OH-isation reduces the nanoribbon band gap value. Nanoribbon edge adsorption of atoms in solution affects p-orbital electron motion. The formation energy of five-ring defects and seven-ring defects is low, and the defects are easier to form. The edges containing defects all reduce the band gap values of graphene nanoribbons. The defects mainly affect the p-orbital electron motion, leading to differences in the band gap values. The bandgap decreases with increasing nanobelt width, and the bandgap value conforms to 3 N+2<3 N<3 N+1, with regular fluctuations in the curve with period 3. The larger the band gap, the smaller the curvature of the curve at the extremes, and the sparser the curve. In this paper, the electronic structures of different edge structures are analysed from a quantum mechanical point of view, and the synthesis of these results will provide theoretical guidance for obtaining high-quality semiconductor nanoribbons by mechanochemical nanocutting.

Moments of the Charge Distribution Observed through Electron Scattering in 3H and 3He

Abstract The moments of the charge distributions obtained by the sum-of-Gaussians (SOG) analysis of electron-scattering data are examined in $^3$H and $^3$He, together with those obtained by the Fourier–Bessel (FB) analysis. The SOG and FB methods reproduce well the experimental form factors available at present, but provide different charge distributions from each other. As a result, they do not yield the same values of the moments of the charge distribution, although their analyses are called “model-independent.” The moments are sensitive to the tail of the charge distribution. The present experimental data are not enough for SOG and FB analyses to determine with reasonable accuracy the shape of the tails, in a quantum mechanical point of view. New, accurate experimental data at small momentum transfer squared less than 0.1 fm$^{-2}$ are desired.

Quantum approach to bound states in field theory

It is well known that (possibly nonunique) suitable field dynamics can be prescribed in spacetimes with timelike boundaries by means of appropriate boundary conditions. In [R. M. Wald, ], Wald derived a conserved energy functional for each prescribed dynamics. This conserved energy is related to the positive self-adjoint extensions of the spatial part A of the wave equation ∂2Φ/∂t2=−AΦ (A may not be, in principle, essentially self-adjoint). This is quite surprising since the canonical energy is not conserved in these cases. In this paper, we rederive this energy functional from an action principle (with appropriate boundary terms) following [A. A. Saharian, ] and consider field dynamics arising from nonpositive self-adjoint extensions of A. The spectrum of the resulting theory fails to be positive and unstable mode solutions for classical fields come to light. By studying fields in half-Minkowski spacetime, we illustrate that these unstable classical solutions come as a consequence of an inverted parabolic potential governing their dynamics. From the quantum mechanical point of view, this leads to an effective inverted harmonic oscillator at the boundary. We then explore these unstable modes behavior, as well as their instabilities, at the quantum level. Published by the American Physical Society 2024

Entanglement in a complex plasma

Quantum mechanical approach is extended to the interaction of dust particles in a complex plasma. Massive and highly charged dust particles interact each other through the exchange of quasi-particles (virtual waves) in a quantum mechanical viewpoint. The interaction is described by the Hamiltonian, which describes the two-particle system as uncoupled harmonic oscillators. When the pair of dust particles are embedded in the injected plasma wave, the Hamiltonian is found to show the presence of coupled harmonic oscillator indicating the emergence of the entanglement in semiclassical nature. The entanglement of a pair of dust particles is encapsulated in the Hamiltonian, which is formulated by the method of second quantization. The frequency of the wave to trigger the emergence of the entanglement is found to be one-half of the dust plasma frequency. The interaction between a pair of dust particles is formulated as a scattering process and is described by the transition probability. Measure of the semiclassical entanglement is shown by the entropy, and the resulting entropy is found to increase with time.

Quantum mechanical approach to plasma waves with helical wavefront

Plasma waves with helical wavefront are studied theoretically from the quantum mechanical viewpoint and are shown to produce a spinning motion of a charged macroparticle in a complex plasma. The electrostatic helical perturbations are described by the wave function for a Laguerre–Gaussian beam mode with the radial/angular mode numbers n/l. The interaction and the transfer of angular momentum from the wave to a particle are analyzed by the method of second quantization with the help of the Feynman diagram. Laguerre function, instead of the Born approximation, is introduced to describe plasma waves with helical wavefront. A pair of dust particles in a complex plasma exchange a quasiparticle (virtual plasmon) resulting in the acquisition of angular momentum, which makes a dust particle spin in motion with rotational frequency Ωϕ. The resonance condition ω−kvz−lΩϕ=0 and the conservation of angular momentum IdΩϕ=lℏ determine the rotational frequency, where ω and k are frequency and axial wave number of the helical wave, and vz and Id are axial velocity and the moment of inertia of a dust particle.

Electronic strengthening mechanism of covalent Si via excess electron/hole doping

Brittle fracture of a covalent material is ultimately governed by the strength of the electronic bonds. Recently, attempts have been made to alter the mechanical properties including fracture strength by excess electron/hole doping. However, the underlying mechanics/mechanism of how these doped electrons/holes interact with the bond and changes its strength is yet to be revealed. Here, we perform first-principles density-functional theory calculations to clarify the effect of excess electrons/holes on the bonding strength of covalent Si. We demonstrate that the bond strength of Si decreases or increases monotonically in correspondence with the doping concentration. Surprisingly, change to the extent of 30–40% at the maximum feasible doping concentration could be observed. Furthermore, we demonstrated that the change in the covalent bond strength is determined by the bonding/antibonding state of the doped excess electrons/holes. In summary, this work explains the electronic strengthening mechanism of covalent Si from a quantum mechanical point of view and provides valuable insights into the electronic-level design of strength in covalent materials.

IARD 2022 The 13th Biennial Conference on Classical and Quantum Relativistic Dynamics of Particles and Fields

Preface The International Association for Relativistic Dynamics was organized in February 1998 in Houston, Texas, with John R. Fanchi as president. Although the subject of relativistic dynamics has been explored, from both classical and quantum mechanical points of view, since the work of Einstein and Dirac, its most striking development has been in the framework of quantum field theory. The very accurate calculations of spectral and scattering properties, for example, of the anomalous magnetic moment of the electron and the Lamb shift in quantum electrodynamics, and many qualitative features of the strong and electroweak interactions, demonstrate the very great power of description achieved in this framework. Yet, many fundamental questions remain to be clarified, such as the structure of classical relativistic dynamical theories on the level of Hamilton and Lagrange in Minkowski space as well as on the curved manifolds of general relativity. There, moreover, remain the important questions of the covariant classical description of systems at high energy for which particle production effects are not large, such as discussed in Synge’s book, The Relativistic Gas, and in Balescu’s book on relativistic statistical mechanics, and the development of a consistent single and many body relativistic quantum theory. In recent years, highly accurate telescopes and advanced facilities for computation have brought a high level of interest in cosmological problems, such as the structure of galaxies (dark matter) and the apparently anomalous expansion of the universe (dark energy). Some of the papers reported here deal with these problems, as well as other fundamental related issues.It was for this purpose, to bring together researchers from a wide variety of fields, such as particle physics, astrophysics, cosmology, foundations of relativity theory, and mathematical physics, with a common interest in relativistic dynamics, to investigate fundamental questions of this type, that this Association was founded. The second meeting took place in 2000 at Bar Ilan University in Israel, the third, in 2002, at Howard University in Washington, D.C., and the fourth, in 2004, in Saas Fee, Switzerland. Subsequent meeting took place in 2006 at the University of Connecticut Storrs, in 2008 at Aristotle University of Thessalonica, in 2010 at National Dong Hwa University, Hualien, Taiwan, in 2012 at the Galileo Galilei Institute for Theoretical Physics (GGI) in Florence, in 2014 as the University of Connecticut Storrs, Connecticut, in 2016 at Jožef Stefan Institute in Ljubljana, Slovenia, and in 2018 in Mérida, Yucatán, Mexico, under the sponsorship of the Instituto Politécnic Nacional. The 2020 meeting, planned for Czech Technical University in Prague, was successfully held online at the height of the Covid-19 pandemic, and the physical meeting in Prague was delayed to 2022.The 2022 meeting forms the basis for the Proceedings that are recorded in this issue of the Journal of Physics: Conference Series. Along with the work of some of the founding and newer but already much engaged members of the Association, we were fortunate to have lecturers from application areas that provided strong challenges for further developments in quantum field theory, cosmological problems, and in the dynamics of systems subject to accelerations and the effects of general relativity. Topics treated in this issue include studies in general relativity and astrophysics, relativistic dynamics and electrodynamics, quantum theory and particles, and foundations of relativistic dynamics.This first physical meeting of the Covid-19 era took place 6 - 9 June at Czech Technical University in Prague, as originally planned for 2020. The meeting was divided into seven plenary sessions over four days. As a result of continued travel restrictions in some areas, a small number of talks were delivered by videoconferencing. The papers presented in this volume represent extensions and refinements to the conference talks, building on feedback and discussions associated with the lectures. We once again express our gratitude to Czech Technical University, and especially the local conference chair Petr Jizba, for their generous hospitality.List of Scientific Advisory Committee, International Organizing Committee and Editorial Board of the proceedings, Dedication are available in this Pdf.

The Yukawa interaction in ordinary quantum mechanics

The Yukawa interaction is considered in 0 + 1 dimensions as a pedagogical example to illustrate quantum field theory methods. From the quantum mechanical point of view the system is trivially exactly solvable, but this can be difficult to see from the path integral perspective. It is shown how despite initial appearances the perturbation series in terms of Feynman diagrams is consistent with the quantum mechanical picture for finite temperature.

Non-adiabatic quantum dynamics of tribovoltaic effects at sliding metal–semiconductor interfaces

Recent experiments observe electric current generation at sliding metal–semiconductor interfaces. Here, we present a detailed theoretical study on how electric voltage is generated at such a sliding interface. Our study is based on a two-band Anderson–Holstein model, where we solve the coupled electron–phonon dynamics using a surface hopping method. We show that the high local temperature induced by mechanical motion at the interfaces can lead to electron–hole pair generation through electron–phonon couplings. We quantify the efficiency of electron–hole generation as well as electric voltage as a function of local temperatures and semiconductor bandgaps. We find that increasing the local temperatures can lead to higher electron–hole generation and electric voltage. Furthermore, we find that there is a turnover for the electric voltage as a function of the bandgap. Such an observation is in agreement with the experimental results. Our study offers a theoretical framework to understand tribovoltaic effects from a quantum mechanical point of view, and our approach can be used to quantitatively simulate realistic sliding metal–semiconductor junctions.

NCI: looking at solute/solvent interactions

Understanding solvation interactions is a key problem for many industrial fields: from pharmaceutical to material sciences. From a quantum mechanical viewpoint, two main difficulties arise: firstly, solvation takes place through weak interactions (hydrogen bonds, van der Waals interactions), which are inherently difficult to describe. Secondly, solvation properties are dynamic in nature, which means a proper statistical averaging is required to reproduce experimental properties. In this contribution, we dwell on the analysis of solute–solvent interactions by means of the averaged-NCI index, derived from an MD averaged picture of the electron density in the system. Firstly, we show how the approach enables to distinguish static vs labile and strong vs weak hydrogen bonds. Then, by means of this approach we are able to characterize the fact that the strength of hydrogen bonds with water solvent remains similar upon branching for aliphatic alcohols. On the contrary large differences have been observed between aliphatic alcohols and phenol derivatives. This statistical analysis of interactions is expected to be useful in the derivation of microscopic parameters for solute/solvent interactions.

Preface

IARD 2020The 12th Biennial Conference on Classical and Quantum Relativistic Dynamics of Particles and FieldsThe International Association for Relativistic Dynamics was organized in February 1998 in Houston, Texas, with John R. Fanchi as president. Although the subject of relativistic dynamics has been explored, from both classical and quantum mechanical points of view, since the work of Einstein and Dirac, its most striking development has been in the framework of quantum field theory. The very accurate calculations of spectral and scattering properties, for example, of the anomalous magnetic moment of the electron and the Lamb shift in quantum electrodynamics, and many qualitative features of the strong and electroweak interactions, demonstrate the very great power of description achieved in this framework. Yet, many fundamental questions remain to be clarified, such as the structure of classical relativistic dynamical theories on the level of Hamilton and Lagrange in Minkowski space as well as on the curved manifolds of general relativity. There, moreover, remain the important questions of the covariant classical description of systems at high energy for which particle production effects are not large, such as discussed in Synge’s book, The Relativistic Gas, and in Balescu’s book on relativistic statistical mechanics, and the development of a consistent single and many body relativistic quantum theory. In recent years, the very high accuracy of telescopes and advanced facilities for computation have brought a high level of interest in cosmological problems such as the structure of galaxies (dark matter) and the apparently anomalous expansion of the universe (dark energy). Some of the papers reported here deal with these problems, as well as other fundamental related issues.It was for this purpose, to bring together researchers from a wide variety of fields, such as particle physics, astrophysics, cosmology, foundations of relativity theory, and mathematical physics, with a common interest in relativistic dynamics, to investigate fundamental questions of this type, that this Association was founded. The second meeting took place in 2000 at Bar Ilan University in Israel, the third, in 2002, at Howard University in Washington, D.C., and the fourth, in 2004, in Saas Fee, Switzerland. Subsequent meeting took place in 2006 at the University of Connecticut Storrs, in 2008 at Aristotle University of Thessalonica, in 2010 at National Dong Hwa University, Hualien, Taiwan, in 2012 at the Galileo Galilei Institute for Theoretical Physics (GGI) in Florence, in 2014 as the University of Connecticut Storrs, Connecticut, in 2016 at Jožef Stefan Institute in Ljubljana, Slovenia, and in 2018 in Mérida, Yucatán, Mexico, under the sponsorship of the Instituto Politécnic Nacional.The 2020 meeting forms the basis for the Proceedings that are recorded in this issue of the Journal of Physics: Conference Series. Along with the work of some of the founding and newer but already much engaged members of the Association, we were fortunate to have lecturers from application areas that provided strong challenges for further developments in quantum field theory, cosmological problems, and in the dynamics of systems subject to accelerations and the effects of general relativity. Topics treated in this issue include studies in general relativity and astrophysics, relativistic dynamics and electrodynamics, quantum theory and particles, and foundations of relativistic dynamics.List of Scientific Advisory Committee, International Organizing Committee and Editorial Board of the proceedings and Editors Dedication are available in this pdf.

Dynamical Invariant and Exact Mechanical Analyses for the Caldirola-Kanai Model of Dissipative Three Coupled Oscillators.

We study the dynamical invariant for dissipative three coupled oscillators mainly from the quantum mechanical point of view. It is known that there are many advantages of the invariant quantity in elucidating mechanical properties of the system. We use such a property of the invariant operator in quantizing the system in this work. To this end, we first transform the invariant operator to a simple one by using a unitary operator in order that we can easily manage it. The invariant operator is further simplified through its diagonalization via three-dimensional rotations parameterized by three Euler angles. The coupling terms in the quantum invariant are eventually eliminated thanks to such a diagonalization. As a consequence, transformed quantum invariant is represented in terms of three independent simple harmonic oscillators which have unit masses. Starting from the wave functions in the transformed system, we have derived the full wave functions in the original system with the help of the unitary operators.

Future directions on low-energy radiation dosimetry

For more than one century, low-energy (< 100 keV) photons (x-rays and gamma) have been widely used in different areas including biomedical research and medical applications such as mammography, fluoroscopy, general radiography, computed tomography, and brachytherapy treatment, amongst others. It has been demonstrated that most of the electrons produced by low photon energy beams have energies below 10 keV. However, the physical processes by which these low energy electrons interact with matter are not yet well understood. Besides, it is generally assumed that all the energy deposited within a dosimeter sensitive volume is transformed into a response. But such an assumption could be incorrect since part of the energy deposited might be used to create defects or damages at the molecular and atomic level. Consequently, the relationship between absorbed dose and dosimeter response can be mistaken. During the last few years, efforts have been made to identify models that allow to understand these interaction processes from a quantum mechanical point of view. Some approaches are based on electron-beam − solid-state-interaction models to calculate electron scattering cross-sections while others consider the density functional theory method to localize low energy electrons and evaluate the energy loss due to the creations of defects and damages in matter. The results obtained so far could be considered as a starting point. This paper presents some methodologies based on fundamental quantum mechanics which can be considered useful for dealing with low-energy interactions.

The Weyl – Wigner – Moyal Formalism on a Discrete Phase Space. II. The Photon Wigner Function

AbstractClassical model of light in helicity formalism is presented. Then quantum mechanical point of view at photons – construction and interpretation of two equivalent photon wave functions are proposed. Quantum mechanics of photon is investigated. The Białynicki – Birula scalar product and the generalized Hermitian conjugation of linear operator are discussed. Quantum description of light on a phase space based on the Weyl – Wigner – Moyal approach is developed. A photon Wigner function is built. Some explicit photon Wigner functions for different kernels are obtained.

A Quantitative Explanation of the Dynamics Underlying the Franck–Condon Principle: A Mostly Classical Viewpoint

The Franck–Condon Principle (FCP), the key concept for describing vibronic spectra, results from the large disparity between the time scales of electrons and nuclei in molecules. Yet in an undergraduate lecture, the FCP is nearly always rationalized from a time independent quantum mechanical viewpoint, due to students’ lack of knowledge of time dependent quantum theory. Here we present a quantitative way to describe the essence of the FCP from a mostly classical, time dependent approach. On the short time scales relevant to the FCP, the phase space centers of time evolving wavepackets follow their classical counterparts; thus, it is not unreasonable to describe the FCP using classical/semiclassical mechanics. In this work, we show how the dynamical interplay between the FCP and the Born–Oppenheimer approximation (BOA) leads to the observed vibronic spectrum of a molecule. A student who has learned about quantum operators and harmonic oscillators, and the BOA, can understand nearly all the theory presented herein. We provide, as a supplement, an Excel Workbook and set of Suggested Exercises. These Exercises, along with the Workbook, can be used to lead a student through nearly all the equations presented in this paper, and can thus augment the typical Quantum Chemistry undergraduate vibronic spectroscopy laboratory experiment or be used as an assignment in an undergraduate course in Quantum Chemistry.

The 11th Biennial Conference on Classical and Quantum Relativistic Dynamics of Particles and Fields

PrefaceThe International Association for Relativistic Dynamics was organized in February 1998 in Houston, Texas, with John R. Fanchi as president.Although the subject of relativistic dynamics has been explored, from both classical and quantum mechanical points of view, since the work of Einstein and Dirac, its most striking development has been in the framework of quantum field theory. The very accurate calculations of spectral and scattering properties, for example, of the anomalous magnetic moment of the electron and the Lamb shift in quantum electrodynamics, and many qualitative features of the strong and electroweak interactions, demonstrate the very great power of description achieved in this framework. Yet, many fundamental questions remain to be clarified, such as the structure of classical relativistic dynamical theories on the level of Hamilton and Lagrange in Minkowski space as well as on the curved manifolds of general relativity. There, moreover, remained the important questions of the covariant classical description of systems at high energy for which particle production effects are not large, such as discussed in Synge’s book, The Relativistic Gas, and in Balescu’s book on relativistic statistical mechanics, and the development of a consistent single and many body relativistic quantum theory.In recent years, the very high accuracy of telescopes and advanced facilities for computation have brought a high level of interest in cosmological problems such as the structure of galaxies (dark matter) and the apparently anomalous expansion of the universe (dark energy). Some of the papers reported here deal with these problems, as well as other fundamental related issues.

The Einstein-Podolsky-Rosen paradox and SU(2) relativity

The EPR paradox dates back to 1935 when Einstein et al., through the use of non commuting operators, proposed that quantum mechanics was not complete[1] in that it suggested a “spooky action at a distance.” Later in 1964 John Bell was able to express the dilemma in a simple inequality[2] involving spin singlet states. If the inequality were satisfied then Einstein was correct and if it were violated then it favored the quantum mechanics point of view. In what follows, we present two approaches to Bell’s inequality, and then offer an interpretation from the viewpoint of quantum mechanics based on the principle that the whole is more than the sum of its parts. This is then combined with the properties of the SU(2) group to give a more intuitive understanding of non-locality and spin entanglement from the perspective of the relativistic characteristics of rotations.

Interdisciplinary Approach to Combine Science and Art: Understanding of the Paintings of René Magritte from the Viewpoint of Quantum Mechanics

In the twentieth century, science and art had a grand paradigmatic shift each other. This study aims at comparing the epistemologies of surrealism and quantum mechanics that emerged in the 1930s and interpreting the paintings from a physical viewpoint, with a focus on the Copenhagen interpretation. In terms of epistemologies, the arbitrary relationship between an object and an image advocated by Magritte may correspond to the indeterminacy between physical entities and measurement. This study analysed the paintings of Magritte from the point of view of the features of the Copenhagen interpretation categories of wave–particle duality, indeterminacy, probabilistic interpretation and quantum hypothesis. Based on such discussions, this study gives some implications for enhancing creativity through an interdisciplinary approach.

State-to-state dynamics of the Cl(2P) + C2H6(ν5, ν1 = 0, 1) → HCl(v′, j′) + C2H5 hydrogen abstraction reactions

Using quasi-classical trajectory calculations on a recently developed full-dimensional potential energy surface, the effects of ethane reactant vibrational excitation, ν5 = 1, on the dynamics of the title reaction were analyzed. By analyzing the classical results from a quantum-mechanical point of view, we performed state-to-state calculations to show the influence of vibrational excitation on the vibrational populations of the two coproducts, as well as rotational distributions of the diatomic HCl(v′, j′) product. We found that excitation of the C2H6(ν5 = 1) mode by one quantum increases reactivity by 9% with respect to the ground-state reaction, where the ethyl radical coproduct receives an important internal energy, ~ 30% of the available energy, There are many populated vibrational states in the ethyl radical, although the population in each is very low, 1–5%. In fact, the most populated vibrational state, C2H5 ground state, presents a population of only ~ 10%. The HCl(v′ = 0, 1) product shows non-inverted vibrational populations, 88:12%, with relatively hot rotational distributions, and where the HCl(v′ = 1) product is forward-scattered. These theoretical results qualitatively reproduce the only experimental study by Zare et al., 20 years ago, taking into account that the authors themselves recognized that their results were not quantitative. In addition, we analyze two related issues: mode specificity and translational versus vibrational efficiency to promote reactivity, which have not been experimentally studied. We found that independent excitation of the ethane C–H stretching ν5 and ν1 modes, which differ by only 15 cm−1, shows similar dynamics behavior, which discards mode specificity. Finally, vibrational energy promotes reactivity only slightly more effectively than an equal amount of energy as translation. This result was rationalized by the sudden vector projection model for this “central” barrier reaction, to which Polanyi’s rules cannot be applied.

Spectral and quantum mechanical study of some azo-derivatives

Three azo-derivatives: 2, 2′-Dihydroxyazobenzene (DHAB), Sudan Orange G (SOG) and 4-(Phenylazo) diphenylamine (PDA) were studied in this paper from quantum-mechanical and spectral point of view. The nature and the contribution of the intermolecular interactions to the spectral shifts in the solutions of the studied azo-derivatives were established based on the existent theories. Some electro-optical parameters of the studied molecules were calculated with Spartan 14 software using Density Functional Theory (DFT) employing the B3LYP model and the standard 6-31G* basis set. The polarizability and dipole moment in the excited states were estimated considering the variation of the angle between dipole moments in electronic states giving the visible absorption band.