Basis Of Quantum Mechanics Research Articles

The Quantum Phenomena in Computational Model of Neuro-Cognition States: An Analytical Approach

The modeling of neurobiologic brain functions such as, cognition and consciousness are important research challenges having applications to other disciplines such as, bio-inspired soft computing and, adaptive distributed computing systems. The functions of brain and distributed computing structures have resemblances. This paper proposes a computational model of cognitive function and consciousness by using algebraic methods. Furthermore, the quantum mechanical basis of the cognitive model is formulated by using linear Hermitian. A set of choice functions is computed following the neurodynamics. The neuronal excitation is modeled by using trigonometric wave functions closely matching the neuronal firing. This paper illustrates an analytical approach to model neuronal excitation and, associated cognitive functions having quantum mechanical behaviour.

Torsional buckling analysis of chiral multi-walled carbon nanotubes based on an accurate molecular mechanics model

This study is concerned with the torsional buckling behavior of chiral multi-walled carbon nanotubes (MWCNTs) based on a molecular mechanics model. An analytical solution is carried out to calculate the elastic critical buckling shear strain of MWCNTs with different types of chirality. To determine the force constants used in the molecular mechanics model, on the basis of quantum mechanics, density functional theory is employed. Through comparison of the results obtained from the present molecular mechanics model and ones from available molecular dynamics simulations, the validity of the present approach is assessed. The influence of chirality on the critical buckling shear strain of nanotubes is then investigated. It is indicated that nanotubes with (n, n/2) chirality buckle at lower values of critical buckling shear strain compared with zigzag and armchair nanotubes.

A relativistically interacting exactly solvable multi-time model for two massless Dirac particles in 1 + 1 dimensions

The question how to Lorentz transform an N-particle wave function naturally leads to the concept of a so-called multi-time wave function, i.e., a map from (space-time)N to a spin space. This concept was originally proposed by Dirac as the basis of relativistic quantum mechanics. In such a view, interaction potentials are mathematically inconsistent. This fact motivates the search for new mechanisms for relativistic interactions. In this paper, we explore the idea that relativistic interaction can be described by boundary conditions on the set of coincidence points of two particles in space-time. This extends ideas from zero-range physics to a relativistic setting. We illustrate the idea at the simplest model which still possesses essential physical properties like Lorentz invariance and a positive definite density: two-time equations for massless Dirac particles in 1 + 1 dimensions. In order to deal with a spatio-temporally non-trivial domain, a necessity in the multi-time picture, we develop a new method to prove existence and uniqueness of classical solutions: a generalized version of the method of characteristics. Both mathematical and physical considerations are combined to precisely formulate and answer the questions of probability conservation, Lorentz invariance, interaction, and antisymmetry.

Analysis of Security of Quantum Key Distribution Based on Entangled Photon Pairs by Model Checking

Quantum key distribution is a technique to securely distribute a bit string between two parties by using the laws of quantum mechanics. The security of this technique depends on the basis of quantum mechanics rather than the difficulty of the mathematical calculation as in the classical encoding. Researches in this field have shown that the quantum key distribution will be fully functioning outside the laboratory in a few years. Due to the complexity and the high efficiency of the device, the verification is needed. In this article, we use PRISM to verify the security of the quantum key distribution protocol, which uses the entangled photon based on BB84 protocol.

Explicit polarization: a quantum mechanical framework for developing next generation force fields.

ConspectusMolecular mechanical force fields have been successfully used to model condensed-phase and biological systems for a half century. By means of careful parametrization, such classical force fields can be used to provide useful interpretations of experimental findings and predictions of certain properties. Yet, there is a need to further improve computational accuracy for the quantitative prediction of biomolecular interactions and to model properties that depend on the wave functions and not just the energy terms. A new strategy called explicit polarization (X-Pol) has been developed to construct the potential energy surface and wave functions for macromolecular and liquid-phase simulations on the basis of quantum mechanics rather than only using quantum mechanical results to fit analytic force fields. In this spirit, this approach is called a quantum mechanical force field (QMFF).X-Pol is a general fragment method for electronic structure calculations based on the partition of a condensed-phase or macromolecular system into subsystems (“fragments”) to achieve computational efficiency. Here, intrafragment energy and the mutual electronic polarization of interfragment interactions are treated explicitly using quantum mechanics. X-Pol can be used as a general, multilevel electronic structure model for macromolecular systems, and it can also serve as a new-generation force field. As a quantum chemical model, a variational many-body (VMB) expansion approach is used to systematically improve interfragment interactions, including exchange repulsion, charge delocalization, dispersion, and other correlation energies. As a quantum mechanical force field, these energy terms are approximated by empirical functions in the spirit of conventional molecular mechanics. This Account first reviews the formulation of X-Pol, in the full variationally correct version, in the faster embedded version, and with systematic many-body improvements. We discuss illustrative examples involving water clusters (which show the power of two-body corrections), ethylmethylimidazolium acetate ionic liquids (which reveal that the amount of charge transfer between anion and cation is much smaller than what has been assumed in some classical simulations), and a solvated protein in aqueous solution (which shows that the average charge distribution of carbonyl groups along the polypeptide chain depends strongly on their position in the sequence, whereas they are fixed in most classical force fields). The development of QMFFs also offers an opportunity to extend the accuracy of biochemical simulations to areas where classical force fields are often insufficient, especially in the areas of spectroscopy, reactivity, and enzyme catalysis.

A dynamical time operator in Dirac's relativistic quantum mechanics

A self-adjoint dynamical time operator is introduced in Dirac's relativistic formulation of quantum mechanics and shown to satisfy a commutation relation with the Hamiltonian analogous to that of the position and momentum operators. The ensuing time-energy uncertainty relation involves the uncertainty in the instant of time when the wave packet passes a particular spatial position and the energy uncertainty associated with the wave packet at the same time, as envisaged originally by Bohr. The instantaneous rate of change of the position expectation value with respect to the simultaneous expectation value of the dynamical time operator is shown to be the phase velocity, in agreement with de Broglie's hypothesis of a particle associated wave whose phase velocity is larger than c. Thus, these two elements of the original basis and interpretation of quantum mechanics are integrated into its formal mathematical structure. Pauli's objection is shown to be resolved or circumvented. Possible relevance to current developments in electron channeling, in interference in time, in Zitterbewegung-like effects in spintronics, graphene and superconducting systems and in cosmology is noted.

The Concept of Quantum Mechanics and A Reading of Thomas Pynchon's Gravity's Rainbow

Jo, Il-Jae & Kim, Sangkoo. “The Concept of Quantum Mechanics and A Reading of Thomas Pynchons Gravitys Rainbow.” The Journal of Modern British & American Language & Literature. 32.1 (2014): 163-186. This article is intended to examine the interactive relationship, and interdisciplinarity between literature and science. It gives a hermeneutic explanation and analytical interpretation of how Thomas Pynchons novel Gravitys Rainbow is connected with quantum mechanics and how it is represented, based on variable in modern science. Thus major character Slothrop and other characters related to him are analyzed for their mysterious, difficult actions in connection with principles and characteristics of quantum mechanics. The hidden variable theory contains field concept, relativity theory, quantum mechanics, and etc. Gravitys Rainbow shows various scientific theories and discourses, and postmodern societys traits and falls to the fiction in the quantum universe. Many characters, images and motifs in this novel are interconnected and they are not separated from the whole, but placed as a individual whole in the world. The parallel between literature and science is provided on the basis of quantum mechanics. (Pusan National University)

Quantum Mechanical Basis for Kinetic Diameters of Small Gaseous Molecules

Kinetic diameters are often invoked in discussing gas adsorption and permeation in porous and polymeric materials. However, how these empirical kinetic diameters relate to the size and shape of the molecules as manifested by their "electron cloud" is unclear. In this paper, we obtain the quantum mechanical (QM) diameters of several common gaseous molecules by determining the cross-sectional sizes of their iso-electronic density surfaces at a predetermined small value. We show that the QM diameters are in good agreement with the kinetic diameters. For example, the trends for important gas pairs such as O2 versus N2 and CO2 versus N2 are consistent between the QM diameters and the most often quoted kinetic diameters. Hence, our work now provides a quantum mechanical basis for the empirical kinetic diameters and will be useful for designing separation media for small gaseous molecules according to their sizes.

Using Extended Hückel Theory as a Platform To Introduce Jahn–Teller Distortion: The Spontaneous Distortion of 1,3,5,7-Cyclooctatetraene from a Perfect Octagon

Herein, a slightly enhanced version of extended Huckel molecular orbital theory is applied to demonstrate the spontaneous distortion of 1,3,5,7-cyclooctatetraene from a perfect octagon, a consequence of the Jahn-Teller effect. The exercise is accessible to students who have been introduced to basic quantum mechanics and extended Huckel molecular orbital theory and is easily implemented with widely available algebraic manipulation software such as Maple or Mathematica. This exercise is suitable for inclusion in the physical chemistry curriculum at the upper-level undergraduate or introductory graduate level.

A toy model of a macroscopic quantum coherent system

This paper deals with macroscopic quantum coherence while using only basic quantum mechanics. A square double well is used to illustrate Leggett–Caldeira oscillations. The effect of thermal radiation on two-level systems is discussed. The concept of decoherence is introduced at an elementary level. Reference values are deduced for the energy, temperature and time scales involved in macroscopic quantum coherence.

Quantum mechanics and the second law of thermodynamics: an insight gleaned from magnetic hysteresis in the first order phase transition of an isolated mesoscopic-size type I superconductor

J Bardeen proposed that the adiabatic phase transition of mesoscopic-size type I superconductors must be accompanied by magnetic hysteresis in the critical magnetic field of sufficient magnitude to satisfy the second law of thermodynamics, herein referred to as ‘Bardeen Hysteresis’. Bardeen Hysteresis remains speculative in that it has not been reported in the literature. This paper investigates Bardeen Hysteresis as a possible accompaniment to the adiabatic phase transition of isolated mesoscopic-size type I superconductors and its implications with respect to the second law of thermodynamics. A causal mechanism for Bardeen Hysteresis is discussed which contrasts with the long accepted causal mechanism of magnetic hysteresis, as first summarized by Pippard, herein referred to as ‘Pippard Hysteresis’. The paper offers guidance for an experimental verification and comments on how the existence of Bardeen Hysteresis has relation to a quantum mechanical basis for the second law of thermodynamics.

Basic Quantum Algorithms and Applications

Quantum computation, the ultimate goal of future computing, is an interesting field for researchers. The concept of quantum computation is based on basics of quantum mechanics. A quantum computer is a device for computation that makes direct use of quantum mechanical phenomena such as superposition and entanglement, to perform operations on data. The basic principle behind quantum computation is that quantum properties can be used to represent data and perform operations on these data. A quantum computer operates by manipulating the qubits with a fixed sequence of quantum logic gates. The sequence of gates to be applied is called a quantum algorithm. The field of quantum computation algorithm is fast moving and the scope is vast. Major quantum algorithms are summarized in this paper along with their applications. General Terms Quantum Algorithms.

Cumulative quantum mechanics (CQM) Part II. Application of cumulative quantum mechanics in describing the Vysikaylo polarization quantum-size effects

The processes of physical doping of nanostructured (meta-) materials have been investigated. Two types of interference and diffraction (in the center) in hollow quantum resonators for the de Broglie waves of electrons and two types of the Vysikaylo quantum-size effects due to the polarization capture of electrons in the cavity of quantum resonators are described on the basis of the cumulative quantum mechanics (CQM) formulated by the author. The first type of interference and, accordingly, diffraction in the resonator center corresponds to de Broglie-Fresnel interference (sin-wave with a node in the resonator center). This type is used to describe the localization (cumulation) of electrons in the atom quantum resonator with an atomic nucleus in the center. The second type of interference and, accordingly, diffraction is called Vysikaylo-de Broglie-Fraunhofer interference (diffraction with the antinode of the electron de Broglie wave in the center of a hollow resonator), wherein the Ψ n -functions of the electron infinitely cumulate (are focused by a polarization “mirror”) towards the center of a hollow quantum spherically or cylindrically symmetric resonator (Ψ n (r) ∼ cos(k n r)/r k ). It is shown that the cos-solutions, irregular in the resonator center, are regularized for any wave phenomena by the geometric coefficient. It is proved in the framework of CQM that, alongside with the classical energy spectrum for asymmetric Ψ n -functions (sin waves (overtones)) with E n ∼ n 2, for hollow quantum resonators, there exist and are realized in experiments the quantum resonances for symmetric Ψ n -functions (cos waves (the principal tone)) with E n ∼ (n − 1/2)2. The spectrum of energy states, localized by a barrier, with E n > 0 (a metastable IQ-particle (a partially open quantum dot, line, or well)), as in the case of E n < 0 (a stable FQ-particle (a close dot, line, or well)), is determined by the effective internal sizes of the box (R + r ind) with polarization forces effectively acting at the distance of r ind from the molecule. The comparison of the analytical results with the experimental observations proves convincingly the validity of the CQM application in describing the quantum-size effects in the case of physical doping of metamaterials. It has been demonstrated for the first time that, in nanocomposite materials, the pair of “eigenfunction Ψ n —self-energy E n” comprising the quantum state in the nanoworld noted by the basic quantum number n and in the mesoworld of nanocomposites by physically doped by traps is replaced by two nanoworld parameters: the nanocrystal diameter D and the relative resonance concentration of the modifier (a trap, such as C60, 70) ζn. The self-assembly of hollow allotropic forms of carbon on resonant electrons is discussed.

Computational Analysis of Liquid Crystalline Biphenylcyclohexane Derivatives: Estimation of Configurational Entropy, and Phase Stability

A comparative computational analysis of two liquid crystalline disubstituted biphenylcyclohexanes (BCHs) of general formula R-C6H10-C6H4-X with R: C3H7; X: H (BCH30), and R: C5H11; X: CN (BCH5CN) has been carried out on the basis of quantum mechanics, statistical mechanics, and intermolecular forces. The atomic net charge and dipole moment at each atomic center have been evaluated using the complete neglect differential overlap (CNDO/2) method. The modified Rayleigh–Schrodinger perturbation theory, along with multicentered–multipole expansion method, has been employed to evaluate the long-range intermolecular interactions, while a “6-exp” potential function has been assumed for short-range interactions. The interaction energy values obtained through these computations have been taken as input to estimate the configurational entropy and Helmholtz free energy at room temperature, transition temperature, and above transition temperature. The present investigation provides valuable information in understanding the flexibility of a particular configuration at different temperatures. Further, it serves as a molecular model to yield the structure-phase stability relationship.

Quantum heat engine cycle working with a strongly correlated electron system

A new model of a quantum heat engine (QHE) cycle is established, in which the working substance consists of an interacting electrons system. One of our purposes is to test the validity of the second law of thermodynamics by this model, which is more general than the spin-1/2 antiferromagnetic Heisenberg model since it would recover the spin model when the on-site Coulomb interaction U is strong enough. On the basis of quantum mechanics and the first law of thermodynamics, we show no violation of the second law of thermodynamics during the cycle. We further study the performance characteristics of the cycle by investigating in detail the optimal relations of efficiency and dimensionless power output. We find that the efficiency of our engine can be expressed as η = 1 − t 2 2 /t 2 1 in the large-U limit, which is valid even for a four sites QHE.

Teaching Basic Quantum Mechanics in Secondary School Using Concepts of Feynman Path Integrals Method

This paper discusses the teaching of basic quantum mechanics in high school. Rather than following the usual formalism, our approach is based on Feynman's path integral method. Our presentation makes use of simulation software and avoids sophisticated mathematical formalism.

Physics Didactic, Affect and Conceptualization

This paper discusses the relation between affects and conceptualization in physics didactics. We present a theoretical framework that has been used in an investigation about basic Quantum Mechanics teaching in the high school. The Path Integrals method of Feynman has been adopted as a Reference Conceptual Structure that is an alternative to the canonical formalism. The Proposed Conceptual Structure for Teaching is described and the conceptualization and its related affective aspects are analysed.

One-Dimensional Uneven Peanut-Shaped C60 Polymer: A Quantum Electronic System in Riemannian Space

When a C60 film is irradiated with a 3 kV electron-beam in an ultrahigh vacuum (base pressure: 10−7 Pa), C60 molecules are coalesced to form a one-dimensional (1D) uneven peanut-shaped C60 polymer. From a topological viewpoint, since the polymer has both positive and negative Gaussian curvatures, it can be regarded as a new allotrope of nanocarbons different from graphene, fullerenes, and nanotubes. We will present our recent results of the electronic, optical, and electron-transport properties of the 1D uneven peanut-shaped C60 polymer and discuss its novel electronic properties on the basis of quantum mechanics in Riemannian space.

Effects of hydrogen adsorption on mechanical properties of chiral single-walled zinc oxide nanotubes

Size- and chirality-dependent mechanical properties of single-walled zinc oxide nanotubes (ZnONTs) under four different states of hydrogen adsorption have been investigated in this paper. A molecular mechanics model is developed to derive analytical expressions for surface Young’s modulus and Poisson’s ratio of chiral hydrogenated ZnONTs (H-ZnONTs). On the basis of quantum mechanics, density functional theory (DFT) is utilized to obtain the force constants of molecular mechanics theory. Also, the values of surface Young’s modulus, bending stiffness, Poisson’s ratio, and atomic structure of a hydrogenated zinc oxide (H-ZnO) sheet associated with the four positions of adsorption are determined via the DFT calculations. The related results indicate that the bending stiffness of a H-ZnO sheet is chirality-independent. The present analysis provides the possibility of considering nanotubes with different types of chirality. It is indicated that, for all positions of hydrogen adsorption, the values of surface Young’s modulus for armchair H-ZnONTs are higher than those of zigzag H-ZnONTs and the results of chiral H-ZnONTs are between the results of armchair and zigzag nanotubes. Also, the maximum stability happens when the hydrogen atoms are adsorbed on zinc and oxygen atoms at the two opposite sides of a ZnO sheet.

A Didactic Proposed for Teaching the Concepts of Electrons and Light in Secondary School Using Feynman´s Path Sum Method

This work comprises an investigation about basic Quantum Mechanics (QM) teaching in the high school. The organization of the concepts does not follow a historical line. The Path Integrals method of Feynman has been adopted as a Reference Conceptual Structure that is an alternative to the canonical formalism. We have designed a didactic sequence for teaching the basic ideas of Quantum Mechanics according to our theoretical frame (Otero, 2006), eluding the mathematical formalism and using simulation software. In the first part of this work we show our proposal for teach the quantum character of the electrons. At the end, we present the outlines of an approach the quantum character of the light with students of the secondary school, where also we use Feynman's technique as the most universal explanation of the light.