scholarly journals Dynamic Symmetry in Dozy-Chaos Mechanics

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1856 ◽  
Author(s):  
Vladimir V. Egorov
Keyword(s):  
Chaotic Dynamics ◽  
Classical Mechanics ◽  
Transient State ◽  
Final States ◽  
Electron Phonon Interaction ◽  
Nuclear Reorganization ◽  
Nuclear Subsystem ◽  
Quantum Transitions ◽  
Franck Condon ◽  
Energy Denominator

All kinds of dynamic symmetries in dozy-chaos (quantum-classical) mechanics (Egorov, V.V. Challenges 2020, 11, 16; Egorov, V.V. Heliyon Physics 2019, 5, e02579), which takes into account the chaotic dynamics of the joint electron-nuclear motion in the transient state of molecular “quantum” transitions, are discussed. The reason for the emergence of chaotic dynamics is associated with a certain new property of electrons, consisting in the provocation of chaos (dozy chaos) in a transient state, which appears in them as a result of the binding of atoms by electrons into molecules and condensed matter and which provides the possibility of reorganizing a very heavy nuclear subsystem as a result of transitions of light electrons. Formally, dozy chaos is introduced into the theory of molecular “quantum” transitions to eliminate the significant singularity in the transition rates, which is present in the theory when it goes beyond the Born–Oppenheimer adiabatic approximation and the Franck–Condon principle. Dozy chaos is introduced by replacing the infinitesimal imaginary addition in the energy denominator of the full Green’s function of the electron-nuclear system with a finite value, which is called the dozy-chaos energy γ. The result for the transition-rate constant does not change when the sign of γ is changed. Other dynamic symmetries appearing in theory are associated with the emergence of dynamic organization in electronic-vibrational transitions, in particular with the emergence of an electron-nuclear-reorganization resonance (the so-called Egorov resonance) and its antisymmetric (chaotic) “twin”, with direct and reverse transitions, as well as with different values of the electron–phonon interaction in the initial and final states of the system. All these dynamic symmetries are investigated using the simplest example of quantum-classical mechanics, namely, the example of quantum-classical mechanics of elementary electron-charge transfers in condensed media.

Periodicity of the Oscillatory J Dependence of Diatomic Molecule Franck–Condon Factors

1975 ◽  
Vol 53 (16) ◽  
pp. 1560-1572 ◽  
Author(s):  
Robert J. Le Roy ◽  
Edward R. Vrscay
Keyword(s):  
Simple Formula ◽  
Radial Wave Function ◽  
Wave Functions ◽  
Final States ◽  
Rotational Constants ◽  
Radial Wave ◽  
Condon Factors ◽  
Oscillating Functions ◽  
Vibration Rotation ◽  
Franck Condon

Numerical calculations have shown that vibration–rotation interaction often contributes significantly to the J dependence of transition intensities of diatomic molecules. This occurs because centrifugal displacements of the vibrational wave functions cause the Franck–Condon amplitudes (radial overlap integrals) to behave as oscillating functions of J(J + 1). The present paper discusses the origin of this behavior and derives and tests a simple formula for predicting the periodicity of such oscillations. This procedure requires only a knowledge of the rotational constants and vibrational spacings of the initial and final states. It utilizes the result that the average centrifugal displacement rate of a diatomic molecule's radial wave function is approximately [Formula: see text], where Bν and Dν are the usual diatomic rotational constants.

What Could Be Worse than the Butterfly Effect?

2008 ◽  
Vol 38 (4) ◽  
pp. 519-547 ◽  
Author(s):  
Robert C. Bishop
Keyword(s):  
Nonlinear Systems ◽  
Chaotic Dynamics ◽  
Chaotic Behavior ◽  
Initial Conditions ◽  
Classical Mechanics ◽  
Physical Systems ◽  
Physics Community ◽  
Sensitive Dependence ◽  
Classical Models ◽  
In The Beginning

Our understanding of classical mechanics (CM) has undergone significant growth in the latter half of the twentieth century and in the beginning of the twenty-first. This growth has much to do with the explosion of interest in the study of nonlinear systems in contrast with the focus on linear systems that had colored much work in CM from its inception. For example, although Maxwell and Poincaré arguably were some of the first to think about chaotic behavior, the modern study of chaotic dynamics traces its beginning to the pioneering work of Edward Lorenz (1963). This work has yielded a rich variety of behavior in relatively simple classical models that was previously unsuspected by the vast majority of the physics community (see Hilborn 2001). Chaos is a property of nonlinear systems that is usually characterized by sensitive dependence on initial conditions (SDIC). In CM the behavior of simple physical systems is described using models (such as the harmonic oscillator) that capture the main features of the systems in question (Giere 1988).

A Discussion on photoelectron spectroscopy - The role of autoionization in molecular photoelectron spectra

1970 ◽  
Vol 268 (1184) ◽  
pp. 169-175 ◽  
Keyword(s):  
Excitation Energy ◽  
Relative Intensity ◽  
Intensity Distribution ◽  
Configuration Interaction ◽  
Photoelectron Spectroscopy ◽  
Photoelectron Spectra ◽  
Final States ◽  
Condon Factors ◽  
Franck Condon

The Fano-Mies theory of configuration interaction is applied to the photoionization of diatomic molecules, yielding an expression which gives the relative intensity of vibrational peaks in photoelectron spectra when one or more autoionizing states are in the vicinity of the excitation energy. In some cases the vibrational intensity distribution depends only on Franck-Condon factors connecting autoionizing and final states. Illustrative calculations for O2 show the transition from this limit to the limit of direct photoionization as the line profile index decreases.

Multiple-plane wave calculation of the electron–phonon interaction in Al

1976 ◽  
Vol 54 (15) ◽  
pp. 1585-1599 ◽  
Author(s):  
H. K. Leung ◽  
J. P. Carbotte ◽  
D. W. Taylor ◽  
C. R. Leavens
Keyword(s):  
Plane Wave ◽  
Fermi Surface ◽  
Plane Waves ◽  
Spectral Weight ◽  
Model Fit ◽  
Final States ◽  
Electron Phonon Interaction ◽  
Self Energy ◽  
Multiple Plane ◽  
Migdal's Theorem

We have computed from first principles the electron–phonon spectral weight αk2(ω)Fk(ω) for many points k on the aluminum Fermi surface (FS). According to Migdal's theorem this spectral weight completely determines the self-energy of the electrons. The calculations involve an integral over final states on the Fermi surface which we calculate from Ashcroft's 4-plane wave pseudopotential model fit to the de Haas–van Alphen data. For the electron–phonon matrix element 15 plane waves are included. The phonons are taken from a Born–von Karman model fit to the measured dispersion curves. From the spectral weights we compute the Fermi surface variation of the electron–phonon effective mass and the quasiparticle lifetimes at various temperatures.

Analyzing reactions of single mechanoenzyme molecules by light microscopy

1992 ◽  
Vol 50 (1) ◽  
pp. 426-427
Author(s):  
Jeff Gelles
Keyword(s):  
Image Processing ◽  
Reaction Mechanisms ◽  
Transient State ◽  
Nanometer Scale ◽  
Reaction Intermediates ◽  
Enzyme Molecule ◽  
Directed Movement ◽  
Enzyme Molecules ◽  
Individual Enzyme ◽  
Single Reaction

Mechanoenzymes are enzymes which use a chemical reaction to power directed movement along biological polymer. Such enzymes include the cytoskeletal motors (e.g., myosins, dyneins, and kinesins) as well as nucleic acid polymerases and helicases. A single catalytic turnover of a mechanoenzyme moves the enzyme molecule along the polymer a distance on the order of 10−9 m We have developed light microscope and digital image processing methods to detect and measure nanometer-scale motions driven by single mechanoenzyme molecules. These techniques enable one to monitor the occurrence of single reaction steps and to measure the lifetimes of reaction intermediates in individual enzyme molecules. This information can be used to elucidate reaction mechanisms and determine microscopic rate constants. Such an approach circumvents difficulties encountered in the use of traditional transient-state kinetics techniques to examine mechanoenzyme reaction mechanisms.

Laser scanning confocal microscopic analysis of cytoskeletal and nuclear reorganization in live Drosophila embryos

1993 ◽  
Vol 51 ◽  
pp. 174-175
Author(s):  
William Theurkauf
Keyword(s):  
Laser Scanning ◽  
Microscopic Analysis ◽  
Large Cell ◽  
Early Embryo ◽  
Drosophila Embryo ◽  
Cortical Actin ◽  
Nuclear Reorganization ◽  
Cytoskeletal Elements ◽  
Microtubule Structure ◽  
Drosophila Embryos

Cell division in eucaryotes depends on coordinated changes in nuclear and cytoskeletal components. In Drosophila melanogaster embryos, the first 13 nuclear divisions occur without cytokinesis. During the final four divisions, nuclei divide in a uniform monolayer at the surface of the embryo. These surface divisions are accompanied by dramatic changes in cortical actin and microtubule structure (Karr and Alberts, 1986), and inhibitor studies indicate that these changes are essential to orderly mitosis (Zalokar and Erk, 1976). Because the early embryo is syncytial, fluorescent probes introduced by microinjection are incorporated in structures associated with all of the nuclei in the blastoderm. In addition, the nuclei divide synchronously every 10 to 20 min. These characteristics make the syncytial blastoderm embryo an excellent system for the analysis of mitotic reorganization of both nuclear and cytoskeletal elements. However, the Drosophila embryo is a large cell, and resolution of cytoskeletal filaments and nuclear structure is hampered by out-of focus signal.

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