Framework Of Classical Dynamics Research Articles

Quasiclassical approach to the interpretation of the Barkas effect

A correction to the Bohr formula making it possible to explain the difference between the stopping powers of positively and negatively charged particles (the Barkas effect) is obtained in the quasiclassical approximation taking into account the difference between electron motion in a hydrogen atom as a function of the charge sign of the moving particle. The influence on the atomic electron of the moving particle leads to a change in the contribution of the adiabatic interaction, in the case of which the energy is not transferred in the majority of collisions, which is the reason for a decrease in the energy losses of slow particles compared with Bohr theory. The results of calculations show that the energy losses per path length unit can be represented in the form of the product of two functions, namely, the energy loss function (in accordance with Bohr theory) and the dynamic function taking into account corrections related to correction of the electron position in the target atom during the collision. Calculations carried out within the framework of classical dynamics make it possible to qualitatively estimate differences between the interaction of protons and antiprotons with target material atoms.

Towards chemically accurate simulation of molecule–surface reactions

This perspective addresses four challenges facing theorists whose aim is to make quantitatively accurate predictions for reactions of molecules on metal surfaces, and suggests ways of meeting these challenges, focusing on dissociative chemisorption reactions of H(2), N(2), and CH(4). Addressing these challenges is ultimately of practical importance to a more accurate description of overall heterogeneously catalysed reactions, which play a role in the production of more than 90% of man-made chemicals. One challenge is to describe the interaction of a molecule with a metal surface with chemical accuracy, i.e., with errors in reaction barrier heights less than 1 kcal mol(-1). In this framework, the potential of a new implementation of specific reaction parameter density functional theory (SRP-DFT) will be discussed, with emphasis on applications to reaction of H(2) with metal surfaces. Two additional challenges are to come up with improved descriptions of the effects of phonons and electron-hole pairs on reaction of molecules like N(2) on metal surfaces. Phonons can be tackled using sudden approximations in quantum dynamics, and through Ab Initio Molecular Dynamics (AIMD) calculations using classical dynamics. To additionally achieve an accurate description of the effect of electron-hole pair excitation on dissociative chemisorption within a classical dynamics framework, it may be possible to combine AIMD with electronic friction. The fourth challenge we will consider is how to achieve an accurate quantum mechanical description of the dissociative chemisorption of a polyatomic molecule, like methane, on a metal surface. A method of potential interest is the Multi-Configuration Time-Dependent Hartree (MCTDH) method.

Pythagorean Metric in Particle's Relativistic Dynamics

A new non-traditional quasi-classical description of the particle dynamics (QCDPD) is outlined. The “quasi-classical” attribute is suggested by the closeness—although not identity—to the description of a classical system, in the framework of classical dynamics. Founded on a suitable one-to-one mapping of the timelike 4-vectors of Minkowski's spacetime onto the real 4-dimension vector space, QCDPD is mathematically equivalent to the traditional description of special relativity. However, in QCDPD a new frequency fulfilling the same transformation law as the frequency of an oscillator is employed. It turns out that the special-relativity particle is, in fact, modeled as an oscillator which is essentially classical. The associated wave is a natural consequence of such a model.

Rydberg atoms in parallel microwave and magnetic fields – classical dynamics

The dynamics of Rydberg atoms in parallel microwave and magnetic fields is studied in the framework of classical dynamics. We calculate the ionization rate of the Rydberg atoms for a wide range of field parameters. Our results show that adding magnetic fields will enhance the microwave ionization rate at weak and super intense microwave, while suppress the ionization rate at moderate intense microwave. These observations are explained satisfactorily with the help of nonlinear analysis on phase space structure and stabilization dynamics.

Nuclear Fragmentation Reactions at Relativistic Energies

Fragmentation reaction cross sections at relativistic energies are investigated using a phenomenological approach. Equations are obtained by a geometrical treatment in the framework of classical dynamics, in which the impact parameter is introduced. A numerical solution is obtained for the 56 Fe + 12 C system at 600 MeV/nucleon incident energy. It is shown that the predicted mass number distribution of fragments reproduces well the experimental data. The Coulomb energy term in the mass formula affects the nuclide dependence of cross sections to a favorable direction.

Polar light charged particles accompanying spontaneous fission

Simple model of emission of light charged polar particles accompanying fission of heavy nuclei is presented. We assume the emission from the whole surface of fragments after scission, taking into account the influence of the accompanying fragment. The initial energy and time of emission are treated phenomenologically. The motion of light particles and fission fragments are subsequently calculated in the framework of classical dynamics. We get a good agreement with experimental data if we assume a prompt emission. The possibility of the connection with giant resonances is discussed.

Necessary and Sufficient Conditions of Reducibility of Gauge Degrees of Freedom without Using Gauge Conditions

For dynamical systems described by singular Lagrangian, the conditions under which gauge degrees of freedom can be eliminated by transformations of variables are obtained within the framework of classical dynamics. All the systems whose gauge degrees of freedom are reducible without using gauge conditions may be classified into the following two cases. (i) A weakly reducible case; there exists a canonical transformation by which some of the gauge dependent variables in a Hamiltonian can be separated from other dynamical variables. Hence their gauge degrees of freedom can be completely isolated. (ii) A strongly reducible case; there is a point transformation by which the number of dynamical variables describing a Lagrangian (also a Hamiltonian) of a system can be reducible. Hence the corresponding gauge degrees of freedom are eliminated from the formula. Necessary and sufficient conditions for the reducibility are presented for each case.