Related papers: Analytical description of classical trajectories a…
It is well known that the action functional can be used to define classical, quantum, closed, and open dynamics in a generalization of the variational principle and in the path integral formalism in classical and quantum dynamics,…
We discuss the final stages of the simultaneous ionization of two or more electrons due to a strong laser pulse. An analysis of the classical dynamics suggests that the dominant pathway for non-sequential escape has the electrons escaping…
A simple method for taking into account the multiple Coulomb scattering in construction of a separatrix (the line separating the regions of runaway and decelerating electrons in an electric field) is described. The desired line is obtained…
Both the physical picture of the dynamics of atoms and molecules in intense infrared fields and its theoretical description use the concept of electron trajectories. Here we address a key question which arises in this context: Are…
For relativistic energies the small angle classical cross section for scattering on a Coulomb potential agrees with the first Born approximation for quantum cross section for scalar particle only in the leading term. The disagreement in…
Analytical solutions to the chaotic and ergodic motion of a certain class of one-dimensional dissipative and discrete dynamical systems are derived. This allows us to obtain exact expressions for physical properties like the time…
We derive the explicit analytic expression for the efficiency at maximum power in a simple model of classical particle transport.
We study the motion of a particle in a particular magnetic field configuration both classically and quantum mechanically. For flux-free radially symmetric magnetic fields defined on circular regions, we establish that particle escape speeds…
One-dimensional quantum scattering from a local potential barrier is considered. Analytical properties of the scattering amplitudes have been investigated by means of the integral equations equivalent to the Schrodinger equations. The…
In this article one introduces a formalism of classical mechanics where complex Lagrangian functions are admitted. The results include complex versions of the Lagrangian function, of the Euler-Lagrange equation, of the Hamilton principle, a…
The classical and quantum aspects of planar Coulomb interactions have been studied in detail. In the classical scenario, Action Angle Variables are introduced to handle relativistic corrections, in the scheme of time-independent…
Scattering in central attractive potentials is investigated systematically, in the limit of strong interaction, when large-angles scattering dominates. In particular, three important model interactions (Lennard-Jones, Yukawa, and…
We consider a turbulent jet which is moving in a Lane--Emden ($n=5$) medium. The conserved quantity is the energy flux, which allows finding, to first order, an analytical expression for the velocity and an approximate trajectory. The…
An analytical model for the soliton-potential interaction is presented, by constructing a collective coordinate for the system. Most of the characters of the interaction are derived analytically while they are calculated by other models…
In the variational approach to quantum statistics, a smearing formula describes efficiently the consequences of quantum fluctuations upon an interaction potential. The result is an effective classical potential from which the partition…
This paper reports a numerical study of complex classical trajectories of a particle in an elliptic potential. This study of doubly-periodic potentials is a natural sequel to earlier work on complex classical trajectories in trigonometric…
A trajectory in the Schroedinger wave for an electron in an attractive Coulomb potential with the dynamical behavior is proposed and illustrated for a scattering and a bound state. The scattering cross section derived from the trajectories…
This note shows how classical tools from linear control theory can be leveraged to provide a global analysis of nonlinear reaction-diffusion models. The approach is differential in nature. It proceeds from classical tools of contraction…
The concept of dominant interaction hamiltonians is introduced and applied to classical planar electron-atom scattering. Each trajectory is governed in different time intervals by two variants of a separable approximate hamiltonian.…
This paper presents a new approach to phase space trajectories in quantum mechanics. A Moyal description of quantum theory is used, where observables and states are treated as classical functions on a classical phase space. A quantum…