Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userThe reaction-free trajectories of a classical point charge
259
0
0.0
(
0
)
Authors
M. Ibison
Ask ChatGPT about the research
No Arabic abstract
It is well-known that a classical point charge in 1+1 D hyperbolic motion in space and time is reaction-free. But this is a special case of a larger set of reaction-free trajectories that in general are curved paths through space, i.e. in 2+1 D. This note catalogs the full family of reaction-free trajectories, giving a geometrical interpretation by which means the curved path possibility is easily related to the better known case of hyperbolic motion in 1+1 D. Motivated by the geometry, it is shown how the catalog of motions can be naturally extended to include the possibility of lossless reaction-free closed spatial orbits that turn out to be classical pair creation and destruction events. The extended theory can accommodate a vacuum plenum of classical current that could be regarded as a classical version of the Fermionic ZPF of QFT, reminiscent of the relationship between the Electromagnetic ZPF and the classical imitation that characterizes `Stochastic Electrodynamics.
rate research
Read More
Abraham Lorentz (AL) formula of Radiation Reaction and its relativistic generalization, Abraham Lorentz Dirac (ALD) formula, are valid only for periodic (accelerated) motion of a charged particle, where the particle returns back to its original state. Thus, they both represent time averaged solutions for radiation reaction force. In this paper, another expression has been derived for radiation reaction following a new approach, starting from Larmor formula, considering instantaneous change (rather than periodic change) in velocity, which is a more realistic situation. Further, it has been also shown that the new expression for Radiation Reaction is free of pathological solutions; which were unpleasant parts of AL as well as ALD equations; and remained unresolved for about 100 years.
A long-standing challenge in mixed quantum-classical trajectory simulations is the treatment of entanglement between the classical and quantal degrees of freedom. We present a novel approach which describes the emergence of entangled states entirely in terms of independent and deterministic Ehrenfest-like classical trajectories. For a two-level quantum system in a classical environment, this is derived by mapping the quantum system onto a path-integral representation of a spin-1/2. We demonstrate that the method correctly accounts for coherence and decoherence and thus reproduces the splitting of a wavepacket in a nonadiabatic scattering problem. This discovery opens up a new class of simulations as an alternative to stochastic surface-hopping, coupled-trajectory or semiclassical approaches.
This paper examines the complex trajectories of a classical particle in the potential V(x)=-cos(x). Almost all the trajectories describe a particle that hops from one well to another in an erratic fashion. However, it is shown analytically that there are two special classes of trajectories x(t) determined only by the energy of the particle and not by the initial position of the particle. The first class consists of periodic trajectories; that is, trajectories that return to their initial position x(0) after some real time T. The second class consists of trajectories for which there exists a real time T such that $x(t+T)=x(t) pm2 pi$. These two classes of classical trajectories are analogous to valence and conduction bands in quantum mechanics, where the quantum particle either remains localized or else tunnels resonantly (conducts) through a crystal lattice. These two special types of trajectories are associated with sets of energies of measure 0. For other energies, it is shown that for long times the average velocity of the particle becomes a fractal-like function of energy.
It is feasible to obtain any basic rule of the already known Quantum Mechanics applying the Hamilton-Jacobi formalism to an interacting system of 2 fermionic degrees of freedom. The interaction between those fermionic variables unveils also a primitive spin and zitterbewegung.
We show that Anderson localization in quasi-one dimensional conductors with ballistic electron dynamics, such as an array of ballistic chaotic cavities connected via ballistic contacts, can be understood in terms of classical electron trajectories only. At large length scales, an exponential proliferation of trajectories of nearly identical classical action generates an abundance of interference terms, which eventually leads to a suppression of transport coefficients. We quantitatively describe this mechanism in two different ways: the explicit description of transition probabilities in terms of interfering trajectories, and an hierarchical integration over fluctuations in the classical phase space of the array cavities.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
