Related papers: One-dimensional relativistic particle as a movable…
The dynamical behavior of non-uniform cellular automata is compared with the one of classical cellular automata. Several differences and similarities are pointed out by a series of examples. Decidability of basic properties like…
We consider the quantum dynamics of a single particle in the plane under the influence of a constant perpendicular magnetic and a crossed electric potential field. For a class of smooth and small potentials we construct a non-trivial…
Quantum cellular automata are important tools in understanding quantum dynamics, thanks to their simple and effective list of rules. Here we investigate explicitly how coherence is built and lost in the evolution of one-dimensional automata…
A synopsis is offered of the properties of discrete and integer-valued, hence "natural", cellular automata (CA). A particular class comprises the "Hamiltonian CA" with discrete updating rules that resemble Hamilton's equations. The…
Relativistic action-at-a-distance theories with interactions that propagate at the speed of light in vacuum are investigated. We consider the most general action depending on the velocities and relative positions of the particles. The…
The solution of the problem of describing the Friedmann observables (the Hubble law, the red shift, etc.) in quantum cosmology is proposed on the basis of the method of gaugeless Hamiltonian reduction in which the gravitational part of the…
We propose a form for the action of a relativistic particle subject to a positional force that is invariant under time reparametrization and therefore allows for a consistent Hamiltonian formulation of the dynamics. This approach can be…
We conjecture that for a wide class of interacting particle systems evolving in discrete time, namely conservative cellular automata with piecewise linear flow diagram, relaxation to the limit set follows the same power law at critical…
The dynamics of a test particle interacting with diffusing impurities in one dimension is investigated analytically and numerically. In the absence of an applied external force, the dynamics of the particle can be characterized by a…
The two-component formulation of quantum electrodynamics is studied. The relation with the usual Dirac formulation is exhibited, and the Feynman rules for the two-component form of the theory are presented in terms of familiar objects. The…
The study of the evolution of the dynamics of a massive or massless particle shows that in special relativity theory, the energy is not conserved. From the law of evolution of the velocity over time of a particle subjected to a constant…
Cellular Automata (CA) are discrete dynamical systems and an abstract model of parallel computation. The limit set of a cellular automaton is its maximal topological attractor. A well know result, due to Kari, says that all nontrivial…
We present a model that extends the standard model by incorporating the simplest discrete symmetry groups, $Z_2$ and $Z_3$. This model introduces vector-like leptons and a real scalar singlet. Based on this framework, we generate Dirac…
Soluble model of a relativistic particle describing a bag of matter with fixed radius held together in perfect balance by a self-consistent combination of three forces generated by electromagnetic and massive scalar and vector fields is…
We establish a connection between percolation on the Cayley graphs of a group and the dynamical diversity of cellular automata on that group. Specifically, we demonstrate that Gilman's dichotomy between equicontinuity and sensitivity with…
Classical relativistic system of point particles coupled with an electromagnetic field is considered in the three-dimensional representation. The gauge freedom connected with the chronometrical invariance of the four-dimensional description…
We extend the equations of motion that describe non-relativistic elastic collision of two particles in one dimension to an arbitrary associative algebra. Relativistic elastic collision equations turn out to be a particular case of these…
In this paper, we generalize a previous relativistic $1+1$-dimensional model for two mass-less Dirac particles with relativistic contact interactions to the $N$-particle case. Our model is based on the notion of a multi-time wave function…
Cellular Automata are discrete--time dynamical systems on a spatially extended discrete space which provide paradigmatic examples of nonlinear phenomena. Their stochastic generalizations, i.e., Probabilistic Cellular Automata, are discrete…
We consider model of a complex particle that consists of a rigid shell and a nucleus with spatial asymmetric interaction. The particle's dynamics with the nucleus driven by a periodic excitation is considered. It is shown that…