Related papers: Evolution loops and spin-1/2 systems
Internal dynamical evolution can drive stellar systems into states of high central density. For many star clusters and galactic nuclei, the time scale on which this occurs is significantly less than the age of the universe. As a result,…
Properties of time evolution of wave packets built up from rotator eigenstates are discussed. The mechanism of perfect cloning of the initial wave packet for "circular states" at fractional revival times is explained. The smooth transition…
The evolution of entanglement in a one-dimensional Ising chain is numerically studied under various initial conditions. We analyze two problems concerning the dynamics of the entanglement: (i) generation of the entanglement from the…
We study the dynamics of planetary systems with two planets moving in the same plane, when frictional forces act on the two planets, in addition to the gravitational forces. The model of the general three-body problem is used. Different…
The spin mixing dynamics of spin-1 Bose-Einstein condensates with zero magnetization and under an external magnetic field is investigated. The time-dependent solutions are obtained via a diagonalization of the Hamiltonian, which has a…
Evolutionary complexity is here measured by the number of trials/evaluations needed for evolving a logical gate in a non-linear medium. Behavioural complexity of the gates evolved is characterised in terms of cellular automata behaviour. We…
We consider a one dimensional evolution problem modeling the dynamics of an acoustic field coupled with a set of mechanical oscillators. We analyze solutions of the system of ordinary and partial differential equations with time-dependent…
This paper reviews how a two-state, spin-one-half system transforms under rotations. It then uses that knowledge to explain how momentum-zero, spin-one-half annihilation and creation operators transform under rotations. The paper then…
The magnetic fields of spiral galaxies are so strong that they cannot be primordial. Their typical values are over one billion times higher than any value predicted for the early Universe. Explaining this immense growth and incorporating it…
By analogue of [1,2] we define a cubic stochastic process and study evolution (dynamics) of a system $E$ which contains at least three elements.
The motion of spinning relativistic particles in external electromagnetic and gravitational fields is considered. A simple derivation of the spin interaction with gravitational field is presented. The self-consistent description of the spin…
The nature and source of evolutionary trends in complexity is difficult to assess from the fossil record, and the driven vs. passive nature of such trends has been debated for decades. There are also questions about how effectively…
We consider the magnetic and spin evolution of isolated neutron stars assuming that the magnetic field is initially confined to the crust. The evolution of the crustal field is determined by the conductive properties of the crust which, in…
Since the discovery of the first extra-solar planets, we are confronted with the puzzling diversity of planetary systems. Processes like planet radial migration in gas-disks and planetary orbital instabilities, often invoked to explain the…
We develop a theory of loops with involution. On this basis we define a Cayley-Dickson doubling on loops, and use it to investigate the lattice of varieties of loops with involution, focusing on properties that remain valid in the…
We consider response function and spin evolution in spin-orbit coupled cold atomic gases in a synthetic gauge magnetic field influencing solely the orbital motion of atoms. We demonstrate that various regimes of spin-orbit coupling…
A family of discontinuous symplectic maps on the cylinder is considered. This family arises naturally in the study of nonsmooth Hamiltonian dynamics and in switched Hamiltonian systems. The transformation depends on two parameters and is a…
About a dozen exoplanetary systems have been discovered with three or more planets participating in a sequence of mean-motion resonances. The unique and complex architectures of these so-called "resonant chains" motivate efforts to…
The time evolution of a spin-1/2 particle under the influence of a locally applied external magnetic field, and interacting with anisotropic spin environment in thermal equilibrium at temperature $T$ is studied. The exact analytical form of…
A method for constructing evolution equations admitting a master symmetry is proposed. Several examples illustrating the method are presented. It is also noted that for certain evolution equations master symmetries can be useful for…