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We take causality and uniqueness of events observation as our driving forces. They are built in in the way we define distinct observers, which then require a finite time to communicate between each other. This unavoidably leads to the…
Admitting the validity of Lorentz transformations for the space as time coordinates of the same event we derive their differential form in order to underline the correct prerequisites for the application of time and length contraction or…
The dynamical behavior of matter wave solitons of two-component Bose-Einstein condensates (BEC) in combined linear and nonlinear optical lattices (OLs) is investigated. In particular, the dependence of the frequency of the oscillating…
A self-consistent theory is developed based on the principle of relativity for a plane wave in a moving non-dispersive, lossless, non-conducting, isotropic, uniform medium. A light-momentum criterion is set up for the first time, which…
We revisit the classification of polarization observables of the cosmic microwave background. There exists a unified approach to the $3 \times 3$ density matrix by which intensity, linear and circular polarization are treated on an equal…
A self-action problem for a point-like charged particle arbitrarily moving in flat space-time of six dimensions is considered. A consistent regularization procedure is proposed which relies on energy-momentum and angular momentum balance…
We explore vortices in non-equilibrium Dirac Bose-Einstein condensates (Dirac BEC) described by a stationary Dirac Gross-Pitaevskii equations (GPE). We find that the multi-component structure of Dirac equation enables the difference in…
Rotational transformations describe relativistic effects in rotating frames. There are four major kinematic rotational transformations: the Langevin metric; Post transformation; Franklin transformation; and the rotational form of the…
We study relaxation in a one-dimensional two-mass mixture of hard-core particles. A heavy-light-heavy triplet of three neighboring particles can form a little known unequal mass generalization of Newton's cradle at particular light-to-heavy…
We revisit the classical theory of a relativistic massless charged point particle with spin and interacting with an external electromagnetic field. In particular, we give a proper definition of its kinetic energy and its total energy, the…
The Lorentz transformation is derived without assuming the existence of Maxwell's equations, or that the speed of light is a constant, or even that light exists. This leads us logically to sonsider the existence of a primal field called…
The dynamics of "dipolar particles", i.e. particles endowed with a four-vector mass dipole moment, is investigated using an action principle in general relativity. The action is a specific functional of the particle's world line, and of the…
We investigate regular configurations of a small number of particles settling under gravity in a viscous fluid. The particles do not touch each other and can move relative to each other. The dynamics is analyzed in the point-particle…
We discuss the possibility of explaining the observation of ultra-high-energy cosmic rays with energy above the GZK cutoff, saving the relativity principle and the (possibly deformed) Lorentz symmetry, as proposed recently by several…
A deformation of the canonical algebra for kinematical observables of the quantum field theory in Minkowski space-time has been considered under the condition of Lorentz invariance. A relativistic invariant algebra obtained depends on…
We investigate the dynamical instability of Bose-Einstein condensates (BECs) with higher-order interactions immersed in an optical lattice with weak driving harmonic potential. For this, we compute both analytically and numerically a…
We study a quantum-mechanical system of three particles in a one-dimensional box with two-particle harmonic interactions. The symmetry of the system is described by the point group $D_{3d}$. Group theory greatly facilitates the application…
We consider particles on a one-dimensional lattice whose evolution is governed by nearest-neighbor interactions where particles that have reached size zero are removed from the system. Concentrating on configurations with infinitely many…
The dynamics of a particle moving in background electromagnetic and gravitational fields is revisited from a Lie group cohomological perspective. Physical constants characterising the particle appear as central extension parameters of a…
In a numerical experiment based on Gross-Pitaevskii formalism, we demonstrate unique topological quantum coherence in optically trapped Bose-Einstein condensates (BECs). Exploring the fact that vortices in rotating BEC can be pinned by a…