Related papers: Generalized particle dynamics: modifying the motio…
In the timescape scenario cosmic acceleration is understand as an apparent effect, due to gravitational energy gradients that grow when spatial curvature gradients become significant with the nonlinear growth of cosmic structure. This…
Mathematical descriptions of dynamical systems are deeply rooted in topological spaces defined by non-Euclidean geometry. This paper proposes leveraging structure-rich geometric spaces for machine learning to achieve structural…
Let a finite set of interacting particles be given, together with a symmetry Lie group $G$. Here we describe all possible dynamics that are jointly equivariant with respect to the action of $G$. This is relevant e.g., when one aims to…
Allowing the energy of a gravitational field to serve partially as its own source allows gravitating bodies to exhibit stronger fields, as if they were more massive. Depending on degree of compaction of the body, the field could be one to…
The Newtonian dynamics of particles in brane gravity is investigated. Due to the coupling of the particles' energy-momentum tensor to the tension of the brane, the particle is semi-confined and oscillates along the extra dimension. We…
We consider the consequences of applying general relativity to the description of the dynamics of a galaxy, given the observed flattened rotation curves. The galaxy is modeled as a stationary axially symmetric pressure-free fluid. In spite…
It is shown that, with some reasonable assumptions, the theory of general relativity can be made compatible with quantum mechanics by using the field equations of general relativity to construct a Robertson-Walker metric for a quantum…
Technical results are presented on motion in N(>4)D manifolds to clarify the physics of Kaluza-Klein theory, brane theory and string theory. The so-called canonical or warp metric in 5D effectively converts the manifold from a coordinate…
The new, complex-dynamical mechanism of the universal gravitation naturally incorporating dynamical quantization, wave-particle duality, and relativity of physically emerging space and time (quant-ph/9902015,16) provides the realistic…
By incorporating spinning particles into the framework of classical General Relativity, the theory is changed insofar, as, though using holonome coordinates, the connexion becomes asymmetrical. This implies, that partial derivatives do not…
The action principle is frequently used to derive the classical equations of motion. The action may also be used to associate group elements with curves in the space-time manifold, similar to the gauge transformations. The action principle…
Many-particles quantum walks of particles obeying Bose statistics moving on graphs of various topologies are introduced. A single coin tossing commands the conditional shift operation over the whole graph. Vertices particle densities, the…
We consider the dynamics of Dirac particles moving in the curved spaces with one coordinate subjected to compactification and thus interpolating smoothly between three- and two-dimensional spaces. We use the model of compactification, which…
General relativity is highly successful in explaining a wide range of gravitational phenomena including the gravitational waves emitted by binary systems and the shadows cast by supermassive black holes. From a modern perspective the theory…
We develop a dynamical theory, based on a system of ordinary differential equations describing the motion of particles which reproduces the results of quantum mechanics. The system generalizes the Hamilton equations of classical mechanics…
We investigate the cosmological behavior in a universe governed by time asymmetric extensions of general relativity, which is a novel modified gravity based on the addition of new, time-asymmetric, terms on the Hamiltonian framework, in a…
A novel generalization of photon surfaces to the case of massive charged particles is given for spacetimes with at least one isometry, including stationary ones. A related notion of glued massive particle surfaces is also defined. These…
A generalized physics-based expression for the drag coefficient of spherical particles moving in a fluid is derived. The proposed correlation incorporates essential rarefied physics, low-speed hydrodynamics, and shock-wave physics to…
With the aid of a Fermi-Walker chart associated with an orthonormal frame attached to a time-like curve in spacetime, a discussion is given of relativistic balance laws that may be used to construct models of massive particles with spin,…
We provide a general construction of quantum generalized master equations with memory kernel leading to well defined, that is completely positive and trace preserving, time evolutions. The approach builds on an operator generalization of…