Related papers: Generalized macroscopic Schrodinger equation in sc…
A scalar bimetric theory of gravity with a preferred reference frame is summarized. Dynamics is governed by an extension of Newton's second law. In the static case, geodesic motion is recovered together with Newton's attraction field. In…
This paper considers a main particle and an incident particle classical mechanics elastic collision preserving energy and momentum while ignoring the angular momentum, spin or other particle characteristics. The main result of the paper…
In this paper we consider generalization of classical and quantum mechanics that directly follows from the causality principle and topology of a system state space. In generalized mechanics, the Hamiltonian/Schrodinger equations remain the…
A variational technique is established to deal with the Schrodinger equation with parity-time(PT) symmetric Gaussian complex potential. The method is extended to the linear and self-focusing and defocusing nonlinear cases. Some unusual…
I review the basic ``gravitational instability'' model for the growth of structure in the expanding Universe. This model requires the existence of small initial irregularities in the density of a largely uniform universe. These grow through…
In textbooks on statistical mechanics, one finds often arguments based on classical mechanics, phase space and ergodicity in order to justify the second law of thermodynamics. However, the basic equations of motion of classical mechanics…
The evolution equations of Einstein's theory and of Maxwell's theory---the latter used as a simple model to illustrate the former--- are written in gauge covariant first order symmetric hyperbolic form with only physically natural…
It is widely accepted that the fundamental geometrical law of nature should follow from an action principle. The particular subset of transformations of a system's dynamical variables that maintain the form of the action principle comprises…
In this paper we derive the leading quantum gravitational corrections to the geodesics and the equations of motion for a scalar field in the spacetime containing a constant density star. It is shown that these corrections can be calculated…
The functional Schrodinger equation is used to study the quantum collapse of a gravitating, spherical domain wall and a massless scalar field coupled to the metric. The approach includes backreaction of pre-Hawking radiation on the…
The spacetime evolution of massless spinning particles in a Robertson-Walker background is derived using the deterministic system of equations of motion due to Papapetrou, Souriau and Saturnini. A numerical integration of this system of…
We have investigated the motion of timelike particles along geodesic in the background of accelerating and rotating black hole spacetime. We confirmed that the chaos exists in the geodesic motion of the particles by Poincar\'e sections, the…
We study the cosmology of an extended version of Horndeski theories with second-order equations of motion on the flat Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) background. In addition to a dark energy field $\chi$ associated with the…
It is shown that the Schrodinger equation is a byproduct of more deterministic Boltzmann-like equation. All physical information is derived from the solution of this equation, which is a function of space and momentum. The additional terms…
It is is explained why physical consistency requires substituting linear observables by nonlinear ones for quantum systems with nonlinear time evolution of pure states. The exact meaning and the concrete physical interpretation are…
We derive several kinetic equations to model the large scale, low Fresnel number behavior of the nonlinear Schrodinger (NLS) equation with a rapidly fluctuating random potential. There are three types of kinetic equations the longitudinal,…
Nottale's special scale-relativity principle was proposed earlier by the author as a plausible geometrical origin to string theory and extended objects. Scale Relativity is to scales what motion Relativity is to velocities. The universal,…
We consider Schrodinger equations for a non-relativistic particle obeying N+1-th order higher derivative classical equation of motion. These equations are invariant under N(odd)-extended Galilean conformal (NGC) algebras in general d+1…
We consider variation of energy of the light-like particle in Riemann space-time, find lagrangian, canonical momenta and forces. Equations of the critical curve are obtained by the nonzero energy integral variation in accordance with…
The identification of a cosmic scale function with the volume integral of a spacelike hypersurface defines the cosmic evolution in General Relativity as a collective motion along a geodesic in the field space of the metric components,…