相关论文: On the Effects of Bohm's Potential on a Stationary…
We consider an instationary macroscopic system of self-interacting particles with an additional potential, the so called Bohm's potential. We study the existence of non-negative global solutions to the (4-th order) system of equations and…
Many self-gravitating systems often show scaling properties in their mass density, system size, velocities and so on. In order to clarify the origin of these scaling properties, we consider the stationary state of N-body system with inverse…
We investigate the effects of the gravitational field on the quantum dynamics of non-relativistic particles. We consider N non-relativistic particles, interacting with the linearized gravitational field. Using the Feynman - Vernon influence…
We investigate systems of self-propelled particles with alignment interaction. Compared to previous work, the force acting on the particles is not normalized and this modification gives rise to phase transitions from disordered states at…
We investigate a relativistic self-interacting gas in the field of an external {\it pp} gravitational wave. Based on symmetry considerations we ask for those forces which are able to compensate the imprint of the gravitational wave on the…
The Dirac delta function potential is considered within the real Hilbert space approach for complex wave functions, as well as quaternionic wave functions. As has been previously determined, the real Hilbert space approach enables the…
We consider a discrete particle system of two species coupled through nonlocal interactions driven by the one-dimensional Newtonian potential, with repulsive self-interaction and attractive cross-interaction. After providing a suitable…
We examine the nonperturbative effect of maximum momentum on the relativistic wave equations. In momentum representation, we obtain the exact eigen-energies and wavefunctions of one-dimensional Klein-Gordon and Dirac equation with linear…
The Schr\"odinger-Newton equation has gained attention in the recent past as a nonlinear modification of the Schr\"odinger equation due to a gravitational self-interaction. Such a modification is expected from a fundamentally semi-classical…
We consider a hamiltonian system on the real line, consisting of real scalar field $\phi(x,t)$ and point particle with trajectory $y(t)$. The dynamics of this system is defined by the system of two equations: wave equation for the field,…
Scalar particles are a common prediction of many beyond the Standard Model theories. If they are light and cold enough, there is a possibility they may form Bose-Einstein condensates, which will then become gravitationally bound. These…
We investigate, in the framework of the linearized quantum gravity and the leading-order perturbation theory, the quantum correction to the classical Newtonian interaction between a pair of gravitationally polarizable objects in the…
We prove the possibility of existence of stationary bound states of spin-half particles in the Reissner-Nordstroem gravitational field using a self-conjugate Hamiltonian with a flat scalar product of wave functions. Bound states of Dirac…
The gravitational interaction is generally considered to be too weak to be easily submitted to systematic experimental investigation in the quantum, microscopic, domain. In this paper we attempt to remedy this situation by considering the…
This paper deals with the Klein-Gordon-Maxwell system in a bounded spatial domain. We study the existence of solutions having a specific form, namely standing waves in equilibrium with a purely electrostatic field. We prescribe Dirichlet…
Explaining the behavior of macroscopic objects from the point of view of the quantum paradigm has challenged the scientific community for a century today. A mechanism of gravitational self-interaction, governed by the so-called…
We derive the effect of the Schr\"odinger--Newton equation, which can be considered as a non-relativistic limit of classical gravity, for a composite quantum system in the regime of high energies. Such meson-antimeson systems exhibit very…
The Schrodinger-Newton equation has frequently been studied as a nonlinear modification of the Schrodinger equation incorporating gravitational self-interaction. However, there is no evidence yet as to whether nature actually behaves this…
The one-dimensional Klein-Gordon equation is investigated with the most general Lorentz structure for the external potentials. The analysis and calculation of the reflection and transmission coefficients for the scattering of particles in a…
It is shown that a recently proposed model for the gravitational interaction in non relativistic quantum mechanics is the instantaneous action at a distance limit of a field theoretic model containing a negative energy field. It reduces to…