相关论文: Curved, extended classical solutions I. The undula…

Particles traveling in aligned crystals at small angles w.r.t. crystallographic axes or planes are principally steered by the continuous Lindhard potential. This interaction conserves the energy E, the longitudinal momentum p_parallel, the…

This work explores the dynamical stability of cosmological models where dark matter and dark energy can non-minimally couple to spacetime (scalar) curvature. Two different scenarios are presented here. In the initial case, only dark matter…

It is shown that electromagnetic vortices can act as beam guides for charged particles. The confinement in the transverse directions is due to the rotation of the electric and magnetic fields around the vortex line. Large class of exact…

We derive the gravitational and electrostatic self-energies of a particle at rest in the background of a cosmic dispiration (topological defect), finding that the particle may experience potential steps, well potentials or potential…

We study the mathematical properties of a kinetic equation which describes the long time behaviour of solutions to the weak turbulence equation associated to the cubic nonlinear Schr\"odinger equation. In particular, we give a precise…

We solve the equations of motion and find the Lorentz transformation associated with a kink in superconducting cosmic string. The kink velocity does not depend on its amplitude. The kink amplitude cannot be arbitrary but it varies within…

We show that a cosmological negative spatial curvature can account for both a recently identified phenomenological imprint of the global Hubble flow on galactic rotation curves and for the recently detected cosmic repulsion and cosmic…

We construct two complete invariants of oriented classical knots in space. The value of each invariant on any knot is a set, infinite for the first invariant and finite for the second. The finite set is computed algorithmically from any…

A class of five-dimensional warped solutions is presented. The geometry is everywhere regular and tends to five-dimensional anti-de Sitter space for large absolute values of the bulk coordinate. The physical features of the solutions change…

We study solutions of the mean curvature flow which are defined for all negative curvature times, usually called ancient solutions. We give various conditions ensuring that a closed convex ancient solution is a shrinking sphere. Examples of…

The hypothesis is proposed that under the approximation that the quantum equations of motion reduce to the classical ones, the quantum vacuum also reduces to the classical vacuum--the empty space. The vacuum energy of QED is studied under…

Provided a quantum superconducting condensate is allowed to occupy a curved hyper-plane of space-time, a geometric potential from the kinetic term arises. An energy conservation relation involving the geometric field at every material point…

We discuss the phenomenological model in which the potential energy of the quintessence field depends linearly on the energy density of the spatial curvature. We find that the pressure of the scalar field takes a different form when the…

If spacetime possesses extra dimensions of size and curvature radii much larger than the Planck or string scales, the dynamics of these extra dimensions should be governed by classical general relativity. We argue that in general…

We solve a $1+5$-dimensional cylindrical gravitational-wave solution of the Einstein equation, in which there are two curvature singularities. Then we show that one of the curvature singularities can be removed by an extension of the…

The dynamics of one and two pointlike vortices in a planar quantum gas of spin-0 particles confined in an annular region is considered. New analytical and numerical solutions are found. The concept of stationarity radius, related to the…

We use quantum graphs as a model to study various mathematical aspects of the vacuum energy, such as convergence of periodic path expansions, consistency among different methods (trace formulae versus method of images) and the possible…

We address the problem of the energy conditions in modified gravity taking into account the additional degrees of freedom related to scalar fields and curvature invariants. The latter are usually interpreted as generalized {\it geometrical…

We consider perturbations in a cosmological model with a small coupling between dark energy and dark matter. We prove that the stability of the curvature perturbation depends on the type of coupling between dark sectors. When the dark…

We study the transition between quantum and classical behavior of particles in a gravitational quantum well. We analyze how an increase in the particles mass turns the energy spectrum into a continuous one, from an experimental point of…