Abstract: Considering a scenario where our universe is taken
as a 3d domain wall embedded in a 5d dimensional Minkowski
space-time, we explore the existence of a richer class of solitonic
solutions and their consequences for accelerating universes driven by
collisions of bulk particle excitations with the walls. In particular it
is shown that some of these solutions should play a fundamental role
at the beginning of the expansion process. We present some of these
solutions in cosmological scenarios that can be applied to models
that describe the inflationary period of the Universe.
Abstract: In this paper, we investigate the low-lying energy
levels of the two-dimensional parabolic graphene quantum dots
(GQDs) in the presence of topological defects with long range
Coulomb impurity and subjected to an external uniform magnetic
field. The low-lying energy levels of the system are obtained within
the framework of the perturbation theory. We theoretically
demonstrate that a valley splitting can be controlled by geometrical
parameters of the graphene quantum dots and/or by tuning a uniform
magnetic field, as well as topological defects. It is found that, for
parabolic graphene dots, the valley splitting occurs due to the
introduction of spatial confinement. The corresponding splitting is
enhanced by the introduction of a uniform magnetic field and it
increases by increasing the angle of the cone in subcritical regime.