20 research outputs found
Understanding oscillons: standing waves in a ball
Oscillons are localised long-lived pulsating states in the three-dimensional
theory. We gain insight into the spatio-temporal structure and
bifurcation of the oscillons by studying time-periodic solutions in a ball of a
finite radius. A sequence of weakly localised {\it Bessel waves} -- nonlinear
standing waves with the Bessel-like -dependence -- is shown to extend from
eigenfunctions of the linearised operator. The lowest-frequency Bessel wave
serves as a starting point of a branch of periodic solutions with exponentially
localised cores and small-amplitude tails decaying slowly towards the surface
of the ball. A numerical continuation of this branch gives rise to the
energy-frequency diagram featuring a series of resonant spikes. We show that
the standing waves associated with the resonances are born in the
period-multiplication bifurcations of the Bessel waves with higher frequencies.
The energy-frequency diagram for a sufficiently large ball displays sizeable
intervals of stability against spherically-symmetric perturbations.Comment: 13 pages, 12 figure
Monopole Vacuum in Non-Abelian Theories
It is shown that, in the theory of interacting Yang -Mills fields and a Higgs
field, there is a topological degeneracy of Bogomol'nyi-Prasad-Sommerfield
(BPS) monopoles and that there arises, in this case, a chromoelectric monopole
characterized by a new topological variable that describes transitions between
topological states of the monopole in the Minkowski space (in just the same way
as an instanton describes such transitions in the Euclidean space). The limit
of an infinitely large mass of the Higgs field at a finite density of the BPS
monopole is considered as a model of the stable vacuum in the pure Yang-Mills
theory. It is shown that, in QCD, such a monopole vacuum may lead to a rising
potential, a topological confinement and an additional mass of the
meson. The relationship between the result obtained here for the generating
functional of perturbation theory and Faddeev-Popov integral is discussed