When an important part of the dynamics of multiple particles, or fields, is described in terms of a reduced dynamics with just a few collective coordinates, then the reduced dynamics is generally characterised by a curved configuration space together with a potential function. Applications include soliton/antisoliton dynamics, coupling of soliton dynamics to internal shape modes, and oscillon...
We show in a constructive fashion that, contrary to the long-held belief, there is plenty of nonlinear partial differential systems in four independent variables that are integrable in the sense of soliton theory beyond a few previously known examples like (anti-)self-dual Yang--Mills equations or (anti-)self-dual vacuum Einstein equations.
Namely, using a novel class of Lax pairs related...
In 1+1 dimensions, soliton quantum states are usually described by coherent states, but as Coleman noted in his 1975 Erice lectures, this approach fails in higher dimensions because of divergent energy densities. We show that even in 1+1 dimensions the proper states are deformations of coherent states. In the 3+1-dimensional ϕ4 double-well model, the leading deformation—a squeeze—already...
We investigate phenomenological features in Standard Model on a domain world brane in five-dimensional space-time, which is constructed in arXiv: 1802.06649. In this model, the gauge fields non-minimally couple to the Higgs field, by which the gauge fields are localized on the four-dimensional space-time. At the same time, this coupling gives rise to a new interaction such as Zhh. This...
Dislocations, as topological defects in crystal lattices, are fundamental to understanding plasticity in materials. Similar periodic structures also arise in continuum field theories, such as chiral soliton lattices (CSLs), which appear in condensed matter systems like chiral magnets and in high-energy contexts such as quantum chromodynamics in strong magnetic field or under rapid rotation....
Calorons are finite action solutions to (anti-)selfdual Yang-Mills equations on partially compact space S^1 times R^3.
These objects can be constructed as a periodic array of instantons in R^4 naively, however, the topological character of calorons is quite different from that of instantons. In this talk, we focus on this difference and re-examine the prior research on the topological...
This is possible because the su(2) algebra only reflects some
properties of the SO(3) and SU(2) groups. I show that in a realization
of spin-1/2 configurations as topological solitons with long-range
Coulomb interaction, pairs of such solitons can be coupled to spin-0
and spin-1 states. Numerical calculations of these configurations show
that the spin-1 states have slightly higher energy...
For liquid crystals there are experimentally recreated long-range e.g. Coulomb-like interactions between topological charges. Combining liquid crystal Landau-de Gennes model having Higgs-like potential of SO(3) vacuum, with 4-th order Skyrme term, we get effective Coulomb potential with Gauss law counting topological charge, then electromagnetism from Lorentz invariance. Regularization of...
This talk concerns long-range kinks, topological solitons in 1+1 dimensions. Because of their highly interactive nature, studying their dynamics becomes complex and requires specialized numerical methods to initiate the dynamics. We will mainly focus on the extreme cases with double long-range kinks, which are long-range in both tails. We search for resonance windows and possible energy...
Using quantum arguments, Witten proposed that a magnetic monopole acquires electric charge in a theta vacuum. In a formulation where the theta vacua of a gauge theory are described by the vacua of a massless Chern-Simons 3-form, we showed that the Witten effect can already be captured at the level of effective classical equations of motion. Beyond this, we numerically demonstrated that a...