All Questions
11
questions
4
votes
0
answers
110
views
Why are non-perturbative solutions important and how to take them into account?
I am guilty of studying physics with an almost complete focus on the mathematical constructions (together with the motivating physical premisses) and ignoring the semantic physical intuition, which I'...
- 1,742
3
votes
1
answer
306
views
Stability and topological charge of kink (anti-kink) solutions (soliton)
I am reading the book << Gauge theory of elementary particle physics >>. In chapter 15, it presents a model having finite-energy solution.
First, we have a $1+1D$ spacetime model
\begin{...
- 995
7
votes
0
answers
286
views
Non-topological solitons in condensed matter physics
As I know most well-known soliton solutions in condensed matter physics are topological ones: kinks, domain walls etc.
In field theory there are several examples on non-topological solitons: Q-balls, ...
- 546
3
votes
2
answers
502
views
From the viewpoint of field theory and Derrick's theorem, what's the classical field configuration corresponding to particle? Is it a wavepacket?
In the framework of QM, we have known that particle, like electron, cannot be a wavepacket, because if it is a wavepacket then it will become "fatter" due to dispersion and it's impossible.
However ...
- 5,971
3
votes
2
answers
328
views
Why can kink not tunnel to the vacuum, making it topologically stable?
Why can the kink
$$\phi(x)=v\tanh\left(\frac{x}{\xi}\right)$$
not tunnel into vacuum $+v$ or $-v$ (with spontaneous symmetry breaking in the vacuum)?
From the boundary condition, $\phi(x)\rightarrow \...
- 49
2
votes
1
answer
643
views
Dimension analysis in Derrick theorem
The following image is taken from p. 85 in the textbook Topological Solitons by N. Manton and P.M. Sutcliffe:
What I don't understand from the above statement:
why $e(\mu)$ has minimum for ...
- 651
0
votes
1
answer
550
views
Vortex in D dimensions soliton
let us consider
the two-dimensional configuration shown in Fig. 3.1a. The lengths of the arrows
represent the magnitude of φ, while their directions indicate the orientation in
the $φ_1 -φ_2$ plane. ...
user12906
1
vote
0
answers
668
views
Domain wall and kink solutions from solitions equations
A general solition equation can be obtaion from scalar field theory $$\varphi(x) = v\tanh\Bigl(\tfrac{1}{2}m(x - x_0)\Bigr),\tag{92.6}$$
where $x_0$ is a constant of integration when we drived this ...
user12906
-1
votes
1
answer
297
views
Oscillon and soliton
I want to know the major difference between oscillon and soliton in terms of radiating energy with respect to time and position. And what about their localization?
- 21
4
votes
0
answers
194
views
Asymptotic limit of the two kink solution of the sine-gordon equation
I am reading a paper on the sine-gordon model. The solution for a two kink solution is given as:
$$\phi=4\arctan\left(\frac{\sinh\frac{1}{2}(\theta_1-\theta_2)}{(a_{12})^\frac{1}{2}\cosh\frac{1}{2}(\...
user7757
15
votes
1
answer
993
views
Could this model have soliton solutions?
We consider a theory described by the Lagrangian,
$$\mathcal{L}=i\bar{\Psi}\gamma^\mu\partial_\mu\Psi-m\bar{\Psi}\Psi+\frac{1}{2}g(\bar{\Psi}\Psi)^2$$
The corresponding field equations are,
$$(i\...
- 1,714