All Questions
12
questions
0
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35
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How to derive the ODE from the EOM of vortex?
In the Lagrangian mode we have the equation of motion
\begin{align}
\partial_\mu F^{\mu\nu}&=j^\nu. \\
D_{\mu }D^{\mu}\phi +\mu^{2}\phi-\lambda(\phi^{*}\phi)\phi &=0.
\end{align}
Since we ...
- 29
0
votes
0
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99
views
What is the topology of sine-Gordon equation?
In one pdf on solitons, I am finding the following written
For the sine-Gordon theory, it is much better to think of $\phi$ as a field modulo $2\pi$, i.e. as a function $\phi: R \rightarrow S_{1}$. ...
1
vote
0
answers
140
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Topological charge change in QFT
Is it possible for the topological charge to change in quantum field theory?
The proofs in the following paper: Quantum soliton operators for vortices and superselection rules
are all based on the ...
- 1,212
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41
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Boundary conditions for radial solution of gauged topological vortices
I am following the book Topological Solitons by Manton and Sutcliffe and I am struggling to understand a boundary condition they choose to find the radial solutions of gauged vortices with finite ...
6
votes
0
answers
286
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An interesting observation: Ordered, up and down movement of vortex rings in water
I was watching a video on David Tong's research work when I stumbled upon a peculiar movement of vortex rings in water. Around the 1:20 time mark, Baths and Quarks: Solitons explained, David Tong uses ...
user242231
4
votes
1
answer
804
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How does the $U(1)$ global symmetry break in the gauged $XY$ model?
I'm studying the particle vortex duality, and I'm confused how we're able to say that in the Coulomb phase, the "hidden" $U(1)$ global magnetic symmetry spontaneously breaks.
gauged XY model: $\...
- 737
2
votes
0
answers
83
views
Topological solitons in general dimension
Let's begin with a simple model of a field theory:
$$
\mathcal{H} = \int ( \nabla \phi ) ^2
$$
where $\phi$ is an angle valued field defined on some space. We suppose for the moment to freeze out ...
- 781
2
votes
2
answers
160
views
Violation of Derrick's theorem for finite energy, time independent solutions?
How are vortices the finite energy time independent solutions for 2+1 dimensions abelian Higgs model? Doesn't it violate Derrick's theorem that there are no finite energy time independent solutions in ...
- 381
2
votes
0
answers
62
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Why do vortices scatter at right-angles
I have been taking a course on non-perturbative physics and currently the teacher is away so I cannot ask him.
In the lectures, he made the claim that a pair of vortices in the abelian-Higgs model ...
- 841
1
vote
0
answers
301
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Mathematical understanding of vortex solitons
I am wondering if anyone has ever come up with a mathematical description of something that (to me, and I am no expert) look like soliton vortexes.
The example I can think of is if you create two ...
- 129
1
vote
1
answer
160
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What is beam confinement?
In the context of the propagation of an electromagnetic wave and optical vortex solitons, I came across the term "beam confinement". Particularly, beam confinement requires the amplitude of the ...
2
votes
2
answers
395
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Nomenclature clarification concerning solitons
My experience with solitons is restricted to the classical setting, namely solutions to the quartic interaction $\phi^4$, the Sine-Gordon equation, and Korteweg–de Vries equations. I was explicit to ...
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