Questions tagged [solitons]
Solitons are self-stabilizing solitary wave packets maintaining their shape propagating at a constant velocity. They are caused by a balance of nonlinear and dispersive (where the speed of the waves varies with frequency) effects in the medium.
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$\phi^4$ theory kinks as fermions?
In 1+1 dimensions there is duality between models of fermions and bosons called bosonization (or fermionization). For instance the sine-Gordon theory $$\mathcal{L}= \frac{1}{2}\partial_\mu \phi \...
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Causes of hexagonal shape of Saturn's jet stream
NASA has just shown a more detailed picture of the hexagonal vortex/storm on Saturn:
http://www.ibtimes.com/nasa-releases-images-saturns-hexagon-mega-storm-may-have-been-swirling-centuries-1496218
...
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Soliton Moduli Spaces and Homotopy Theory
The four-dimensional $SU(N)$ Yang-Mills Lagrangian is given by $$\mathcal{L}=\frac{1}{2e^2}\mathrm{Tr}F_{\mu\nu}F^{\mu\nu}$$
and gives rise to the Euclidean equations of motion $\mathcal{D}_\mu F^{\...
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Will tsunami waves travel forever if there was no land?
If there was no land for tsunami waves to collide with, can the waves travel around the globe for forever?
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Does the existence of Higgs imply the existence of Magnetic Monopoles?
I am aware that in theories with spontaneous symmetry breaking, Magnetic Monopoles can exist as topological solitons. Can the same be done with the Standard Model gauge group. I am familiar with the ...
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Could this model have soliton solutions?
We consider a theory described by the Lagrangian,
$$\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\...
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No monopoles in the Weinberg-Salam model
I'm reading Chapter 10.4 on the 't Hooft-Polyakov monopoles in Ryder's Quantum Field Theory.
On page 412 he explains why magnetic monopoles cannot appear in the Weinberg-Salam model.
I'm I right by ...
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Magnetic field lines and knots
As I was reading the book The Trouble With Physics, I encountered a small paragraph which seemed bit confusing. The paragraph goes as follows:
Picture field lines, like the lines of magnetic field ...
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Explanation of the waves on the water planet in the movie Interstellar?
We will ignore some of the more obvious issues with the movie and assume all other things are consistent to have fun with some of these questions.
Simple [hopefully] Pre-questions:
1) If the water ...
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Erik Lentz's faster-than-light soliton
It's well known that, in relativity, if you can go faster than light, you can go backwards in time and create a paradox.
Also, attempts to create "warp-drive" space-times in which something ...
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What is the definition of soliton?
What is the definition of soliton? I've encountered this name in different situations like when the topic discussed is about QFT, fluid dynamics or optics, but I cannot find a general definition. I've ...
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KdV suggests a connection between waves in shallow water and the potential in the Schrödinger equation. What is the intuitive explanation?
The KdV equation
$$v_t+\frac{1}{4}v_{xxx}-\frac{3}{2}vv_x=0$$
was originally invented to model waves in shallow water.
However, it is well known that it also has applications in quantum mechanics. ...
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How do instantons look in real time/spacetime?
Instantons, as I understand it, are mathematical constructions in Euclidean spacetime. Does it imply that instantons do not exist in real spacetime or the instanton tunneling effects does not have ...
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About solitons, what is the difference between kinks and vortices?
I am reading papers about solitons for my small reports, and i could not understand its physical meaning in detail.
I know soliton is solitary wave which behaves like particle. And many text they ...
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Non-chiral skyrmion v.s. Left/Right chiral skyrmion
A skyrmion in a 3-dimensional space (or a 3-dimensional spacetime) is detected by a topological index
$$n= {\tfrac{1}{4\pi}}\int\mathbf{M}\cdot\left(\frac{\partial \mathbf{M}}{\partial x}\times\frac{...
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Why does this condition guarantees there exists only a finite number of discrete energy levels?
I'm reading section 2.2.1 of the book Solitons, Instantons and Twistors by Maciej Dunajski. The section is on the subject of direct scattering.
It is claimed that, considering Schrodinger's equation ...
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Do instantons support quantum bound states?
When one quantizes a scalar in the 1+1 dimensions in the kink background of a double well potential, one finds a spectrum that includes: (1) a zero mode corresponding to the classical particle ...
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Can a "depressive soliton" wave exist? That is, can we have a trough without any crest? Why or why not?
I know that "soliton" waves can consist of a crest without a trough. One would expect the reverse to be true as well.
However, this Wikipedia excerpt says,
So for this nonlinear gravity ...
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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, ...
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Are QFT solitons expected to represent standard model particles? Or strings?
Is work on solitons in QFT's focused on finding solutions that could represent the fundamental particles of the Standard Model, or is the work focused on finding particles Beyond The Standard Model? ...
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Distinction of Dirac monopole and Polyakov-'t Hooft monopole
Can anybody explain the physical difference between Dirac monopole and Polyakov monopole?
First, let me write down what I know briefly.
Dirac monopole
It comes from the symmetry of Maxwell ...
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Spontaneous discrete symmetry breaking always implies domain walls
I've read several times that if a discrete symmetry is spontaneously broken, then there exist domain walls that interpolate between the different vacua. However, Weinberg says that if the former ...
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Link between integrability and soliton solutions
I have been doing some research on the properties and dynamics of solitons (in particular, solitons in superfluids) and several works and papers mention the link between solitonic solutions and ...
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Significance of massive states in string theory
A free superstring has an infinite tower of states with increasing mass. The massless states correspond to the fields of the corresponding SUGRA. In "Quantum Fields and Strings: A Course for ...
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Theory on domain walls
In Baryons in Quantum Chromodynamics, Zohar Komargodski have slide:
I wanna understand:
Why domein wall can have nontrivial worldvolume theory?
When such solitonic objects have interior degrees of ...
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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 ...
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Is optical-illusion responsible for Loch Ness monster? [closed]
When you look out at the white-caps on a wind-swept lake, you can see a dark, undulating pattern under the crests of the white-caps.
Could this shadow-like area explain the sightings? Revised, see ...
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Do plane waves exist in nature? [duplicate]
Drop a stone in the pond...a wave propagates radially from the source. The conservation of energy says the wave must decay proportionally to the radial distance. If I drop a steel I-beam in the pond, ...
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How to Diagonalize Self-Interacting Scalar Hamiltonian for Mass Term from Polyakov Paper?
So, I'm reading through Polyakov's paper from 1974, "Particle Spectrum in Quantum Field Theory." I'm trying to work through all of the steps and properly understand everything. For context, ...
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Why can you make $V$ stationary with respect to a parameter of the field in Derrick's theorem?
I'm going over Coleman's derivation of Derrick's theorem for real scalar fields in the chapter Classical lumps and their quantum descendants from Aspects of Symmetry (page 194).
Theorem: Let $\phi$ ...
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Are static black holes solitons?
If we start with the Einstein-Hilbert action with no matter, and consider time independent finite energy field configurations, then any static solution (e.g Schwarzchild metric) seems to be a soliton-...
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Hilbert transform in soliton paper
I asked this question over at the Mathematics SE, see here, but have not gotten any responses, so I figured I might as well try here as well. While the question is mathematical, it does appear in a ...
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Different between droplet and a soliton
I am working on the droplet state in a Bose-Bose mixture. I have a question about the difference between the droplet liquid state and the soliton state: How we can treat a droplet state? And how do we ...
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Besides vortex rings, are there other types of traveling waves that can carry matter as well as energy?
Vortex rings are a special soliton wave that are known to carry matter over a distance as well as energy. This can easily be demonstrated using a cardboard 'vortex canon' filled with smoke. The smoke ...
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$AdS_3$ soliton of Witten - for Hawking-Page transition
Are there explicit AdS$_3$ soliton solution?
in the sense of Witten's Anti De Sitter Space And Holography and Hawking-Page transition paper, by doing a
$$\tau_E, y ,r \to y, \tau_E ,r$$
from a ...
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Moduli spaces in string theory vs. soliton theory
In both string theory and soliton theory, moduli spaces are frequently used.
As far as I known, for soliton theory, moduli spaces are something like collective coordinates for solitons, and for ...
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Soliton solutions of the Gross-Pitaevskii equation
The Gross-Pitaevskii equation admits soliton solutions such as: $$\psi(x)=\psi_0 sech(x/\xi),$$
where $\xi$ is the healing length defined by: $\xi=\frac{\hbar}{\sqrt{m \mu}}$, with $\mu$ being the ...
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Few basic questions about instantons
For the $SU(2)$ Yang-Mill's theory, (1) how can one understand that the finite action solutions of the Euclidean equations of motion (called Instantons) exhibit tunneling effects? (2) Since, this ...
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Why linear wave equation does not have solitonic solutions?
As many people define solitary waves they are localized pulses that propagate without changing the shape. As far as I know the same pulses exist in ordinary wave equation ! why should we look for ...
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Derrick’s theorem
Consider a theory in $D$ spatial dimensions involving one or more scalar fields $\phi_a$, with a Lagrangian density of the form
$$L= \frac{1}{2} G_{ab}(\phi) \partial_\mu \phi_a \partial^\mu \phi_b- ...
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Energy of moving Sine-Gordon breather
A few days ago I stumbled across the formula for the energy of a moving breather for the sine-Gordon equation
$$ \Box^2 \phi = -\sin\phi.$$ The energy in general is given by ($c=1$)
$$ E = \int_{-\...
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What is the intuition for topological currents?
The reason for topological stability of a kink solution in scalar field theory in $1+1$ dimensions is the fact that the finite energy scalar field cannot be continuously deformed into a vacuum.
How ...
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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: $\...
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Must a field approach one of its vacua to have finite energy?
I'm reading these Cornell lectures on solitons (link doesn't work right now, but it just worked yesterday), and I can't seem to prove what I thought would be a simple analysis exercise.
Namely, ...
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Domain walls intersection
I was reading this article(On domain shapes and processes in supersymmetric
theories). In the paragraph about domain walls intersection (paragraph $4$, page $7$) the authors say:
In a one-field ...
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Is there a difference between topological defects and topological soliton?
Is there a difference between topological defects and topological soliton? Or are these objects the same thing? I ask this because it very common find some papers whose the authors itself refer, for ...
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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'...
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Spin of skyrmion
Baryons can be considered as solitions in Skyrme model(See also this post.):
Such Lagrangian haven't any information about number of colors. Bosonic or fermionic nature of baryons depends on number ...
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Intuition about ADHM construction
I'm trying to understand reasons, why self-dual Yang-Mills equation can be reduced to algebraic equations. It's seem like a miracle.
In article Construction of Instanton and Monopole Solutions and ...
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How solitons are related to particle physics?
Recently, I read a paper about introduction to solitons.
Author said that the solutions of sine-Gordon equation can be candidate for modeling elementary particles and there are some applications in ...
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