37 votes

Will tsunami waves travel forever if there was no land?

The waves will not travel forever. Water particles moving against and around each other will have friction, and the friction will cause motion energy to be converted to heat (which will dissipate ...
22 votes

Will tsunami waves travel forever if there was no land?

To answer this, I would appeal to the general principle which we call the 2nd law of thermodynamics. One way of expressing it is that the entropy of an isolated system cannot decrease. This means that ...
13 votes

Will tsunami waves travel forever if there was no land?

Of course, no. Tsunamis are a series of pressure waves with a longitudinal mode and have much higher wavelengths, speed, and period than the normal ones. Normal ocean waves only involve motion of the ...
  • 3,192
9 votes
Accepted

Moduli spaces in string theory vs. soliton theory

This is a situation where knowing the history of the terminology can be helpful. The QFT/string theory terminology comes from algebraic geometry, where the term moduli space is used for any space ...
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9 votes
Accepted

About solitons, what is the difference between kinks and vortices?

A soliton is a localized, non-dispersive solution of a nonlinear theory in Euclidean space. It certainly is a real object: you have a famous story about a certain John Russell who observed soliton-...
  • 374
7 votes
Accepted

Explanation of the waves on the water planet in the movie Interstellar?

The following interpretations are taken from Thorne [2014]. Chapter 17, entitled Miller's Planet, discusses the issue of the large waves on the water planet in the movie Interstellar. There Kip ...
7 votes
Accepted

KdV suggests a connection between waves in shallow water and the potential in the Schrödinger equation. What is the intuitive explanation?

I'm not sure what intuition you are seeking in similarities of mathematical modeling... It's like intuition about the similar beat of two very different pieces of music? I fear it is all in the math. ...
7 votes
Accepted

How to Diagonalize Self-Interacting Scalar Hamiltonian for Mass Term from Polyakov Paper?

can someone point me in the right direction at least to diagonalize the modified Hamiltonian? This answer explains how to diagonalize the Hamiltonian and how to derive the $n$-dependent term in $M_n$....
7 votes

Erik Lentz's faster-than-light soliton

This new question links a recent paper J. Santiago, S. Schuster and M. Visser, 2021, “Generic warp drives violate the null energy condition”, arXiv:2105.03079. which counts as “technical analysis” ...
  • 13.1k
7 votes
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Soliton solutions of the Gross-Pitaevskii equation

If you relabel $x$ as "$t$" can think of it as mechanics problem $$ \frac{d^2 \psi}{dt^2}= g \psi^3 -\mu \psi. $$ As $$ g \psi^3 -\mu \psi = \frac{d}{d\psi}\left(\frac 14 g \psi^4 -\frac 12 ...
  • 43.4k
6 votes

Do plane waves exist in nature?

No, "real" plain waves do not exist in nature and neither does anything "exist" the way a physical theory describes it. That's about as trivial as it is irrelevant. We are not performing experimental ...
6 votes

From the viewpoint of field theory and Derrick's theorem, what's the classical field configuration corresponding to particle? Is it a wavepacket?

A particle is not a wavepacket. And there are no particle states for interacting theories. We define particle states in QFT by expanding the free field into its Fourier modes and using these modes as ...
  • 111k
5 votes
Accepted

Why can you make $V$ stationary with respect to a parameter of the field in Derrick's theorem?

OK, perhaps the notation in Ref. 1 is a bit confusing. Let us elaborate on Derrick's No-Go theorem: Derrick's No-Go theorem: For the number of spatial dimensions $D>2$, the only time-...
  • 175k
5 votes
Accepted

Few basic questions about instantons

1) Suppose that you have two configurations (here I've used Coulomb gauge with euclidean time $\tau$): $$ \tag 0 A_{i}(x) = \begin{cases} 0 = U^{(0)}\partial_{i}(U^{(0)})^{-1}, \quad \tau = -\infty \\ ...
  • 8,609
5 votes
Accepted

Distinction of Dirac monopole and Polyakov-'t Hooft monopole

A (generalized) 't Hooft-Polyakov monopole and a Dirac monopole with a Dirac string attached are two types of magnetic monopoles, which differ in several ways, as OP and user ACuriousMind correctly ...
  • 175k
5 votes
Accepted

What is the intuition for topological currents?

The topological charge which is the space integral of the zeroth component of the topological curent is responsible for the stability of the kink: A configuration with a nonvanishing topological ...
5 votes

Spontaneous discrete symmetry breaking always implies domain walls

If we start in the unbroken phase, and if there are multiple degenerate vacua after spontaneously breaking the symmetry, generically we should have domain walls. The reason is that as we pass the ...
  • 6,712
4 votes

$\phi^4$ theory kinks as fermions?

Quantum fluctuations in the kink sectors of Sin-Gordon and the quartic interaction theory are described by reflectionless Pöschl-Teller-Operators, which form a SUSY-Chain with $N$ elements. The second ...
  • 333
4 votes

Do plane waves exist in nature?

Plane waves are useful because we can take any physical function of space, e.g. some field, and Fourier transform it to represent it as a sum (well, integral) of plane waves. This is often a very ...
4 votes

Why can kink not tunnel to the vacuum, making it topologically stable?

Here we assume that OP's question asks about $\phi^4$-theory in 1+1D, where the lagrangian density reads $$\tag{1} {\cal L}~=~\frac{1}{2}\dot\phi^2 -{\cal U}, \qquad {\cal U}~:=~ \frac{1}{2} \phi^{\...
  • 175k
4 votes

Could this model have soliton solutions?

The answer to this question is no assuming dimensions higher than 1+1. This can be seen observing that the equation of motion for the fermionic field is just the limit of mass going to infinity of a ...
  • 3,630
4 votes
Accepted

In which representation are monopoles of grand unifying theories classified?

Monopoles are somewhat subtle, and there are different layers towards their classification, each being more correct than the previous one. Quick remark: what is usually called the $\text{SO}(10)$ ...
4 votes
Accepted

Soliton solution of the NLS equation

The usual soliton for the NLS is $$ \psi(x,t)=e^{ikx-i\omega t}\sqrt{\frac{\alpha}{m\lambda}}{\rm sech}(\sqrt{\alpha}(x-Ut) $$ where $m$ is the mass and $\lambda$ is the coeficient of the $|\psi|^2\...
  • 43.4k
4 votes
Accepted

Sum of topological charges is the Euler characteristic

You don't explain what you mean by "topological charges" but I expect you mean the sum of the Hopf indices of the zeros of a tangent-vector field on a manifold. The resulting Poincare-Hopf ...
  • 43.4k
4 votes

Erik Lentz's faster-than-light soliton

Put shortly, there are physical subliminal warp drive solutions in the literature, while superluminal solutions are/have been known earlier to be problematic. There were the following recent inputs on ...
4 votes

Non-Perturbative Effects Of Soliton in Quantum Field Theory

More generally, if one is doing perturbation theory in some coupling constant $g$, the result is a power series in $g$, i.e. non-negative powers of $g$. To get negative/inverse powers of $g$, one must ...
  • 175k
3 votes

How do instantons look in real time/spacetime?

This question has been studied in some detail for instantons in QM, for example the standard instanton in the potential $V=(x^2-x_0^2)^2$. Naive analytic continuation $\tau\to it$ gives a complex ...
  • 17.5k
3 votes
Accepted

Why does this condition guarantees there exists only a finite number of discrete energy levels?

It follows from Bargmann's limit. The Bargmann bound is well known for a three-dimensional central potential [1, Thm. XIII.9] [2,3]: $$ N(\ell) < \frac{1}{2\ell + 1} \int_0^\infty r V^-(r) dr $$ ...
  • 6,416
3 votes

M branes/D branes are solitons?

A brane is not "by definition" "just a soliton". What is true is that the M2- and the M5-branes are mostly described by being certain "solitonic" solutions to eleven-dimensional supergravity. "...
  • 111k

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