This site has a 3d grid looking like a sombrero as a logo. Does it represent some specific physical phenomenon or is it just art?
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$\begingroup$ Mexican Hat Potential. $\endgroup$– Abhimanyu Pallavi SudhirJan 24, 2014 at 12:53
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1$\begingroup$ Possible duplicate: meta.physics.stackexchange.com/q/949/17609 $\endgroup$– ŘídícíJan 24, 2014 at 16:54
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3 Answers
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It could very well be the diagram that is always drawn for spontaneous symmetry breaking (SSB)! SSB is quite an important phenomenon, and its sort of the foundation for the Higgs mechanism that got a Nobel prize this past October.
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4$\begingroup$ Right. It's called the "Mexican hat potential" in much of the world, especially the third world, "champagne bottle profile" (bottom of the bottle) in the rich communities of the first world. In the second, post-socialist world, we still call it "the Landau buttocks" because Lev Landau (USSR) found the basic two-minimum quartic function underlying the Higgs mechanism in the 1930s and constructed his precious theory of second-order phase transitions using this function. $\endgroup$ Jan 24, 2014 at 11:53
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$\begingroup$ The Higgs mechanism is pretty much a direct result of the translation of Landau's insights from the 1930s using the dictionary between statistical physics (and its partition sums) and the quantum field theory (and its partition sums expressed by the path integral) on the other side. The circle of minima (just two points in the Landau's real case) correspond to the places where the system actually wants to find itself, the vacuum configuration. $\endgroup$ Jan 24, 2014 at 11:54
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1$\begingroup$ A proof that the person who included the image actually meant the Mexican hat potential: en.wikipedia.org/wiki/File:Mexican_hat_potential_polar.svg $\endgroup$ Jan 24, 2014 at 11:56
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$\begingroup$ Just for definiteness, I think the earliest suggestion to use this potential comes from DavidZ's comment on my answer in the first "What should our site look like?" question. $\endgroup$ Jan 26, 2014 at 16:37
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Whilst I can almost guarantee the author of the logo did not have this in mind when creating it; a physical phenomenon that may be described via such a potential is the Two-Level-System (TLS) defects we see in superconducting circuitry that involve Josephson junctions. In a recent paper we describe what occurs when an oxygen atom delocalises around an Al-Al bond axis. The potential of the rotationally symmetric case is a "mexican hat" - exactly like the logo.
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1$\begingroup$ Just for definiteness, I think the earliest suggestion to use this potential comes from DavidZ's comment on my answer in the first "What should our site look like?" question. $\endgroup$ Jan 26, 2014 at 16:37
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I don't know the original motivation of the author, but I reckon it could represent a wave on a membrane or the wave function of a particle for a symmetrical condition.
