Particles in Interaction and Wave Turbulence, by Isabelle Gallagher

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Abstract: A huge system of equations describes the interactions of waves, such as those found in fluid dynamics and quantum mechanics. The theory of wave turbulence is designed to extract from those equations a ‘master equation’ that retains the physical system’s essential features. The interest of such a procedure is to drastically decrease the complexity of the system while exhibiting some universal behavior despite the underlying complexity of the interactions. This theory is yet to be set on rigorous foundations. In this talk, Isabelle Gallagher will focus on the more tractable case where the interactions are between particles (like atoms in a gas) instead of waves. She will show that the ‘master equation’ turns out to be Boltzmann’s famous equation, which he formally derived in 1872.