Drowning by numbers: topology and physics in fluid dynamics

Amaury Mouchet (1, 2)

1 FDP - Fédération de recherche Denis Poisson
2 LMPT - Laboratoire de Mathématiques et Physique Théorique

Since its very beginnings, topology has forged strong links with physics and the last Nobel prize in physics, awarded in 2016 to Thouless, Haldane and Kosterlitz " for theoretical discoveries of topological phase transitions and topological phases of matter" , confirmed that these connections have been maintained up to contemporary physics. To give some (very) selected illustrations of what is, and still will be, a cross fertilization between topology and physics, hydrodynamics provides a natural domain through the common theme offered by the notion of vortex, relevant both in classical (§ 2) and in quantum fluids (§ 3). Before getting into the details, I will sketch in § 1 a general perspective from which this intertwining between topology and physics can be appreciated: the old dichotomy between discreteness and continuity, first dealing with antithetic thesis, eventually appears to be made of two complementary sides of a single coin.

Mots clés: Kosterlitz-Thouless transition; vortex; knots; topology; topological phase

Domaines: Enseignement de la physique [physics.ed-ph]; Histoire de la Physique [physics.hist-ph]; Physique Quantique [quant-ph]; Histoire et perspectives sur les mathématiques [math.HO]; Topologie générale [math.GN]; Dynamique des Fluides [physics.flu-dyn]

Amaury Mouchet. Drowning by numbers: topology and physics in fluid dynamics. Imagine maths 6, Between culture and mathematics,, 2018. ⟨hal-01530467⟩