Statut  Confirmé 
Série  IPHTGEN 
Domaines  physics 
Date  Mardi 3 Septembre 2019 
Heure  11:00 
Institut  IPHT 
Salle  Salle Claude Itzykson, Bât. 774 
Nom de l'orateur  Alexander Turbiner 
Prenom de l'orateur  
Addresse email de l'orateur  
Institution de l'orateur  ICNUNAM, Mexico and Stony Brook University, USA 
Titre  Choreography in Physics (living in motion, moving polymers, superintegrability etc) 
Résumé  By definition the choreography (dancing curve) is a closed trajectory on which $n$ classical bodies move chasing each other without collisions. The first choreography (the Remarkable Figure Eight) at zero angular momentum was discovered unexpectedly by C Moore (Santa Fe Institute) at 1993 for 3 equal masses in $R^3$ Newtonian gravity numerically. At the moment about 6,000 choreographies in $R^3$ Newtonian gravity are found, all numerically for different $n > 2$. A number of 3body choreographies is known in $R^2$ Newtonian gravity, for LennardJones potential (hence, relevant for molecular physics), and for some other potentials, again numerically; it might be proved their existence for quarkonia potential. \par Does exist (non)Newtonian gravity for which dancing curve is known analytically?  Yes, a single example is known  it is algebraic lemniscate by Jacob Bernoulli (1694)  and it will be a concrete example of the talk. Astonishingly, $R^3$ Newtonian Figure Eight coincides with algebraic lemniscate with $\chi^2$ deviation $\sim 10^{7}$. Both choreographies admit any odd numbers of bodies on them. Both 3body choreographies define maximally superintegrable trajectory with 7 constants of motion. \par Talk will be accompanied by numerous animations. 
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