Status  Confirmed 
Seminar Series  IPHTGEN 
Subjects  physics 
Date  Tuesday 3 September 2019 
Time  11:00 
Institute  IPHT 
Seminar Room  Salle Claude Itzykson, Bât. 774 
Speaker's Last Name  Alexander Turbiner 
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Speaker's Institution  ICNUNAM, Mexico and Stony Brook University, USA 
Title  Choreography in Physics (living in motion, moving polymers, superintegrability etc) 
Abstract  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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