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SUMMARY:The Subtle Road to Equilibrium in the FPUT Model - David K. Campbe
 ll (Boston University)
DTSTART:20190523T120000Z
DTEND:20190523T130000Z
UID:TALK125395@talks.cam.ac.uk
CONTACT:Anne Herrmann
DESCRIPTION:The interpretation and consequences of the celebrated Fermi\, 
 Pasta\, Ulam\, Tsingou (FPUT) numerical experiment have challenged scienti
 sts for more than six decades. \nThe history of how the original FPUT disc
 overy led to the theory of “solitons\,” was key in the understanding o
 f Hamiltonian chaos\, and led to the birth of “nonlinear science” is w
 ell documented\, but there are many fascinating details which are only now
  being explored and understood. In this presentation\, I will discuss two 
 recently studied examples: namely\, the details of the existence and break
 down of recurrences and super-recurrences in both the alpha- and beta- ver
 sions of the FPUT system\, and the remarkable intermittent dynamics\, invo
 lving long-time\, large deviations\, that occur once the systems has nomin
 ally reached equilibrium. \n\nIn the first study [1]\, we find  higher-ord
 er recurrences (HoR)s—which amount to “super-super-recurrences” in b
 oth the alpha and beta models.  The periods of these HoR scale non-trivial
 ly with energy due to apparent singularities caused by nonlinear resonance
 s\, which differ in the two models. Further\, the mechanisms by which the 
 HoR breakdown differ strikingly in the two models. \n\nIn the second study
  [2]\,  we find that the dynamics at equilibrium is characterized by a pow
 er-law distribution of excursion times far off equilibrium\, with divergin
 g variance. Long excursions arise from sticky dynamics close to localized 
 excitations in normal mode space (q-breathers). Measuring the exponent all
 ows to predict the transition into nonergodic dynamics. \n\n*Work in colla
 boration with Carlo Danielli\, Sergej Flach\, and Salvatore Pace.\n\n[1]  
 Salvatore D. Pace and David K. Campbell\, “Behavior and Breakdown of Hig
 her-Order-Fermi- \n   Pasta-Ulam-Tsignou Recurrences\,” arXiv:181100663 
 (Chaos\, to appear)\n\n[2]  C. Danieli\, D. K. Campbell\, and S. Flach\, 
 “Intermittent many-body dynamics at equilibrium\,”\n   Phys. Rev. E 95
  060202(R) (2017).\n
LOCATION:MR14\,  Centre for Mathematical Sciences\, Wilberforce Road\, Cam
 bridge
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