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SUMMARY:Chaotic processes\, erratic functions and random matrix theory
DTSTART:20260422T131000Z
DTEND:20260422T141000Z
DTSTAMP:20260503T013300Z
UID:indico-event-51592@agenda.infn.it
DESCRIPTION:Speakers: Jacob Sonnenschein\n\nChaotic processes often admit 
 a description in terms of erratic functions of a certain continuous varia
 ble. Examples of such a behavior are the scattering angle as a function of
  the incident angle in a pinball experiment\, the leaky torus phase shift
  as a function of the wave-number and the decay amplitude of highly excit
 ed string state (HES) into two low-mass states or a scattering amplitude 
 of a HES with three low-mass states as a function of an angle. I will pre
 sent a novel measure of chaotic behavior based on a map between the set of
  maxima of the erratic functions and the eigenvalues of random matrices a
 nd the corresponding spectral form factor. I will introduce the notion o
 f multi-dimensional chaos that applies to processes described by erratic 
 functions of several dynamical variables.The classical and quantum scatter
 ing off a pinball system will be described. I will show that the eigenval
 ues of the S-matrix are distributed according to the Circular Orthogonal E
 nsemble (COE) in random matrix theory (RMT)\, provided the setup be asymme
 tric and the wave-number be large enough. I will then consider the elect
 ric potential associated with charges randomly located on a plane as a to
 y model that generalizes the scattering from a leaky torus. I will propose
  several methods to analyze the two dimensional spacings between the extr
 ema of this function. The latter follow a repulsive Gaussian β-ensemble 
 distribution even for Poisson-distributed positions of the charges. Thes
 e methods will be applied to the case of a chaotic S-matrix and of the qua
 ntum pinball scattering. The spacings between nearest neighbor extrema po
 ints and ratios between adjacent spacings for this case follow a logistic
  and Beta distributions correspondingly. A generalization of the spectral
  form factor will be introduced and determined. We conjecture about a pot
 ential relation with random tensor theory.\n\nhttps://agenda.infn.it/event
 /51592/
LOCATION:GGI - Room B
URL:https://agenda.infn.it/event/51592/
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