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SUMMARY:Numerical approaches for investigating the chaotic behavior of non
 linear disordered lattice models - Haris Skokos (University of Cape Town)
DTSTART:20230526T151500Z
DTEND:20230526T160000Z
UID:TALK200653@talks.cam.ac.uk
DESCRIPTION:We present various numerical tools for studying the chaotic dy
 namics of multidimensional Hamiltonian systems\, focusing our analysis on 
 the chaotic evolution of initially localized energy excitations in the dis
 ordered Klein-Gordon (DKG) oscillator chain in one spatial dimension. The 
 system&rsquo\;s linear modes are exponentially localized by disorder and c
 onsequently Anderson localization [1] is observed in the absence of nonlin
 earity. On the other hand\, nonlinear interactions result to the destructi
 on of the initial energy localization\, leading to the eventual subdiffusi
 ve spreading of wave packets in two different dynamical regimes (the so-ca
 lled &lsquo\;weak&rsquo\; and &lsquo\;strong chaos&rsquo\; spreading regim
 es)\, which are characterized by particular power law increases of the wav
 e packet&rsquo\;s second moment and participation number [2-6].\nQuantifyi
 ng the strength of chaos through the computation of the maximum Lyapunov e
 xponent (MLE\, see for example [7] and references therein)\, we observe th
 at the index exhibits power law decays\, with different exponents for the 
 weak and strong chaos regimes\, whose values are distinct from -1 seen in 
 the case of regular motion [8-10]. The spatiotemporal evolution of the coo
 rdinates&rsquo\; distribution of the deviation vector used to compute the 
 MLE (the so-called deviation vector distribution &ndash\; DVD) reveals tha
 t chaos is spreading through the random oscillation of localized chaotic h
 ot spots in the excited part of the wave packet [8-10]. Furthermore\, the 
 implementation of the SALI/GALI2 chaos indicator [11-13] permits the effic
 ient discrimination between localized and spreading chaos\, with the forme
 r dominating the dynamics for lower energy values\, for which the system i
 s approaching its linear limit [14]. In addition\, by computing the time v
 ariation of the fundamental frequencies of the motion of each oscillator i
 n the lattice\, i.e. the so-called frequency map analysis (FMA) technique 
 [15-17]\, we reveal several characteristics of the dynamics for both the w
 eak and strong chaos regimes [18]\, related to the location of highly chao
 tic oscillators and the propagation of chaos.\nReferences[1] &nbsp\; &nbsp
 \;Anderson\, 1958\, Phys. Rev.\, 109\, 1492[2] &nbsp\; &nbsp\;Flach\, Krim
 er\, Skokos\, 2009\, PRL\, 102\, 024101[3] &nbsp\; &nbsp\;Skokos\, Krimer\
 , Komineas\, Flach\, 2009\, PRE\, 79\, 056211[4] &nbsp\; &nbsp\;Skokos\, F
 lach S.\, 2010\, PRE\, 82\, 016208[5] &nbsp\; &nbsp\;Laptyeva\, Bodyfelt\,
  Krimer\, Skokos\, Flach\, 2010\, EPL\, 91\, 30001[6] &nbsp\; &nbsp\;Bodyf
 elt\, Laptyeva\, Skokos\, Krimer\, Flach\, 2011\, PRE\, 84\, 016205[7] &nb
 sp\; &nbsp\;Skokos\, 2010\, Lect. Notes Phys.\, 790\, 63[8] &nbsp\; &nbsp\
 ;Skokos\, Gkolias\, Flach\, 2013\, PRL\, 111\, 064101[9] &nbsp\; &nbsp\;Se
 nyange\, Many Manda\, Skokos\, 2018\, PRE\, 98\, 052229[10] &nbsp\; &nbsp\
 ;Many Manda\, Senyange\, Skokos\, 2020\, PRE\, 101\, 032206[11] &nbsp\; &n
 bsp\;Skokos\, 2001\, J. Phys. A\, 34\, 10029[12] &nbsp\; &nbsp\;Skokos\, B
 ountis\, Antonopoulos\, 2007\, Physica D\, 231\, 30[13] &nbsp\; &nbsp\;Sko
 kos\, Manos\, 2016\, Lect. Notes Phys.\, 915\, 129[14] &nbsp\; &nbsp\;Seny
 ange\, Skokos\, 2022\, Physica D\, 432\, 133154[15] &nbsp\; &nbsp\;Laskar\
 , 1990\, Icarus\, 88\, 266[16] &nbsp\; &nbsp\;Laskar\, Froeschl&eacute\;\,
  Celletti\, 1992\, Physica D\, 56\, 253[17] &nbsp\; &nbsp\;Laskar\, 1993\,
  Physica D\, 67\, 257[18] &nbsp\; &nbsp\;Skokos\, Gerlach\, Flach\, 2022\,
  IJBC\, 32\, 2250074
LOCATION:Seminar Room 1\, Newton Institute
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