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SUMMARY:Destruction of Anderson localization in nonlinear Schrödinger lat
 tices with disorder - Alexander Milovanov (ENEA C.R. Frascati)
DTSTART:20240423T103000Z
DTEND:20240423T113000Z
UID:TALK216196@talks.cam.ac.uk
DESCRIPTION:Anderson localization is the absence of diffusion of waves in 
 random media. It is a generic wave phenomenon\, which applies to any kind 
 of wave regardless of its nature. Experimentally\, Anderson localization h
 as been found for electron gases\, acoustic waves\, spin waves\, matter wa
 ves\, and more recently also for light waves. The localization occurs beca
 use a disordered medium induces multiple scattering paths along which the 
 components of the wave function interfere destructively. Lately\, it has b
 een discussed that a weak nonlinearity might destroy the localized state g
 iving rise to unlimited spreading of the wave function along the lattice d
 espite the underlying disorder. The statistics of this spreading process h
 as remained a matter of debate. In this talk\, I will review the state of 
 the art\, with several toy models predicting asymptotic spreading from the
  nonlinear Schr&ouml\;dinger dynamics on a lattice. The key words will be 
 continuous time random walks\, chaos (strong\, weak)\, percolation\, fract
 ional kinetics\, Cayley trees. Time permitting\, I will touch upon topics 
 concerning nonlinear Schr&ouml\;dinger models with\nsubquadratic power non
 linearity leading to L&eacute\;vy flights. A summary of the discussion may
  be found in a recent work [A.V. Milovanov and A. Iomin\, Phys. Rev. E. 10
 7\, 034203 (2023)].
LOCATION:Seminar Room 1\, Newton Institute
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