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SUMMARY:The nonlinear Anderson problem: A vital\, if openly recognized cha
 llenge - Alexander Milovanov (ENEA C.R. Frascati)
DTSTART:20240819T130000Z
DTEND:20240819T140000Z
UID:TALK219763@talks.cam.ac.uk
DESCRIPTION:Anderson localization&mdash\;so named after the American physi
 cist P. W. Anderson&mdash\;is the absence of diffusion of waves in a disor
 dered medium. It is a generic wave phenomenon\, which applies to any kind 
 of wave regardless of its nature (light\, acoustic\, matter\, spin\, etc.)
 . The localization occurs because strong disorder induces multiple scatter
 ing paths along which the components of the wave field interfere destructi
 vely. Given this insight\, it has been discussed that a small (Ginzburg-La
 ndau style) nonlinearity might destroy the localized state (because overla
 pping components of the nonlinear field produce internal pressure favoring
  spreading). The phenomenon has been discussed theoretically and demonstra
 ted numerically suggesting that above a certain critical strength of nonli
 near interaction a (weakly) nonlinear field may propagate to infinite dist
 ances despite the underlying disorder&mdash\;in contrast to the correspond
 ing linear field. The statistics of this spreading process\, as well as th
 e type of nonlinearity destroying localization\, has remained a matter of 
 debate. In this talk\, I will review the state of the art\, with several t
 oy models predicting asymptotic spreading of the wave field from the discr
 ete nonlinear Schr&ouml\;dinger equation with random potential. The keywor
 ds will be continuous time random walks\, chaos (strong\, weak)\, percolat
 ion\, fractional kinetics\, Cayley trees. Time permitting\, I will touch u
 pon topics concerning the nonlinear Schr&ouml\;dinger models with subquadr
 atic power nonlinearity. The main issue here is that subquadratic power re
 presents a form of long-range self-interaction in the system and as such m
 ight have important implications with regard to the asymptotic spreading p
 rocess. A summary of the talk can be found in a recent publication [A.V. M
 ilovanov and A. Iomin\, Phys. Rev. E. 107\, 034203 (2023)].
LOCATION:Seminar Room 2\, Newton Institute
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