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SUMMARY:Numerical simulation of nonlinear Schrödinger equations\; Pro
 f. Dr. Daniel Peterseim (Universität Augsburg)
UID:500b4429-df1e-4164-a03b-a556f9912708
DESCRIPTION:ABSTARCT: This talk reviews numerical methods for the simu
 lation of Bose-Einstein-Condensates modeled by nonlinear Schrödinger 
 (Gross-Pitaevskii) equations with possibly rough (highly oscillatory\,
  disordered) potentials. The first part addresses the computation of s
 tationary states. Among the methodological and mathematical novelties 
 for the nonlinear Schrödinger eigenvalue problem are globally converg
 ent and energy-diminishing gradient flows as well as shift-accelerated
  nonlinear inverse iterations. The second part concerns the dynamics a
 nd the numerical analysis of time-stepping schemes in the presence of 
 disorder potentials. Under low regularity assumptions\, that are compa
 tible with rough potentials\, we prove convergence with rates for the 
 mass- and energy conserving variant of the Crank-Nicolson time discret
 ization scheme due to Sanz-Serna. A series of numerical experiments de
 monstrates the computational efficiency of all methods and their abili
 ty to capture interesting physical phenomena such as Anderson localiza
 tion and quantum phase transitions.
DTSTART:20200604T141500Z
DTEND:20200604T151500Z
LOCATION:Online (contact marius.yamakou@fau to get the data for the VC)
DTSTAMP:20260729T092736Z
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