Time-Adiabatic Theory Seminar - Christof Sparber (University of Illinois, Chicago)

Event Date: 

Friday, May 15, 2015 -
3:00pm to 4:00pm

Event Location: 

  • 4607B South Hall

Event Price: 

Free

Event Contact: 

Carlos Garcia-Cervera

Email: cgarcia@math.ucsb.edu

Phone: 8055638873

  • Applied Math/PDE Seminar

We revisit the time-adiabatic theorem of quantum mechanics and show that it can be extended to weakly nonlinear situations, that is to nonlinear Schrödinger equations in which either the nonlinear coupling constant or, equivalently, the solution is asymptotically small. To this end, a notion of criticality is introduced at which the linear bound states stay adiabatically stable, but nonlinear effects start to show up at leading order in the form of a slowly varying nonlinear phase modulation. In addition, we show that in the same regime a class of nonlinear bound states also stays adiabatically stable, at least in terms of spectral projections.