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 prove that in the same regime a class of nonlinear bound states also stays adiabatically stable, at least in terms of spectral projections. We then compare our result to a theorem by Gang & Grech and discuss several remaining open questions. Speaker(s): Christof Sparber (University of Illinois, Chicago)
Building: | East Hall |
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Event Type: | Workshop / Seminar |
Tags: | Mathematics |
Source: | Happening @ Michigan from Department of Mathematics, Differential Equations Seminar - Department of Mathematics |