BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Loss of phase, universality of stochastic interactions, uncertainty quantification, and loss of reversibility Fibich, Gadi


Previously, we showed that for all continuations of NLS blowup solutions, the phase is lost after the singularity. In this talk I will show that ``loss of phase'' can occur even if the NLS solution does not collapse. Therefore, if two NLS solutions travel a sufficiently long distance (time) before interacting, it is not possible to predict whether they would intersect in- or out-of-phase. Hence, a deterministic prediction of the interaction outcome becomes impossible. ``Fortunately'', because the relative phase between the two solutions becomes uniformly distributed in $[0,2\pi]$, the statistics of the interaction outcome is universal. The statistics can be efficiently computed using a novel Uncertainty-Quantification method, even when the distribution of the noise source is unknown. I will end by arguing that although the NLS has a time-reversal symmetry, its solutions can experience a loss of reversibility.

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