| Abstract: |
| In this talk, we present exact results on the quantization of Benjamin-Ono multi-phase solutions, the periodic analogs of multi-solitons, and asymptotic results for the quantization of spatially-periodic classical initial data at the critical regularity $s=-1/2$. First, we show that the semi-classical soliton spectrum is exact after the renormalization of Abanov-Wiegmann (2006). As an application, we show that in the semi-classical $h->0$ and small dispersion $e->0$ limit, the microscopic wavespeeds of interacting 1-phase waves in the decomposition of a quantum coherent state into quantum multi-phase states exhibit random matrix theory statistics for any $\beta>0$ where $\beta/2 = e^2/h$. |
|