Skip to Content

Search: {{$root.lsaSearchQuery.q}}, Page {{$root.page}}

Integrable Systems and Random Matrix Theory Seminar

Asymptotics in the sharp-line Maxwell-Bloch system without solitons
Monday, November 16, 2020
4:00-5:00 PM
Zoom Meeting: 91617339235 Passcode: 651935 Off Campus Location
In this talk, we discuss the asymptotics in the (characteristic) Cauchy problem for the Maxwell-Bloch equations of light-matter interaction, under assumptions that prevent the generation of solitons. Both cases (initially stable/unstable media) are considered. In particular, we describe a layer phenomenon in which, even for smooth initial data, the solution makes a sudden transition over an infinitesimally small propagation distance. At a formal level, this phenomenon has been described by other authors in terms of a self-similar solution that satisfies an ordinary differential equation related to the Painlev\'e-III (PIII) equation. We show that the two cases of stable/unstable medium are related to different PIII equations and their Riemann-Hilbert problems. Our analysis of the temporal boundary conditions satisfied by the electric field and medium density matrix reveals slow decay of the electric field in one direction that is actually inconsistent with the simplest version of the scattering theory. The results are then carefully compared to direct numerical simulations. Speaker(s): Sitai Li (University of Michigan)
Building: Off Campus Location
Location: Virtual
Event Type: Workshop / Seminar
Tags: Mathematics
Source: Happening @ Michigan from Department of Mathematics, Integrable Systems and Random Matrix Theory Seminar - Department of Mathematics