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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > The Maxwell-Bloch System in the Sharp-Line Limit

## The Maxwell-Bloch System in the Sharp-Line LimitAdd to your list(s) Download to your calendar using vCal - Peter Miller (University of Michigan)
- Monday 05 September 2022, 14:30-15:30
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact nobody. HY2W02 - Analysis of dispersive systems We study the characteristic Cauchy problem for the Maxwell-Bloch system that describes the interaction of an optical pulse with an active quantum medium. It is well known that in the sharp-line limit that the atoms in the medium are not Doppler-shifted in frequency, this system can be embedded in the integrable hierarchy of the nonselfadjoint Zakharov-Shabat spectral problem. However, it is also known that there are certain difficulties with formulating and using the inverse-scattering transform based on this spectral problem in the usual way. We construct a Riemann-Hilbert problem that returns the unique causal solution of the Cauchy problem and use it to explain features of solutions such as the stimulated decay by a suitable optical pulse of an unstable medium to its stable state and the spontaneous generation of a dispersive tail of the optical pulse with positive time that ruins absolute integrability that would be needed for the standard inverse-scattering transform to make sense. This tail is related to a specific self-similar solution of the Maxwell-Bloch system that in turn is connected with a concrete special solution of the Painlevé-III equation that has become important in several recent application problems for the focusing nonlinear Schrödinger equation. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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