What is it about?
It was observed in prior work that the Maxwell equations admit a natural (coordinate-independent) nonlinear extension. This leads to a specific model for interaction of electromagnetic fields with charge density waves at mesoscale. In this work, it is demonstrated that the resulting nonlinear model predicts magnetic vortices, such as arise in two-dimensional films subjected to strong magnetic fields and low temperature.
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Why is it important?
Nonlinear electronic phenomena are known to occur naturally in nanoscale, e.g. this is exemplified by the emergence of memristance. It is compelling to try and construct a self-consistent universal framework for all of mesoscopic electromagnetism. The geometrical approach explored here is one possibility.
Perspectives
The work was continued in the classical framework for some time. Its quantum version, proposed later on, is an example of nonlinear quantum dynamics that is tied to the Helmholtz free-energy.
Dr Artur P Sowa
University of Saskatchewan
Read the Original
This page is a summary of: Nonlinear Maxwell Theory and Electrons in Two Dimensions, Communications in Mathematical Physics, November 2006, Springer Science + Business Media,
DOI: 10.1007/s00220-006-0138-6.
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