Effective Medium Theory for Disordered Systems: a Non-Markoffian Description in a Markoffian System

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• Vasudev Kenkre (University of New Mexico)
• Tuesday 07 November 2023, 12:00-12:30
• Seminar Room 1, Newton Institute.

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Effective Medium Theory is the name given to an ingenuous method of describing motion in disordered systems in which standard methods fail because of the difficulties in the direct diagonalization of matrices of enormous size. The procedure involves the introduction of a non-Markoffian description, ie., one based on equations of motion non-local in time. The non-locality arises from disorder. The method was originally initiated by civil engineers, has found wide use in physics, but appears not to have been employed routinely in the mathematics of movement in ecology. The talk will address this powerful technique with focus on its validity and its nuances. References:

V.M. (Nitant) Kenkre: Memory Functions, Projection Operators, and the Defect Technique: Tools of the Trade for the Condensed Matter Physicist, Springer Nature Publishing, 4/2021. See Chapters 13 and 14. V.M. Kenkre, Z. Kalay, and P.E. Parris: Extensions of effective-medium theory of transport in disordered systems, Phys. Rev. E 79 , 011114 (2009).

This talk is part of the Isaac Newton Institute Seminar Series series.

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