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Three Alternative Sigma Models of Disorder and Their Relative Merits

Sacksteder, V (Asia Pacific Center)
Thursday 11 December 2008, 14:40-15:20

Seminar Room 2, Newton Institute Gatehouse


Wegner's model of weakly coupled metallic grains is believed to capture the physics of Anderson localization, but has resisted full mathematical control in two or more dimensions. In zero dimensions it can be exactly transformed to two different matrix models, the first involving graded (supersymmetric) matrices. The second was introduced more recently by Fyodorov and avoids the use of graded matrices. The SUSY model was generalized long ago to D dimensions and results in the famous supersymmetric sigma model. However the generalization process lacks mathematical rigor, relying heavily on effective field theory ideas and an implicit continuum limit. In this talk I will briefly review the SUSY generalization process and its difficulties and then describe what can be learned from generalizing Fyodorov's model to D dimensions. Lastly and most importantly I will present my work on a third model originated by Spencer and Disertori which is identical to Fyodorov's model in zero dimensions but which opens new mathematical possibilities in D dimensions.


[ppt ]

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