Anderson localization with self-avoiding walk representation
The Green’s function contains much information about physical systems. Mathematically, the fractional moment method (FMM) developed by Aizenman and Molchanov connects the Green’s function and the transport of electrons in the Anderson model. Recently, it has been discovered that the Green’s functio...
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| Language: | English |
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University of British Columbia
2012
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| Online Access: | http://hdl.handle.net/2429/43096 |
| Summary: | The Green’s function contains much information about physical systems. Mathematically, the fractional moment method (FMM) developed by Aizenman and Molchanov connects the Green’s function and the transport of electrons in the Anderson model.
Recently, it has been discovered that the Green’s function on a graph can be represented using self-avoiding walks on a graph, which allows us to connect localization properties in the system and graph properties.
We discuss FMM in terms of the self-avoiding walks on a general graph with a small number of assumptions. |
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