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Random Matrix Approach to Glassy Physics --- Low Temperatures and Beyond

A random matrix approach to glassy physics is introduced. It leads to a class of models which exhibit both, glassy low-temperature phases, and double-- and single-well configurations in their potential energy. The distribution of parameters characterizing the local potential energy configurations can be computed, and differ from those assumed in the standard tunneling model and its variants. Still, low-temperature anomalies characteristic of amorphous systems are reproduced, and we are able to distinguish properties which can be expected to be universal from those which cannot.