Abstract
The replica trick is a general tool to perform averages for quenched disordered systems. It is mathematically not exact, however. In contrast, exact calculations for quantum-mechanical particles in a random potential can be performed by simultaneous use of complex and anticommuting variables. A first application is the derivation of Wigner’s semi-circle law for the density of states of the Gaussian unitary ensemble.
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Wegner, F. (2016). Disordered Systems. In: Supermathematics and its Applications in Statistical Physics. Lecture Notes in Physics, vol 920. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-49170-6_4
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DOI: https://doi.org/10.1007/978-3-662-49170-6_4
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