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arXiv · 1401.0318

Particle diagrams and embedded many-body random matrix theory

Rupert Small·Sebastian Müller
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Abstract

We present a new method which uses Feynman-like diagrams to calculate the statistical quantities of embedded many-body random matrix problems. The method provides a promising alternative to existing techniques and offers many important simplifications. We use it here to find the fourth, sixth and eighth moments of the level density for k fermions or bosons interacting through a random hermitian potential in the limit where the number of possible single-particle states is taken to infinity. All share the same transition, starting immediately after 2k = m, from moments arising from a semi-circular level density to gaussian moments. The results also reveal a striking feature; the domain of the 2n'th moment is naturally divided into n subdomains specified by the points 2k = m, 3k = m, ..., nk = m.

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Rupert Small, Sebastian Müller. 2014-01-01. Particle diagrams and embedded many-body random matrix theory. https://doi.org/10.1103/physreve.90.010102

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