Universal Fluctuations of Dirac Spectra

A new link between Quantum Chromodynamics (QCD), the theory of strongly interacting elementary particles and mesoscopic systems in condensed matter physics is established through random matrix methods. Ensembles of complete eigenvalue spectra of the QCD Dirac operator are calculated for the first time for different lattice volumes ranging from lattice size 44 to 164. This amounts among other things to diagonalize sparse hermitean matrices of size 40 000 times 40 000 with very high precision for typical several thousand different matrices. The computation is only feasible on a massive paralell processing system like the CRAY T3E The remarkable agreement with the predictions of chiral random matrix models establishes the notion of universal fluctuations in systems with disorder and offers new insights into fundamental questions like spontaneous chiral symmetry breaking and the quark mass puzzle.