Chiral disorder and diffusion of light quarks in the QCD vacuum

We give a pedagogical introduction to the concept that light quarks diffuse in the QCD vacuum following the spontaneous breaking of chiral symmetry. B y analogy with disordered electrons in metals, we show that the diffusion c onstant for light quarks in QCD is D = 2F(pi)(2)/\[((q) over bar q]\ which is about 0.22 fm. We comment on the correspondence between the diffusive ph ase and the chiral phase as described by chiral perturbation theory, as wel l as the cross-over to the ergodic phase as described by random matrix theo ry. The cross-over is identified with the Thouless energy E-c = D/root V-4 which is the inverse diffusion time in an Euclidean four-volume V-4.