Topological field theory approach to intermediate statistics

Random matrix models provide a phenomenological description of vast variety physical phenomena. Prominent examples include the eigenvalue statistics quantum (chaotic) systems, which are characterized by spectral form factor (SFF). Here, we calculate SFF unitary ensembles infinite order with weight function satisfying assumptions Szeg"{o}’s limit theorem. We then consider parameter-dependent critical ensemble has intermediate characteristic ergodic-to-nonergodic transitions such as Anderson localization transition. This same is model U(N) U(N) Chern-Simons theory on S^3 display="inline">S3 , and this proportional to HOMFLY invariant (2n,2) display="inline">(2n,2<mml:mo -torus links one component in fundamental antifundamental representation. example large class arising from topological field string theories. Indeed, absence local parameter suggests that it natural characterize using tools, have done here.