Fermats last theorem, the Riemann hypothesis, and synergistic glasses

Abstract

The synergistic formation of zero (exponentially small) resistance states (ESRS) in high mobility two-dimensional electron systems (2DES) in a static magnetic field B and exposed to strong microwave (MW) radiation exhibits hysteresis and an anomalous logarithmic dependence on MW power. These synergistically organized states appear to be associated with a new kind of energy gap Δ. Here I show that a microscopic quantum model that involves the Prime Number Theorem explains the MW power dependence of the energy gap Δ. The explanation involves remarkable convergence with the most abstract ideas of modern mathematics.