Quantum anomalies and linear response theory

The analysis of diffusive energy spreading in quantized chaotic driven systems, leads to a universal paradigm for the emergence of a quantum anomaly. In the classical approximation a driven chaotic system exhibits stochastic-like diffusion in energy space with a coefficient $D$ that is proportional to the intensity ${ϵ}^2$ of the driving. In the corresponding quantized problem the coherent transitions are characterized by a generalized Wigner time $t_{ϵ}$, and a self-generated (intrinsic) dephasing process leads to non-linear dependence of $D$ on ${ϵ}^2$.