In the context of the driven quantum systems and of their
linear-response theory (LRT) the authors successfully looked for
circumstances where the standard Kubo formula ceased to be
applicable, i.e., where the diffusion $D$ proved anomalous (which
means: Planck-constant-dependent). The emergence of the nonlinear
dependence of $D$ on the driving intensity is attributed to
self-generated (intrinsic) dephasing processes and given the
quantitative form of eq. (10). An illustration is provided via toy
models (19) and (20). In Figure 2 one finds that certain two
alternative forms of the violation of the LRT response may occur.
The picture itself is to be read with necessary care since the
``fast-track" speed of this publication caused certain unfortunate
misprints in its legend.


MR2670526 Sela, Itamar; Aisenberg, James; Kottos, Tsampikos; Cohen,
Doron Quantum anomalies and linear response theory. J. Phys. A:
Math. Theor. 43 (2010), no. 33, 332001, 8 pp. 82C10