In 1999, motivated by a question that has been raised by Wilkinson and Austin, I have conjectured a condition for observing a quantum anomaly in a regime where traditionally linear response theory (LRT) is expected to hold. [A major generalization of the Wigner time concept was required in order to address time dependent circumstances in which it is determined by the rate of the driving, and not only on its amplitude]. This non-perturbative response effect has been confirmed for RMT models (with Tsampikos Kotttos), but later it turned out that it is avoided in quantized chaotic systems due to the underlying semiclassical skeleton. The idea of Semi-linear response theory has emerged during this quest, but the issue of non-linear anomalies has been left speculative.
 
Recently, within the framework of a BSF collaboration, we tried to find circumstances in which anomalies show up. By now we have generalized the analysis of the Wigner decay problem addressing non-Ohmic models, and exploring the regime where universal anomalies may arise.
 
References:

• Quantum anomalies and linear response theory [arXiv] [pdf],
  I. Sela, J. Aisenberg, T. Kottos and D. Cohen, J. Phys. A (FTC) 43, 332001 (2010).


• Quantum decay into a non-flat continuum [arXiv] [pdf],
  J. Aisenberg, I. Sela, T. Kottos, D. Cohen and A. Elgart, J. Phys. A 43, 095301 (2010).


• Anomalous decay of a prepared state due to non-Ohmic coupling to the continuum [arXiv] [pdf],
  I. Sela, J. Aisenberg, T. Kottos, A. Elgart and D. Cohen, Phys. Rev. E 81, 036219 (2010).