Higher time derivatives in effective equations of canonical quantum   systems
  Quantum-corrected equations of motion generically contain higher time derivatives, computed here in the setting of canonically quantized systems. The main example in which detailed derivations are presented is a general anharmonic oscillator, but conclusions can be drawn also for systems in quantum gravity and cosmology. 
Martin Bojowald, Suddhasattwa Brahma, Elliot Nelson
quant-ph gr-qc hep-th