Shortcuts to adiabaticity for non-Hermitian systems
  Adiabatic processes driven by non-Hermitian, time-dependent Hamiltonians may be sped up by generalizing inverse engineering techniques based on Berry's transitionless driving algorithm or on dynamical invariants. We work out the basic theory and examples described by two-level Hamiltonians: the acceleration of rapid adiabatic passage with a decaying excited level and of the dynamics of a classical particle on an expanding harmonic oscillator. 
S. Ib\'a\~nez, S. Mart\'inez-Garaot, Xi Chen, E. Torrontegui, and J.   G. Muga
quant-ph