Time evolution and adiabatic approximation in $PT$-symmetric quantum   mechanics
  In this paper, we discuss time evolution and adiabatic approximation in $PT$-symmetric quantum mechanics. we give the time evolving equation for a class of $PT$-symmetric Hamiltonians and some conditions of the adiabatic approximation for the class of $PT$-symmetric Hamiltonians. 
Zhihua Guo and Huaixin Cao
math-ph math.MP quant-ph