Geometry of the adiabatic theorem
  We present a simple and pedagogical derivation of the quantum adiabatic theorem for two level systems (a single qubit) based on geometrical structures of quantum mechanics developed by Anandan and Aharonov, among others. We have chosen to use only the minimum geometric structure needed for an understanding of the adiabatic theorem for this case. 
A. C. Lobo, R. A. Ribeiro, P. R. Dieguez and C. A. Ribeiro
quant-ph