  We propose a method of accelerating the speed of evolution of an open system
by an external classical driving field for a qubit in a zero-temperature
structured reservoir. It is shown that, with a judicious choice of the driving
strength of the applied classical field, a speed-up evolution of an open system
can be achieved in both the weak system-environment couplings and the strong
system-environment couplings. By considering the relationship between
non-Makovianity of environment and the classical field, we can drive the open
system from the Markovian to the non-Markovian regime by manipulating the
driving strength of classical field. That is the intrinsic physical reason that
the classical field may induce the speed-up process. In addition, the roles of
this classical field on the variation of quantum evolution speed in the whole
decoherence process is discussed.
