  We provide a general dynamical approach for the quantum Zeno and anti-Zeno
effects in an open quantum system under repeated non-demolition measurements.
In our approach the repeated measurements are described by a general dynamical
model without the wave function collapse postulation. Based on that model, we
further study both the short-time and long-time evolutions of the open quantum
system under repeated non-demolition measurements, and derive the
measurement-modified decay rates of the excited state. In the cases with
frequent ideal measurements at zero-temperature, we re-obtain the same decay
rate as that from the wave function collapse postulation (Nature {\bf 405}, 546
(2000)). The correction to the ideal decay rate is also obtained under the
non-ideal measurements. Especially, we find that the quantum Zeno and anti-Zeno
effects are possibly {\it enhanced} by the non-ideal natures of measurements.
For the open system under measurements with arbitrary period, we generally
derive the rate equation for the long-time evolution for the cases with {\it
arbitrary} temperature and noise spectrum, and show that in the long-time
evolution the noise spectrum is effectively tuned by the repeated measurements.
Our approach is also able to describe the quantum Zeno and anti-Zeno effects
given by the phase modulation pulses, as well as the relevant quantum control
schemes.
