This report includes three parts: 1. We study shot noise for entangled electrons in a 4-lead beam-splitterwith one incoming lead driven by adiabatically rotating magnetic fields. Wepropose a setup of an adiabatically rotating magnetic field therefor, which isappropriate for an electron beam to transport through. Using the scatteringmatrix approach, we find that shot noise for the singlet and that for theentangled triplet oscillates between bunching and antibunching due to theinfluence of the Berry phase. It provides us a new approach for testing theBerry phase in electron transport on the basis of entanglement. 2. We apply the perturbation theory to investigate the behavior of theBerry phase of a composite system. The composite system consists of twoweakly coupled spin-particles, in which each particle is driven by a varyingmagnetic field. The result shows that the Berry phase for one subsystem iscontrolled by the state of the other subsystem. The method can also be usedto deal with the effect of a spin environment on a single-particle system ifthe particle is weakly coupled to the spin environment. 3. We study shot noise for electron pairs in a 4-lead beam-splitter witheach incoming lead driven by a Rashba interaction. The Rashba phases mod-ify the symmetry of the spin part of the wave function; hence, intermediatedegrees of bunching and antibunching can be induced.