  We report the investigation of full-counting statistics (FCS) of transferred
charge and spin in the transient regime where the connection between central
scattering region (quantum dot) and leads are turned on at $t=0$. A general
theoretical formulation for the generating function (GF) is presented using a
nonequilibrium Green's function approach for the quantum dot system. In
particular, we give a detailed derivation on how to use the method of path
integral together with nonequilibrium Green's function technique to obtain the
GF of FCS in electron transport systems based on the two-time quantum
measurement scheme. The correct long-time limit of the formalism, the
Levitov-Lesovik's formula, is obtained. This formalism can be generalized to
account for spin transport for the system with noncollinear spin as well as
spin-orbit interaction. As an example, we have calculated the GF of
spin-polarized transferred charge, transferred spin, as well as the spin
transferred torque for a magnetic tunneling junction in the transient regime.
The GF is compactly expressed by a functional determinant represented by
Green's function and self-energy in the time domain. With this formalism, FCS
in spintronics in the transient regime can be studied. We also extend this
formalism to the quantum point contact system. For numerical results, we
calculate the GF and various cumulants of a double quantum dot system connected
by two leads in transient regime. The signature of universal oscillation of FCS
is identified. On top of the global oscillation, local oscillations are found
in various cumulants as a result of the Rabi oscillation. Finally, the
influence of the temperature is also examined.
