Spin-flip rates in GaAs quantum dots can be quite slow, thus opening up the possibilities to manipulate spin states in the dots. We present here estimations of inelastic spin-flip rates mediated by hyperfine interaction with nuclei. Under general assumptions the nucleus-mediated rate is proportional to the phonon relaxation rate for the corresponding non-spin-flip transitions. The rate can be accelerated in the vicinity of a singlet-triplet excited state crossing. The small proportionality coefficient depends inversely on the number of nuclei in the quantum dot. We compare our results with known mechanisms of spin-flip in GaAs quantum dots.

We consider the hyperfine-mediated transition rate between Zeeman split states of the lowest orbital level in a GaAs quantum dot. We separate the hyperfine Hamiltonian into a part which is diagonal in the orbital states and another one which mixes different orbitals. The diagonal part gives rise to an effective ͑internal͒ magnetic field which, in addition to an external magnetic field, determines the Zeeman splitting. Spin-flip transitions in the dots are induced by the orbital-mixing part accompanied by an emission of a phonon. We evaluate the rate for different regimes of applied magnetic field and temperature. The rates we find are bigger than the spinorbit-related rates provided the external magnetic field is sufficiently low.

Motivated by recent interest in the role of the hyperfine interaction in quantum dots, we study the dynamics of a localized electron spin coupled to many nuclei. An important feature of the model is that the coupling to an individual nuclear spin depends on its position in the quantum dot. We introduce a semiclassical description of the system valid in the limit of a large number of nuclei and analyze the resulting classical dynamics. Contrary to a natural assumption of chaoticity of such dynamics, the correlation functions of the electron spin with an arbitrary initial condition show no decay in time. Rather, they exhibit complicated undamped oscillations. This may be attributed to the fact that the system has many integrals of motion and is close to an integrable one. The correlation functions averaged over initial conditions do exhibit a slow decay (ϳ1/ln͑t͒ at t → ϱ).

We calculate the frequency-dependent spin susceptibilities for a two-dimensional electron gas with both Rashba and Dresselhaus spin-orbit interactions. The resonances of the susceptibilities depend on the relative values of the Rashba and Dresselhaus spin-orbit constants, which could be manipulated by gate voltages. We derive exact continuity equations, with source terms, for the spin density and use those to connect the spin current to the spin density. In the free electron model the susceptibilities play a central role in the spin dynamics since both the spin density and the spin current are proportional to them.

We present and review an efficient method to calculate the retarded Green's function in multi-terminal nanostructures; which is needed in order to calculate the conductance through the system and the local particle densities within it. The method uses the recursive Green's function method after the discretized Hamilton matrix has been properly partitioned. We show that this method, the circular slicing scheme, can be modified to accommodate multi-terminal systems as well as the traditional two-terminal systems. Furthermore, we show that the performance and robustness of the circular slicing scheme is on par with other advanced methods and is well suited for large variety of multi-terminal geometries. We end by giving an example of how the method can be used to calculate transport in a non-trivial multi-terminal geometry.