Spin-orbital coupling and coloured noise assisted Landau-Zener (LZ) transition in a quantum dot (QD)

The paper presents the magnetic field effects on an electron in a QD and focuses on spin-orbital coupling and coloured noise assisted Landau-Zener (LZ) transition applying the Dynamic matrix approach (DMA). The system is shown to imitate a noisy driven LZ model with the dynamics being tailored by the dot size. The generalized transition probabilities are observed to depend on the orbital quantum numbers, adiabatic parameter that accounts for the non-linearity of the energy levels and the renormalized noise parameter that account for all noise variables. We redefine the concepts of fast and slow noise in terms of the system's driving frequency with limiting values coinciding with ones in literature. The exact transition probability of the driven LZ system assisted by coloured noise is derived independently of the noise fluctuation speed and valid for fast, slow, weak and strong noise.