We apply the Nonequilibrium Greens Function (NEGF) formalism to the problem of a multi-terminal nanojunction subject to an arbitrary time-dependent bias. In particular, we show that taking a generic one-particle system Hamiltonian within the wide ban
d limit approximation (WBLA), it is possible to obtain a closed analytical expression for the current in each lead. Our formula reduces to the well-known result of Jauho et. al. [doi:10.1103/PhysRevB.50.5528] in the limit where the switch-on time is taken to the remote past, and to the result of Tuovinen et. al. [doi:10.1088/1742-6596/427/1/012014] when the bias is maintained at a constant value after the switch-on. As we use a partition-free approach, our formula contains both the long-time current and transient effects due to the sudden switch-on of the bias. Numerical calculations performed for the simple case of a single-level quantum dot coupled to two leads are performed for a sinusoidally-varying bias. At certain frequencies of the driving bias, we observe `ringing oscillations of the current, whose dependence on the dot level, level width, oscillation amplitude and temperature is also investigated.
This chapter describes the progress made during the past three decades in the finite size scaling analysis of the critical phenomena of the Anderson transition. The scaling theory of localisation and the Anderson model of localisation are briefly ske
tched. The finite size scaling method is described. Recent results for the critical exponents of the different symmetry classes are summarised. The importance of corrections to scaling are emphasised. A comparison with experiment is made, and a direction for future work is suggested.
