Chapter 4
Quantum Dissipative Transport

Charge transport simulations according to the non-equilibrium Green’s function (NEGF) method need enormous computation time and have to be carefully customized for each particular structure. Since recent theoretical studies showed that the steady state transport in QCLs is incoherent and the semiclassical description found to be satisfactory  [58], a simpler approach than NEGF can be used. Although coherent oscillations of the population inversion were observed, the resulting steady state transport is incoherent as the oscillations are damped to the sub-picosecond timescale which is considerable shorter than the average transit time across one stage. Here, we present a rigorous Monte Carlo method based on a semiclassical transport description which takes much less computational time than simulations based on the NEGF formalism.

 4.1 Density Matrix Formulation
  4.1.1 Density Matrix Equations for Dissipative Systems
 4.2 Semiclassical Transport Description
  4.2.1 Pauli Master Equation
  4.2.2 Monte Carlo Method