Dissipation and quantum transport simulations in nanoscale devices

A key simulation issue is the development of a dissipation formalism for the time dependent density operator equation, that is amenable to numerical methods and incorporates the role of the environment on state renormalization and dissipation. Using standard super-operator calculus, projection operators, and separating the system of interest from the reservoir, the relevant operator equation is derived. In addition, the role of the reservoir on renormalizing the energy spectrum is discussed.