Complex potentials have been used in the past to simulate dissipative processes, but the normal form of a simple constant term of the form t / h i serves only to trap/detrap particles and does not properly introduce a process which relaxes a dynamic operator/variable . We have treated a general non-Hermitian Hamiltonian operator, and have developed a modified time-dependent solution of the density matrix equation of motion. An energy-dependent phase-breaking process maintains the wave function while destroying the coherence which leads to the scar itself. In this paper, we discuss the general behavior of these complex potentials, their application to the ballistic quantum dots, and implications for trajectories and histories in the dots. The present formalism will allow the simulation of quantum transport through interfacial regions, rather than having to match boundary conditions, and this is facilitated by a proper inclusion of discontinuities at the interfaces. One can now develop a proper transport theory by using moments of the density matrix, which are valid even in the areas of strong dissipation.
Journal: TechConnect Briefs
Volume: Technical Proceedings of the 1999 International Conference on Modeling and Simulation of Microsystems
Published: April 19, 1999
Pages: 373 - 376
Industry sector: Sensors, MEMS, Electronics
Topics: Modeling & Simulation of Microsystems, Nanoelectronics