A Quantum Many-Body Density Matrix Model for Sub-Femtosecond Transport in Mesoscopic Structures

Abstract

Theoretical model for transient transport in mesoscopic structures was presented, and the approach with numerical simulation of a resonant-tunneling diode (RTD) was illustrated. A second-order master equation for the evolution of the many-body reduced density matrix of the active region was being introduced. This contains full quantum-mechanical information about the processes in the current-limiting active region. The master equation is derived directly form the Liouville equation for the active region+contacts, by using the partial-trace-free approach, and it incorporates the memory terms that describe the information exchange between the contacts and the active region. In this way, the state of the contacts is accounted for, but does not explicitly enter the calculation, allowing us to compute the full many-body reduced density matrix for the active region. The model accounts for the presence of the bias by assuming a special form of the forcing term in the master equation. The numerical simulation shows that incorporation of the memory terms is crucial for description of charging/discharging in the well, and obtaining the proper transient behavior. Electron-electron interaction between the active region and the contacts, as well as phonon scattering (within the relaxation-time approximation), have been taken into account.