Some ad-hoc Methods for Introducing Dissipation to the Schrödinger Equation
Considerable interest has developed in the quantum mechanical simulation of electronic devices with the fabrication of structures whose geometric feature sizes are comparable to the quantum mechanical wavelengths of the carriers in these devices. The inclusion of dissipative effects to the study of quantum mechanical transport phenomena is a difficult fundamental problem. Although considerable progress has been made in the formal theory, these formalisms are computationally difficult to implement in numerical simulations of charge transport in realistic device structures.
Integration of the time-dependent Schrödinger equation has been utilized in various studies to describe the dynamics of charges in small devices. Although the simplicity of the method is promising, the method is applicable only to those systems in which the dissipative effects can be assumed to be negligible. In this study, a number of ad-hoc approximations that result in equations which contain dissipative effects will be discussed. These approximations lead to relatively simple integration procedures which may be useful in the simulation of devices where dissipation effects are weak, but not negligible.
KeywordsWave Function Energy Relaxation Schrodinger Equation Dissipative Effect Quantum Transport
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