Circuit theoretical study on the lifetime of the resonant state

Abstract

AbstractWith a view to investigating the operating speed of a quantum effect device, considerable work has been carried out on the lifetime of the resonant state. The lifetime of the resonant state in a multiple barrier structure is defined as the time constant with which the existence probability of the electron is attenuated. This is a quantum theoretical transient phenomenon.In this paper, by means of a complex‐valued equivalent circuit proposed previously by the authors, this transient problem is discussed from a circuit theoretical viewpoint. First, the complex frequency variable (Laplace variable) is related to the complex energy which permits a circuit theoretical investigation on the lifetime. It was found that the real part of the complex frequency, which makes zero the sum of the admittances looking to the left and the right, corresponds to the lifetime. By means of a numerical experiment, a double‐barrier structure is studied and compared with the research results reported previously. The error of the lifetime estimated from the half‐value width also is studied. In addition, a symmetric triple barrier structure is studied. It is found that a lifetime exists that cannot be estimated from the half‐value width.