Chapter 10: Tunneling in Time-Dependent Barriers

In condensed matter physics, the technology of molecular beam epitaxy and layer by layer growth of semiconductor heterostructures have given rise to numerous tunneling applications. In these structures the time-dependent barriers appear in two ways: An explicit time-dependence arises due to the applied a.c. fields with frequencies reaching into microwaves (10⁷ – 10¹¹ Hz). Secondly, resonant tunneling occurs in a small energy range and this can be modeled by considering an oscillating barrier [1]–[13]. In these problems mostly one-dimensional tunneling is important and therefore we study the motion of a particle of mass m in a barrier V (x, t), where we assume that