FRACTAL DIMENSIONS IN TUNNELING PROCESSES AND EFFECTS OF ENVIRONMENTAL FLUCTUATIONS

We study electron tunneling between two infinite potential square well s connected via an opaque barrier and find that time evolution of the probability of the presence of a Gaussian wave packet, localized initi ally in one of the wells, shares the fractal behavior of tunneling in a quartic potential, discovered by Dekker (H. Dekker, Phys. Rev. A35, 1825 (1987). However, the fractal dimensions are found to be closer to those of a conventional Weierstrass function than those appropriate t o the quasi-Weierstrass behavior of Dekker. It is argued that the usua l exponential decay predicted by conventional relaxation processes can be recovered only as an effect of thermal fluctuations.