The passage of a wave packet through a potential barrier

George H. Rawitscher, I. Simbotin, I. Koltracht

Andrey A. Bocharov

V. V. Dodonov, A. B. Klimov, Vladimir I. Man’ko

Ronald A. Lovett

Aleksei M. Zheltikov

Rapidly progressing laser technologies provide powerful tools to study potential barrier-passage dynamics in physical, chemical, and biological systems with unprecedented temporal and spatial resolution and a remarkable chemical and structural specificity. The available theories of barrier passage, however, operate with equations, potentials, and parameters that are best suited for a specific area of research and a specific class of systems and processes. Making connections among these theories is often anything but easy. Here, we address this problem by presenting a unified framework for the description of a vast variety of classical and quantum barrier-passage phenomena, revealing an innate connection between various types of barrier-passage dynamics and providing closed-form equations showing how the signature exponentials in classical and quantum barrier-passage rates relate to and translate into each other. In this framework, the Arrhenius-law kinetics, the emergence of the Gibbs distribution, Hund's molecular wave-packet well-to-well oscillatory dynamics, Keldysh photoionization, and Kramers' escape over a potential barrier are all understood as manifestations of a potential-driven Markovian dynamics whereby a system evolves from a state of local stability. Key to the irreducibility of quantum tunneling to thermally activated barrier passage is the difference in the ways the diffusion-driving potentials emerge in these two tunneling settings, giving rise to stationary states with a distinctly different structure.

A.B. Kukanov, N. D. Naumov, T'hai K'uatig