Thermal and Quantum Barrier Passage as Potential-Driven Markovian Dynamics

Area of Science:

• Physics
• Chemistry
• Biology
• Quantum Mechanics

Background:

• Laser technologies offer high-resolution tools for studying barrier-passage dynamics.
• Existing theories for barrier passage are often system-specific and difficult to connect.
• A unified framework is needed to bridge diverse barrier-passage theories.

Purpose of the Study:

• To present a unified framework for describing classical and quantum barrier-passage phenomena.
• To reveal innate connections between various barrier-passage dynamics.
• To provide closed-form equations relating different barrier-passage rate signatures.

Main Methods:

• Development of a unified theoretical framework.
• Mathematical derivation of closed-form equations.
• Analysis of potential-driven Markovian dynamics.

Main Results:

• Demonstration of a unified description for diverse barrier-passage phenomena.
• Identification of connections between classical (e.g., Arrhenius law, Kramers' escape) and quantum (e.g., Hund's dynamics, Keldysh photoionization) processes.
• Formulation of equations showing the translation between classical and quantum barrier-passage rate exponentials.

Conclusions:

• Classical and quantum barrier-passage dynamics are unified under potential-driven Markovian dynamics.
• Differences in diffusion-driving potentials distinguish quantum tunneling from thermally activated passage.
• The framework offers a generalized understanding of barrier-passage phenomena across scientific disciplines.