Activated quantum diffusion in a periodic potential above the crossover temperature.

Area of Science:

• Surface science
• Quantum mechanics
• Chemical physics

Background:

• Activated surface diffusion is crucial for various surface phenomena.
• Pollak, Grabert, and Hänggi (PGH) turnover theory models activated surface diffusion.
• Quantum effects become significant at low temperatures and for light particles.

Purpose of the Study:

• To extend the Pollak, Grabert, and Hänggi (PGH) turnover theory to the quantum domain for activated surface diffusion.
• To investigate the influence of finite barrier effects and quantum tunneling on diffusion properties.
• To analyze the behavior of the diffusion coefficient, escape rate, hopping distribution, and mean squared path length.

Main Methods:

• Analytic expressions derived from the extended PGH theory.
• Inclusion of incoherent quantum hopping above the deep tunneling/thermal activation crossover temperature.
• Application to a periodic cosine potential with frictional and Gaussian random forces.
• Consideration of a scaled mass that increases with friction strength.

Main Results:

• Quantum diffusion is slower than classical diffusion in the weak damping regime due to above-barrier quantum reflection.
• Quantum reflection significantly reduces the mean squared path length compared to classical diffusion.
• Finite barrier corrections enhance the quantum suppression of diffusion, leading to an inverse isotope effect (heavier masses diffuse faster).

Conclusions:

• The extended PGH theory provides a framework for understanding quantum activated surface diffusion.
• Quantum reflection acts as a significant impediment to diffusion, particularly in the weak damping regime.
• Finite barrier effects and quantum tunneling play critical roles in determining diffusion dynamics and can lead to counterintuitive phenomena like the inverse isotope effect.