Quantum Tunneling: The Longer the Path, the Less Time it Takes.

Area of Science:

• Quantum mechanics
• Quantum dynamics
• Statistical mechanics

Background:

• Standard tunneling time calculations lack a rigorous quantum mechanical foundation.
• Time correlation functions offer a novel approach to quantum dynamics.

Purpose of the Study:

• To develop a new formalism for quantum mechanical transition times using correlation functions.
• To investigate quantum dynamics and transition time distributions for a parabolic barrier.

Main Methods:

• Utilizing a class of always-positive correlation functions.
• Defining quantum mechanical transition time probability distributions.
• Analyzing a thermal position correlation function for a parabolic barrier Hamiltonian.

Main Results:

• Transition time probability distributions shift to shorter times with reduced temperature and increased tunneling.
• Mean transition time decreases with increasing path length at low temperatures where tunneling dominates.
• Friction's effect on this phenomenon is minimal unless the friction coefficient is very large.

Conclusions:

• The developed correlation function formalism provides a robust method for studying quantum tunneling times.
• Temperature and friction significantly influence quantum transition dynamics.
• The findings offer new insights into the nature of time in quantum mechanics.