Tunneling Flight Time, Chemistry, and Special Relativity

Area of Science:

• Quantum mechanics
• Chemical dynamics
• Atomic physics

Background:

• The concept of tunneling time in quantum mechanics is debated, with different definitions yielding conflicting results.
• A zero tunneling time implies superluminal speeds in nonrelativistic quantum theory, challenging its applicability to tunneling reactions.
• Existing attosecond ionization experiments have not definitively resolved the tunneling time paradox.

Purpose of the Study:

• To define and experimentally measure a new paradigm for tunneling time.
• To resolve the paradoxes associated with zero tunneling time in nonrelativistic quantum theory.
• To clarify the quantum mechanical nature of tunneling processes relevant to chemical reactions.

Main Methods:

• Definition of a novel, experimentally measurable quantity: tunneling flight time.
• Theoretical analysis of scattering through Eckart and square potential barriers.
• Comparison of classical Wigner theory with exact quantum mechanical computations.

Main Results:

• The proposed tunneling flight time vanishes for scattering through Eckart or square barriers, regardless of barrier parameters.
• This vanishing tunneling time generalizes the Hartman effect.
• The study explains why this result does not imply experimental observation of speeds exceeding the speed of light.
• Tunneling is demonstrated to be an incoherent process.

Conclusions:

• The tunneling flight time provides a consistent, measurable definition resolving the quantum tunneling time paradox.
• This framework reconciles tunneling phenomena with nonrelativistic quantum theory, validating its use in quantum dynamics.
• The findings clarify the nature of tunneling in chemical reactions and other quantum processes.