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Updated: Jul 10, 2026
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All-electronic Nanosecond-resolved Scanning Tunneling Microscopy: Facilitating the Investigation of Single Dopant Charge Dynamics
Published on: January 19, 2018
Unstable semiclassical trajectories in tunneling.
D G Levkov1, A G Panin, S M Sibiryakov
1Institute for Nuclear Research of the Russian Academy of Sciences, 60th October Anniversary prospect 7a, Moscow 117312, Russia.
Physical Review Letters
|November 13, 2007
Summary
This study introduces a method to stabilize complex trajectories for calculating quantum tunneling probability. The findings reveal how trajectory instability affects the tunneling prefactor, offering new insights into quantum mechanics.
Area of Science:
- Quantum Mechanics
- Physical Chemistry
- Computational Physics
Background:
- Quantum tunneling is a phenomenon where particles pass through potential barriers, crucial in various physical and chemical processes.
- Semiclassical approximations often utilize complex trajectories to describe tunneling, but these can be unstable.
- Calculating tunneling probability accurately, including its suppression exponent and prefactor, is essential for theoretical and experimental applications.
Purpose of the Study:
- To develop a systematic procedure for stabilizing unstable complex trajectories in semiclassical tunneling calculations.
- To accurately compute the tunneling probability, encompassing both the suppression exponent and the prefactor.
- To investigate the impact of trajectory instability on the prefactor's dependence on Planck's variant.
Main Methods:
- Development of a novel systematic procedure to stabilize complex trajectories.
- Application of the stabilized trajectories to calculate quantum tunneling probability.
- Analysis of the tunneling prefactor's scaling behavior with respect to Planck's variant.
Main Results:
- A robust method for stabilizing unstable complex trajectories in semiclassical tunneling is established.
- The study successfully calculates tunneling probability, including suppression exponent and prefactor.
- Instability of tunneling solutions was found to alter the power-law dependence of the prefactor compared to stable solutions.
Conclusions:
- The developed method provides a reliable approach for analyzing quantum tunneling phenomena.
- Trajectory instability significantly influences the prefactor, necessitating careful consideration in semiclassical models.
- This work advances the understanding of quantum tunneling and its semiclassical description.
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