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Updated: Aug 10, 2026
11:33
All-electronic Nanosecond-resolved Scanning Tunneling Microscopy: Facilitating the Investigation of Single Dopant Charge Dynamics
Published on: January 19, 2018
Semiclassical time evolution of the density matrix and tunneling
1Fakultat fur Physik, Albert-Ludwigs-Universitat Freiburg, Hermann-Herder-Strasse 3, D-79104 Freiburg, Germany.
Summary
This study uses path integrals to explore how systems penetrate potential barriers over time. It reveals that quantum tunneling arises from fluctuations, changing with temperature and linking real-time dynamics to instanton methods.
Area of Science:
- Quantum mechanics
- Statistical mechanics
Background:
- Understanding time-dependent density matrices is crucial for quantum systems.
- Potential barriers govern many physical and chemical processes.
Purpose of the Study:
- To analyze the time evolution of a density matrix for a system with a potential barrier.
- To investigate barrier penetration mechanisms in the semiclassical limit.
Main Methods:
- Utilized path integral formulation for time-dependent density matrix.
- Evaluated a threefold path integral in the semiclassical limit.
- Analyzed semiclassical trajectories in the complex coordinate plane.
Main Results:
- Semiclassical trajectories move in complex coordinates; barrier penetration stems from fluctuations.
- Temperature significantly alters semiclassical paths and fluctuations.
- Identified a transition from thermal activation to quantum tunneling.
Conclusions:
- Developed a real-time description of barrier penetration and quantum tunneling.
- Established connections between real-time tunneling and imaginary-time instanton approaches.
- Demonstrated deep tunneling linked to quasizero modes in fluctuation spectra.
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