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Relation between stable orbits and quantum transmission resonance in ballistic cavities
1Paul-Drude-Institut fur Festkorperelektronik, Hausvogteiplatz 5-7, D-10117 Berlin, Germany.
Summary
Classical and quantum transport in chaotic cavities reveal a direct link. Regular orbits in phase space trap classical trajectories, leading to quantum transmission resonances that match these stable orbits.
Area of Science:
- Physics
- Quantum Mechanics
- Classical Mechanics
Background:
- Investigating transport properties in chaotic cavities is crucial for understanding complex systems.
- Classical and quantum-mechanical behaviors in these systems often diverge, posing a theoretical challenge.
Purpose of the Study:
- To establish a direct link between classical and quantum-mechanical transport properties in chaotic cavities.
- To explain the origin of conductance fluctuations in ballistic cavities.
Main Methods:
- Analysis of classical trajectories in phase space, focusing on 'stickiness' near regular orbits.
- Investigation of quantum wave-function patterns at transmission resonances.
- Application of Bohr and Sommerfeld's quantization rule.
Main Results:
- Classical trajectories exhibit 'stickiness,' spending extended periods near stable orbits.
- Quantum wave-function patterns at transmission resonances precisely match these stable classical orbits.
- This correspondence explains conductance fluctuations in ballistic cavities as arising from quantized stable orbits.
Conclusions:
- A clear correspondence exists between classical sticky orbits and quantum transmission resonances.
- The Bohr and Sommerfeld quantization rule governs these resonances, explaining observed frequency components in conductance fluctuations.
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