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Semiclassical relation between open trajectories and periodic orbits for the Wigner time delay
1School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom. jack.kuipers@bristol.ac.uk
Summary
This study reveals the semiclassical connection between scattering trajectories and periodic orbits for Wigner time delay in chaotic quantum systems. It demonstrates how these two distinct descriptions of quantum dynamics are fundamentally related.
Area of Science:
- Quantum mechanics
- Chaos theory
- Scattering theory
Background:
- Wigner time delay in classically chaotic quantum systems can be described semiclassically using scattering trajectories or trapped periodic orbits.
- The relationship between these two semiclassical descriptions has not been fully elucidated.
Purpose of the Study:
- To demonstrate the semiclassical relationship between scattering trajectory and periodic orbit formulations of Wigner time delay.
- To derive the periodic orbit contributions to time delay from the scattering trajectory formulation.
Main Methods:
- Semiclassical analysis of Wigner time delay.
- Derivation of periodic orbit contributions from scattering trajectory formulas.
- Investigation of correlations between scattering trajectories approaching periodic orbits.
- Analysis of time delay correlation functions.
Main Results:
- Successfully derived the periodic orbit formula for time delay from the scattering trajectory formula.
- Identified correlations between scattering trajectories and trapped periodic orbits as the key link.
- Demonstrated the equivalence of the two pictures through correlation functions.
- Found no leading-order periodic orbit contributions to conductance.
Conclusions:
- The scattering trajectory and periodic orbit pictures for Wigner time delay in chaotic quantum systems are equivalent on the semiclassical level.
- Correlations between scattering trajectories and periodic orbits are crucial for this equivalence.
- The framework provides a unified understanding of quantum chaotic dynamics.
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