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Quantum transport through ballistic cavities: soft vs hard quantum chaos
Huckestein1, Ketzmerick, Lewenkopf
1Institut fur Theoretische Physik, Universitat zu Koln, D-50937 Koln, Germany.
Physical Review Letters
|September 16, 2000
Summary
We investigated quantum transport in a 2D billiard, finding power-law distributions in resonance widths and conductance that differ from chaotic systems and appear at unexpected energy scales.
Area of Science:
- Quantum chaos
- Mesoscopic physics
- Condensed matter theory
Background:
- Understanding quantum transport in complex systems is crucial.
- Billiard models provide insights into electron behavior in confined geometries.
- Mixed phase space dynamics present unique challenges compared to fully chaotic systems.
Purpose of the Study:
- To numerically calculate Landauer conductance and Wigner time delay in a 2D billiard connected to leads.
- To investigate transport properties in a mixed phase space regime.
- To compare findings with predictions for fully chaotic systems and semiclassical expectations.
Main Methods:
- Numerical calculation of Landauer conductance.
- Numerical calculation of Wigner time delay.
- Analysis of transport through a two-dimensional billiard attached to two infinite leads.
Main Results:
- Observed power-law distribution of resonance widths in a mixed phase space.
- Found power-law dependence of conductance increments, reflecting classical dwell time exponent.
- These power laws emerged at energy scales below the mean level spacing, contrary to semiclassical theory.
Conclusions:
- The transport properties of a 2D billiard with mixed phase space exhibit distinct power-law behaviors.
- Findings challenge semiclassical expectations regarding the energy scales of quantum transport phenomena.
- The study highlights the importance of phase space structure in determining quantum transport characteristics.
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