Quantum transport through ballistic cavities: soft vs. hard quantum chaos
Bodo Huckestein, Roland Ketzmerick, and Caio H. Lewenkopf
TL;DR
This paper investigates quantum transport in two-dimensional billiards with mixed phase space, revealing power law behaviors in conductance and resonance widths that challenge semiclassical predictions.
Contribution
It provides a detailed numerical analysis of quantum transport in systems with mixed phase space, highlighting unexpected power law phenomena at energy scales below the mean level spacing.
Findings
Power law distribution of resonance widths
Power law dependence of conductance increments
Power laws occur below the mean level spacing
Abstract
We study transport through a two-dimensional billiard attached to two infinite leads by numerically calculating the Landauer conductance and the Wigner time delay. In the generic case of a mixed phase space we find a power law distribution of resonance widths and a power law dependence of conductance increments apparently reflecting the classical dwell time exponent, in striking difference to the case of a fully chaotic phase space. Surprisingly, these power laws appear on energy scales {\em below} the mean level spacing, in contrast to semiclassical expectations.
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