Conductance and Transmittance of waves through a chaotic cavity (or, equivalently, quantum dot) results in regularization of tunneling rates

Tunneling rates in closed, double well quantum or wave systems in two dimensions or higher are radically different between wells with classically regular or chaotic behavior [1]. Wells with regular dynamics have tunneling rates that fluctuate by several orders of magnitude as a function of energy or frequency. Wells with chaotic dynamics have fluctuations smaller than one order of magnitude (a regularization of the fluctuations). We examine a more realistic experimental system, a single well with two channels with tunneling barriers at their junctions with the wells. Former theories for conductance in quantum dots will not apply here. We developed a theory, which uses proper boundary conditions at the barriers and yields the scattering matrix. Results show that the transmission rates fluctuate by orders of magnitude in the regular-shaped well, but are greatly reduced (regularized) for the chaotic-shaped well. We will show experimental results that test these theoretical findings for microwave transmission through a chaotic-shaped cavity, which is made of copper and has two ports with tunneling barriers. [1] Chaos regularization of quantum tunneling rates, L. M. Pecora, H. Lee, D-H. Wu, T. Antonsen, M-J. Lee, and E. Ott, Phys. Rev. E 83, 065201(R) (2011)