We study the quantum Goos-H{a}nchen(GH) effect for wave-packet dynamics at a normal/superconductor (NS) interface. We find that the effect is amplified by a factor $(E_F/Delta)$, with $E_F$ the Fermi energy and $Delta$ the gap. Interestingly, the GH effect appears only as a time delay $delta t$ without any lateral shift, and the corresponding delay length is about $(E_F/Delta)lambda_F$, with $lambda_F$ the Fermi wavelength. This makes the NS interface sticky when $Delta ll E_F$, since typically GH effects are of wavelength order. This sticky behavior can be further enhanced by a resonance mode in NSNS interface. Finally, for a large $Delta$, the resonance-mode effect makes a transition from Andreev to the specular electron reflection as the width of the sandwiched superconductor is reduced.
Transition State Theory forms the basis of computing reaction rates in chemical and other systems. Recently it has been shown how transition state theory can rigorously be realized in phase space using an explicit algorithm. The quantization has been demonstrated to lead to an efficient procedure to compute cumulative reaction probabilities and the associated Gamov-Siegert resonances. In this letter these results are used to express the cumulative reaction probability as an absolutely convergent sum over periodic orbits contained in the transition state.
