A ribbon is a surface swept out by a line segment turning as it moves along a central curve. For narrow magnetic ribbons, for which the length of the line segment is much less than the length of the curve, the anisotropy induced by the magnetostatic
interaction is biaxial, with hard axis normal to the ribbon and easy axis along the central curve. The micromagnetic energy of a narrow ribbon reduces to that of a one-dimensional ferromagnetic wire, but with curvature, torsion and local anisotropy modified by the rate of turning. These general results are applied to two examples, namely a helicoid ribbon, for which the central curve is a straight line, and a Mobius ribbon, for which the central curve is a circle about which the line segment executes a $180^circ$ twist. In both examples, for large positive tangential anisotropy, the ground state magnetization lies tangent to the central curve. As the tangential anisotropy is decreased, the ground state magnetization undergoes a transition, acquiring an in-surface component perpendicular to the central curve. For the helicoid ribbon, the transition occurs at vanishing anisotropy, below which the ground state is uniformly perpendicular to the central curve. The transition for the Mobius ribbon is more subtle; it occurs at a positive critical value of the anisotropy, below which the ground state is nonuniform. For the helicoid ribbon, the dispersion law for spin wave excitations about the tangential state is found to exhibit an asymmetry determined by the geometric and magnetic chiralities.
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.
