Scattering matrices and conductances of leaky tori
Leaky tori are two-dimensional surfaces that extend to infinity but which have finite area. It is a tempting idea to regard them as models of mesoscopic systems connected to very long leads. Because of this analogy -- scattering matrices on leaky tori are potentially interesting, and indeed -- the scattering matrix on one such object -- ``the'' leaky torus -- was studied by M. Gutzwiller, who showed that it has chaotic behavior. M. Antoine, A. Comtet and S. Ouvry generalized Gutzwiller's result by calculating the scattering matrix in the presence of a constant magnetic field \(B\) perpendicular to the surface. Motivated by these results -- we generalize them further. We define scattering matrices for spinless electrons on a general leaky torus in the presence of a constant magnetic field ``perpendicular'' to the surface. From the properties of these matrices we show the following: (a) For integer values of \(B\), \(T_{ij}\) (the transition probability from cusp \(i\) to cusp \(j\)), and hence also the Büttiker conductances of the surfaces, are \(B\)-independent (this cannot be interpreted as a kind of Aharonov-Bohm effect since a magnetic force is acting on the electrons). (b) The Wigner time-delay is a monotonically increasing function of \(B\).
scientific article; zbMATH DE number 553595