arXiv subjects
Publications and source records attributed to Pavel Hejcik.
We examine one-dimensional quantum scattering of a Dirac particle off relativistic potential barriers. With proper considerations of Dirac sea, existence of anomalous tunneling at zero incident-energy is revealed for a particular type of relativistic potential having same magnitudes and opposite signs for scalar and vector components. It is also shown that this leads to an exotic short range limit of the potentials.
We show that the quantum single particle motion on a one-dimensional line with Fulop-Tsutsui point interactions exhibits characteristics usually associated with nonintegrable systems both in bound state level statistics and scattering amplitudes. We argue that this is a reflection of the underlying stochastic dynamics which persists in classical domain.
We study approximations of billiard systems by lattice graphs. It is demonstrated that under natural assumptions the graph wavefunctions approximate solutions of the Schroedinger equation with energy rescaled by the billiard dimension. As an example, we analyze a Sinai billiard with attached leads. The results illustrate emergence of global structures in large quantum graphs and offer interesting comparisons with patterns observed in complex networks of a different nature.