The metamorphoses of the light cones of a relativistic particle on a ring

In this paper, we investigate the dynamics of a relativistic particle confined to a ring. The focus is on the metamorphoses of the functional form of the particle propagator induced by a change in the asymptotic parameter, proportional to the ratio of the ring length to the particle Compton wavelength. Tackling the divergent nature of the propagator enabled us to describe and classify all patterns produced by particle self-interference, regardless of the shape of the initial wave packet. We shall show under which conditions a quasiperiodic structure, known as quantum carpets, arises and demonstrate that its quartic part of the phase function, which structurally stabilizes the canonical carpet, is not just a correction but explains all features of the exact solution.