-Interactions of atoms and molecules with surfaces PACS 05.45.-a -Nonlinear dynamical systems and chaos PACS 11.15.Yc -Chern-Simons gauge theory Abstract -We investigate the classical dynamics of a Rydberg hydrogen atom near the surface of a planar topological insulator. The system is described by a Hamiltonian consisting of the freehydrogen part and the hydrogen-surface potential. The latter includes the interactions between the electron and both image electric charges and image magnetic monopoles. Owing to the axial symmetry, the z component of angular momentum lz is conserved. Here we consider the lz = 0 case. The structure of the phase space is explored extensively by means of numerical techniques and Poincaré surfaces of section for the recently discovered topological insulator TlBiSe2. The phase space of the system is separated into regions of vibrational and rotational motion. We show that vibrational-rotational-vibrational type transitions can be tuned with the topological magnetoelectric polarizability.

In this paper, we study the Casimir effect in the classical geometry of two parallel conducting plates, separated by a distance L, due to the presence of a minimal length λ arising from a background independent (polymer) quantization scheme. To this end, we polymer-quantize the classical Klein-Gordon Hamiltonian for a massive scalar field confined between the plates and obtain the energy spectrum. The minimal length scale of the theory introduces a natural cutoff for the momenta in the plane parallel to the plates and a maximum number of discrete modes between the plates. The zero-point energy is calculated by summing over the modes, and by assuming λ L, we expressed it as an expansion in powers of 1/N , being N = L/λ the number of points between the plates. Closed analytical expressions are obtained for the Casimir energy in the cases of small and large scalar mass limits.

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