Periodicity and Quasi-Periodicity for Super-Integrable Hamiltonian Systems

Classical trajectories are calculated for two Hamiltonian systems with ring shaped potentials. Both systems are super-integrable, but not maximally super-integrable, having four globally defined single valued integrals of motion each. All finite trajectories are quasi-periodical; they become truly periodical if a commensurability condition is imposed on an angular momentum component

Considering the Case for Biodiversity Cycles: Reexamining the Evidence for Periodicity in the Fossil Record

Medvedev and Melott (2007) have suggested that periodicity in fossil biodiversity may be induced by cosmic rays which vary as the Solar System oscillates normal to the galactic disk. We re-examine the evidence for a 62 million year (Myr) periodicity in biodiversity throughout the Phanerozoic history of animal life reported by Rohde & Mueller (2005), as well as related questions of periodicity in origination and extinction. We find that the signal is robust against variations in methods of analysis, and is based on fluctuations in the Paleozoic and a substantial part of the Mesozoic. Examination of origination and extinction is somewhat ambiguous, with results depending upon procedure. Origination and extinction intensity as defined by RM may be affected by an artifact at 27 Myr in the duration of stratigraphic intervals. Nevertheless, when a procedure free of this artifact is implemented, the 27 Myr periodicity appears in origination, suggesting that the artifact may ultimately be based on a signal in the data. A 62 Myr feature appears in extinction, when this same procedure is used. We conclude that evidence for a periodicity at 62 Myr is robust, and evidence for periodicity at approximately 27 Myr is also present, albeit more ambiguous.Comment: Minor modifications to reflect final published versio

Proposed Detection of the Topological Phase in Ring-Shaped Semiconductor-Superconductor Nanowires Using Coulomb Blockade Transport

In semiconductor-superconductor hybrid structures a topological phase transition is expected as a function of chemical potential or magnetic field strength. We show that signatures of this transition can be observed in nonlinear Coulomb blockade transport through a ring shaped structure. In particular, for a fixed electron parity of the ring, the flux periodicity of the neutral excitation spectrum changes from the usual h/2e periodicity to a characteristic h/e periodicity when tuning the system from the topologically trivial to the nontrivial phase. We relate the h/e periodicity to the recently predicted 4\pi periodicity of the Josephson current across a junction formed by two topological superconductors.Comment: 5 pages, 4 figure

Re-parameterization Invariance in Fractional Flux Periodicity

We analyze a common feature of a nontrivial fractional flux periodicity in two-dimensional systems. We demonstrate that an addition of fractional flux can be absorbed into re-parameterization of quantum numbers. For an exact fractional periodicity, all the electronic states undergo the re-parameterization, whereas for an approximate periodicity valid in a large system, only the states near the Fermi level are involved in the re-parameterization.Comment: 4 pages, 1 figure, minor changes, final version to appear in J. Phys. Soc. Jp

A new proof for the decidability of D0L ultimate periodicity

We give a new proof for the decidability of the D0L ultimate periodicity problem based on the decidability of p-periodicity of morphic words adapted to the approach of Harju and Linna.Comment: In Proceedings WORDS 2011, arXiv:1108.341