An isolated white dwarf with 317 s rotation and magnetic emission

We report the discovery of short-period photometric variability and modulated Zeeman-split hydrogen emission in SDSSJ125230.93−023417.72 (EPIC 228939929), a variable white dwarf star observed at long cadence in K2 Campaign 10. The behavior is associated with a magnetic (B = 5.0 MG) spot on the stellar surface, making the 317.278 s period a direct measurement of the stellar rotation rate. This object is therefore the fastest-rotating, apparently isolated (without a stellar companion) white dwarf yet discovered and the second found to exhibit chromospheric Balmer emission after GD 356, in which the emission has been attributed to a unipolar inductor mechanism driven by a possible rocky planet. We explore the properties and behavior of this object, and consider whether its evolution may hold implications for white dwarf mergers and their remnants.Published versio

Self-trapping transition for nonlinear impurities embedded in a Cayley tree

The self-trapping transition due to a single and a dimer nonlinear impurity embedded in a Cayley tree is studied. In particular, the effect of a perfectly nonlinear Cayley tree is considered. A sharp self-trapping transition is observed in each case. It is also observed that the transition is much sharper compared to the case of one-dimensional lattices. For each system, the critical values of $\chi$ for the self-trapping transitions are found to obey a power-law behavior as a function of the connectivity $K$ of the Cayley tree.Comment: 6 pages, 7 fig