23 research outputs found
A One-Dimensional Model for Many-Electron Atoms in Extremely Strong Magnetic Fields: Maximum Negative Ionization
We consider a one-dimensional model for many-electron atoms in strong
magnetic fields in which the Coulomb potential and interactions are replaced by
one-dimensional regularizations associated with the lowest Landau level. For
this model we show that the maximum number of electrons is bounded above by
2Z+1 + c sqrt{B}.
We follow Lieb's strategy in which convexity plays a critical role. For the
case of two electrons and fractional nuclear charge, we also discuss the
critical value at which the nuclear charge becomes too weak to bind two
electrons.Comment: 23 pages, 5 figures. J. Phys. A: Math and General (in press) 199
Equilibrium Shape of Crystals
This chapter discusses the equilibrium crystal shape (ECS) from a physical
perspective, beginning with a historical introduction to the Wulff theorem. It
takes advantage of excellent prior reviews, particularly in the late 1980's,
recapping highlights from them. It contains many ideas and experiments
subsequent to those reviews. Alternatives to Wulff constructions are presented.
Controversies about the critical behavior near smooth edges on the ECS are
recounted, including the eventual resolution. Particular attention is devoted
to the origin of sharp edges on the ECS, to the impact of reconstructed or
adsorbed surface phases coexisting with unadorned phases, and to the role and
nature of possible attractive step-step interactions.Comment: Review from Handbook of Crystal Growth, Fundamentals, 2nd ed., T.
Nishinaga, ed. (Elsevier, Amsterdam, 2015), vol. 1A (Thermodynamics and
Kinetics), ch. 5, pp. 215-264; ISBN 9780444563699/eBook:9780444593764;
http://www.sciencedirect.com/science/article/pii/B9780444563699000058. 26
figs., reformatted into Phys. Rev. style, 30 pages; slightly modified,
alphabetized bibliography, inc. title