Patchak v. Zinke, Separation of Powers, and the Pitfalls of Form over Substance

Mr. Patchak was a concerned citizen with standing to bring a suit against the federal government. A previous Supreme Court decision, Carcieri v. Salazar, made it clear that Mr. Patchak would win his case. Congress, however, did not want him to do so. Congress passed, and President Obama signed, the Gun Lake Act, which effectively ordered Mr. Patchak’s suit to be dismissed. Mr. Patchak’s suit was subsequently dismissed, and he appealed on the grounds that the Gun Lake Act violated separation of powers principles

The Partially-Split Hall Bar: Tunneling in the Bosonic Integer Quantum Hall Effect

We study point-contact tunneling in the integer quantum Hall state of bosons. This symmetry-protected topological state has electrical Hall conductivity equal to $2 e^2/h$ and vanishing thermal Hall conductivity. In contrast to the integer quantum Hall state of fermions, a point contact can have a dramatic effect on the low energy physics. In the absence of disorder, a point contact generically leads to a partially-split Hall bar geometry. We describe the resulting intermediate fixed point via the two-terminal electrical (Hall) conductance of the edge modes. Disorder along the edge, however, both restores the universality of the two-terminal conductance and helps preserve the integrity of the Hall bar within the relevant parameter regime.Comment: 12 pages, 5 figures; v.2: typos fixed and clarified some argument

Criticality in multicomponent spherical models : results and cautions

To enable the study of criticality in multicomponent fluids, the standard spherical model is generalized to describe an \ns-species hard core lattice gas. On introducing \ns spherical constraints, the free energy may be expressed generally in terms of an \ns\times\ns matrix describing the species interactions. For binary systems, thermodynamic properties have simple expressions, while all the pair correlation functions are combinations of just two eigenmodes. When only hard-core and short-range overall attractive interactions are present, a choice of variables relates the behavior to that of one-component systems. Criticality occurs on a locus terminating a coexistence surface; however, except at some special points, an unexpected ``demagnetization effect'' suppresses the normal divergence of susceptibilities at criticality and distorts two-phase coexistence. This effect, unphysical for fluids, arises from a general lack of symmetry and from the vectorial and multicomponent character of the spherical model. Its origin can be understood via a mean-field treatment of an XY spin system below criticality.Comment: 4 figure