N. D. Mermin

Farkas's Lemma and the nature of reality: Statistical implications of quantum correlations

A general algorithm is given for determining whether or not a given set of pair distributions allows for the construction of all the members of a specified set of higher-order distributions which return the given pair distributions as marginals. This mathematical question underlies studies of quantum correlation experiments such as those of Bell or of Clauser and Horne, or their higher-spin generalizations. The algorithm permits the analysis of rather intricate versions of such problems, in a form readily adaptable to the computer. The general procedure is illustrated by simple derivations of the results of Mermin and Schwarz for the symmetric spin-1 and spin-3/2 Einstein-Podolsky-Rosen problems. It is also used to extend those results to the spin-2 and spin-5/2 cases, providing further evidence that the range of strange quantum theoretic correlations does not diminish with increasing s. The algorithm is also illustrated by giving an alternative derivation of some recent results on the necessity and sufficiency of the Clauser-Horne conditions. The mathematical formulation of the algorithm is given in general terms without specific reference to the quantum theoretic applications.

Topological analysis of the cores of singularities in 3He-A

The methods of homotopy theory are employed to study the internal (core) structure of singularities. The technique is illustrated by several applications to line singularities in the A-phase of superfluid helium-3.

Pitfalls of the relaxation time approximation: hydrodynamic sound in a multicomponent Fermi liquid

When transport in a Fermi liquid is treated in the relaxation time approximation, the quasiparticle energy appearing in the local equilibrium distribution must have the form determined by the nonequilibrium distribution function. Sometimes this requirement is overlooked and the equilibrium quasiparticle energy is used. In applications to unpolarized normal3He the resulting error can be repaired by a simple rescaling of the relaxation rates 1/τ1 by the Fermi liquid corrections 1+Fl/(2l+1). The distinction between the two forms of the relaxation time approximation is thus of little consequence, and quantities independent of the relaxation time are entirely unaffected. We point out that more significant damage results from using this wrong relaxation time approximation in a multicomponent (or spin-polarized single-component) Fermi liquid. In particular, it is essential to use the correct form to derive the velocity of hydrodynamic sound, even though the incorrect form also satisfies all the conservation laws, and even though the sound velocity is independent of the relaxation time.