Second virial coefficient for the Landau diamagnetism of a two component plasma

This paper investigates the density expansion of the thermodynamic properties of a two component plasma under the influence of a weak constant uniform magnetic field. We start with the fugacity expansion for the Helmholtz free energy. The leading terms with respect to the density are calculated by a perturbation expansion with respect to the magnetic field. We find a new magnetic virial function for a low density plasma which is exact in quadratic order with respect to the magnetic field. Using these results we compute the magnetization and the magnetic susceptibility.Comment: 16 pages, 4 figures, to appear in Phys.Rev.

Extracting joint weak values with local, single-particle measurements

Weak measurement is a new technique which allows one to describe the evolution of postselected quantum systems. It appears to be useful for resolving a variety of thorny quantum paradoxes, particularly when used to study properties of pairs of particles. Unfortunately, such nonlocal or joint observables often prove difficult to measure weakly in practice (for instance, in optics -- a common testing ground for this technique -- strong photon-photon interactions would be needed). Here we derive a general, experimentally feasible, method for extracting these values from correlations between single-particle observables.Comment: 6 page

Ground-state energy of a high-density electron gas in a strong magnetic field

The high-density electron gas in a strong magnetic field B and at zero temperature is investigated. The quantum strong-field limit is considered in which only the lowest Landau level is occupied. It is shown that the perturbation series of the ground-state energy can be represented in analogy to the Gell-Mann Brueckner expression of the ground-state energy of the field-free electron gas. The role of the expansion parameter is taken by $r_B= (2/3 \pi^2) (B/m^2) (\hbar r_S/e)^3$ instead of the field-free Gell-Mann Brueckner parameter r_s.Comment: 4 pages, 2 figures, to appear in the proceedings of the 1999 International Conference on Strongly Coupled Coulomb Systems (St.Malo

Beating Rayleigh's Curse by Imaging Using Phase Information

Any imaging device such as a microscope or telescope has a resolution limit, a minimum separation it can resolve between two objects or sources; this limit is typically defined by "Rayleigh's criterion", although in recent years there have been a number of high-profile techniques demonstrating that Rayleigh's limit can be surpassed under particular sets of conditions. Quantum information and quantum metrology have given us new ways to approach measurement ; a new proposal inspired by these ideas has now re-examined the problem of trying to estimate the separation between two poorly resolved point sources. The "Fisher information" provides the inverse of the Cramer-Rao bound, the lowest variance achievable for an unbiased estimator. For a given imaging system and a fixed number of collected photons, Tsang, Nair and Lu observed that the Fisher information carried by the intensity of the light in the image-plane (the only information available to traditional techniques, including previous super-resolution approaches) falls to zero as the separation between the sources decreases; this is known as "Rayleigh's Curse." On the other hand, when they calculated the quantum Fisher information of the full electromagnetic field (including amplitude and phase information), they found it remains constant. In other words, there is infinitely more information available about the separation of the sources in the phase of the field than in the intensity alone. Here we implement a proof-of-principle system which makes use of the phase information, and demonstrate a greatly improved ability to estimate the distance between a pair of closely-separated sources, and immunity to Rayleigh's curse

Markov chains, R\mathscr R-trivial monoids and representation theory

We develop a general theory of Markov chains realizable as random walks on $\mathscr R$-trivial monoids. It provides explicit and simple formulas for the eigenvalues of the transition matrix, for multiplicities of the eigenvalues via M\"obius inversion along a lattice, a condition for diagonalizability of the transition matrix and some techniques for bounding the mixing time. In addition, we discuss several examples, such as Toom-Tsetlin models, an exchange walk for finite Coxeter groups, as well as examples previously studied by the authors, such as nonabelian sandpile models and the promotion Markov chain on posets. Many of these examples can be viewed as random walks on quotients of free tree monoids, a new class of monoids whose combinatorics we develop.Comment: Dedicated to Stuart Margolis on the occasion of his sixtieth birthday; 71 pages; final version to appear in IJA

Directed nonabelian sandpile models on trees

We define two general classes of nonabelian sandpile models on directed trees (or arborescences) as models of nonequilibrium statistical phenomena. These models have the property that sand grains can enter only through specified reservoirs, unlike the well-known abelian sandpile model. In the Trickle-down sandpile model, sand grains are allowed to move one at a time. For this model, we show that the stationary distribution is of product form. In the Landslide sandpile model, all the grains at a vertex topple at once, and here we prove formulas for all eigenvalues, their multiplicities, and the rate of convergence to stationarity. The proofs use wreath products and the representation theory of monoids.Comment: 43 pages, 5 figures; introduction improve