Relativistic quantum plasma dispersion functions

Relativistic quantum plasma dispersion functions are defined and the longitudinal and transverse response functions for an electron (plus positron) gas are written in terms of them. The dispersion is separated into Landau-damping, pair-creation and dissipationless regimes. Explicit forms are given for the RQPDFs in the cases of a completely degenerate distribution and a nondegenerate thermal (J\"uttner) distribution. Particular emphasis is placed on the relation between dissipation and dispersion, with the dissipation treated in terms of the imaginary parts of RQPDFs. Comparing the dissipation calculated in this way with the existing treatments leads to the identification of errors in the literature, which we correct. We also comment on a controversy as to whether the dispersion curves in a superdense plasma pass through the region where pair creation is allowed.Comment: 16 pages, 1 figur

Shear-thickening and entropy-driven reentrance

We discuss a generic mechanism for shear-thickening analogous to entropy-driven phase reentrance. We implement it in the context of non-relaxational mean-field glassy systems: although very simple, the microscopic models we study present a dynamical phase diagram with second and first order stirring-induced jamming transitions leading to intermittency, metastability and phase coexistence as seen in some experiments. The jammed state is fragile with respect to change in the stirring direction. Our approach provides a direct derivation of a Mode-Coupling theory of shear-thickening.Comment: 4 pages, 4 figures, minor changes, references adde

The Rheology and Microstructure of Concentrated, Aggregated Colloids

The rheology of concentrated, aggregated colloidal suspensions is determined through particulate simulations. Aggregating systems experience a large viscous enhancement over nonaggregating systems, this being due to the increase in the component of the viscosity arising from the repulsive colloid ~thermodynamic! forces when attractive forces are present. The shear behavior of aggregating systems, for colloid volume fraction 0.47 < fc < 0.57, is characterized in the steady state regime over a wide range in shear rate, and is found to be power law, shear thinning h; f (fc)ġ2a, where the shear thinning index a 5 0.8460.01. The effect of volume fraction enters as f (fc) 5 (12fc /fmax)21, with fmax 5 0.64, the value of random close packing; similarly, the viscosity also scales with the potential well depth as a power law, of index a. Consequently, we are able to deduce the full constitutive relation for this power law behavior. The associated structural features which emerge as a result of the imposed shear are identified with the rheology. The shear thinning regime crosses over into a state of ordered phase flow at high shear rates likewise simulations of hard sphere fluids. We also show that the high-shear ordered configurations appear to be a function of colloid concentration, with a transition from string phase order through to layered phases as fc increases. © 1999 The Society of Rheology

Elliptic operators on manifolds with singularities and K-homology

It is well known that elliptic operators on a smooth compact manifold are classified by K-homology. We prove that a similar classification is also valid for manifolds with simplest singularities: isolated conical points and fibered boundary. The main ingredients of the proof of these results are: an analog of the Atiyah-Singer difference construction in the noncommutative case and an analog of Poincare isomorphism in K-theory for our singular manifolds. As applications we give a formula in topological terms for the obstruction to Fredholm problems on manifolds with singularities and a formula for K-groups of algebras of pseudodifferential operators.Comment: revised version; 25 pages; section with applications expande

Periodicity and the determinant bundle

The infinite matrix `Schwartz' group $G^{-\infty}$ is a classifying group for odd K-theory and carries Chern classes in each odd dimension, generating the cohomology. These classes are closely related to the Fredholm determinant on $G^{-\infty}.$ We show that while the higher (even, Schwartz) loop groups of $G^{-\infty},$ again classifying for odd K-theory, do \emph{not} carry multiplicative determinants generating the first Chern class, `dressed' extensions, corresponding to a star product, do carry such functions. We use these to discuss Bott periodicity for the determinant bundle and the eta invariant. In so doing we relate two distinct extensions of the eta invariant, to self-adjoint elliptic operators and to elliptic invertible suspended families and show that the corresponding $\tau$ invariant is a determinant in this sense

Rules for transition rates in nonequilibrium steady states

Just as transition rates in a canonical ensemble must respect the principle of detailed balance, constraints exist on transition rates in driven steady states. I derive those constraints, by maximum information-entropy inference, and apply them to the steady states of driven diffusion and a sheared lattice fluid. The resulting ensemble can potentially explain nonequilibrium phase behaviour and, for steady shear, gives rise to stress-mediated long-range interactions.Comment: 4 pages. To appear in Physical Review Letter

Circular Polarization Induced by Scintillation in a Magnetized Medium

A new theory is presented for the development of circular polarization as radio waves propagate through the turbulent, birefringent interstellar medium. The fourth order moments of the wavefield are calculated and it is shown that unpolarized incident radiation develops a nonzero variance in circular polarization. A magnetized turbulent medium causes the Stokes parameters to scintillate in a non-identical manner. A specific model for this effect is developed for the case of density fluctuations in a uniform magnetic field.Comment: 16 pages, 1 figure, Phys. Rev. E, accepte

Instabilities in neutrino-plasma density waves

One examines the interaction and possible resonances between supernova neutrinos and electron plasma waves. The neutrino phase space distribution and its boundary regions are analyzed in detail. It is shown that the boundary regions are too wide to produce non-linear resonant effects. The growth or damping rates induced by neutrinos are always proportional to the neutrino flux and $G_{{\rm F}}^{2}$.Comment: 9 pages, a few words modified to match PRD publicatio

Coincidence of length spectra does not imply isospectrality

Penrose--Lifshits mushrooms are planar domains coming in nonisometric pairs with the same geodesic length spectrum. Recently S. Zelditch raised the question whether such billiards also have the same eigenvalue spectrum for the Dirichlet Laplacian (conjecturing ``no''). Here we show that generically (in the class of smooth domains) the two members of a mushroom pair have different spectra.Comment: 8 pages, 5 figure

The stationary phase point method for transitional scattering: diffractive radio scintillation for pulsar

The stationary phase point (SPP) method in one-dimensional case is introduced to treat the diffractive scintillation. From weak scattering, where the SPP number N=1, to strong scattering (N$\gg$1), via transitional scattering regime (N$\sim$2,3), we find that the modulation index of intensity experiences the monotonically increasing from 0 to 1 with the scattering strength, characterized by the ratio of Fresnel scale \rf to diffractive scale \rdiff.Comment: Hanas Meeting paper, appear in ChJAA, 2006, 6, Su