We calculate expressions for the state-dependent quasiparticle lifetime, the thermal conductivity $kappa$, the shear viscosity $eta$, and discuss the spin diffusion coefficient $D$ for Fermi-liquid films in two dimensions. The expressions are valid f
or low temperatures and arbitrary polarization. The low-temperature expressions for the transport coefficients are essentially exact. We find that $kappa^{-1} sim T ln{T}$, and $eta^{-1} sim T^{2}$ for arbitrary polarizations $0 le {mathcal{P}} le 1$. We note that the shear viscosity requires a unique analysis. We utilize previously determined values for the density and polarization dependent Landau parameters to calculate the transition probabilities in the lowest order $ell = 0$ approximation, and thus we obtain predictions for the density, temperature and polarization dependence of the thermal conductivity, shear viscosity, and spin diffusion coefficient for thin he3 films. Results are shown for second layer he3 films on graphite, and thin he3-he4 superfluid mixtures. The density dependence is discussed in detail. For $kappa$ and $eta$ we find roughly an order of magnitude increase in magnitude from zero to full polarization. For $D$ a simialr large increase is predicted from zero polarization to the polarization where $D$ is a maximum ($sim 0.74$). We discuss the applicability of he3 thin films to the question of the existence of a universal lower bound for the ratio of the shear viscosity to the entropy density.
We derive shape-independent limits to the spectral radiative heat-transfer rate between two closely spaced bodies, generalizing the concept of a black body to the case of near-field energy transfer. Through conservation of energy and reciprocity, we
show that each body of susceptibility $chi$ can emit and absorb radiation at enhanced rates bounded by $|chi|^2 / textrm{Im} chi$, optimally mediated by near-field photon transfer proportional to $1/d^2$ across a separation distance $d$. Dipole--dipole and dipole--plate structures approach restrict
At visible and infrared frequencies, metals show tantalizing promise for strong subwavelength resonances, but material loss typically dampens the response. We derive fundamental limits to the optical response of absorptive systems, bounding the large
st enhancements possible given intrinsic material losses. Through basic conservation-of-energy principles, we derive geometry-independent limits to per-volume absorption and scattering rates, and to local-density-of-states enhancements that represent the power radiated or expended by a dipole near a material body. We provide examples of structures that approach our absorption and scattering limits at any frequency, by contrast, we find that common antenna structures fall far short of our radiative LDOS bounds, suggesting the possibility for significant further improvement. Underlying the limits is a simple metric, $|chi|^2 / operatorname{Im} chi$ for a material with susceptibility $chi$, that enables broad technological evaluation of lossy materials across optical frequencies.
We prove that for every Borel equivalence relation $E$, either $E$ is Borel reducible to $mathbb{E}_0$, or the family of Borel equivalence relations incompatible with $E$ has cofinal essential complexity. It follows that if $F$ is a Borel equivalence
relation and $cal F$ is a family of Borel equivalence relations of non-cofinal essential complexity which together satisfy the dichotomy that for every Borel equivalence relation $E$, either $Ein {cal F}$ or $F$ is Borel reducible to $E$, then $cal F$ consists solely of smooth equivalence relations, thus the dichotomy is equivalent to a known theorem.
We examine in detail the method introduced by Sanchez-Castro, Bedell, and Wiegers (SBW) to solve Landaus linearized kinetic equation, and compare it with the well-known standard method introduced by Abrikosov and Khalatnikov (AK). The SBW approach, h
ardly known, differs from AK in the way that moments are taken with respect to the angular functions of the Fourier transformed kinetic equation. We compare the SBW and AK solutions for zero-sound and first-sound propagation speeds and attenuation both analytically in the zero and full polarization limits, and numerically at arbitrary polarization using Landau parameters appropriate for thin $^{3}$He films. We find that the lesser known method not only yields results in close agreement with the standard method, but in most cases does so with far less analytic and computational
We show that the near-field functionality of hyperbolic metamaterials (HMM), typically proposed for increasing the photonic local density of states (LDOS), can be achieved with thin metal films. Although HMMs have an infinite density of internally-pr
opagating plane-wave states, the external coupling to nearby emitters is severely restricted. We show analytically that properly designed thin films, of thicknesses comparable to the metal size of a hyperbolic metamaterial, yield a LDOS as high as (if not higher than) that of HMMs. We illustrate these ideas by performing exact numerical computations of the LDOS of multilayer HMMs, along with their application to the problem of maximizing near-field heat transfer, to show that thin films are suitable replacements in both cases.
We show that there are shape-independent upper bounds to the extinction cross section per unit volume of randomly oriented nanoparticles, given only material permittivity. Underlying the limits are restrictive sum rules that constrain the distributio
n of quasistatic eigenvalues. Surprisingly, optimally-designed spheroids, with only a single quasistatic degree of freedom, reach the upper bounds for four permittivity values. Away from these permittivities, we demonstrate computationally-optimized structures that surpass spheroids and approach the fundamental limits.
The fraction of cluster galaxies that host luminous AGN is an important probe of AGN fueling processes, the cold ISM at the centers of galaxies, and how tightly black holes and galaxies co-evolve. We present a new measurement of the AGN fraction in a
sample of 13 clusters of galaxies (M >= 10^{14} Msun) at 1<z<1.5 selected from the Spitzer/IRAC Shallow Cluster Survey, as well as the field fraction in the immediate vicinity of these clusters, and combine these data with measurements from the literature to quantify the relative evolution of cluster and field AGN from the present to z~3. We estimate that the cluster AGN fraction at 1<z<1.5 is f_A = 3.0^{+2.4}_{-1.4}% for AGN with a rest-frame, hard X-ray luminosity greater than L_{X,H} >= 10^{44} erg/s. This fraction is measured relative to all cluster galaxies more luminous than M*_{3.6}(z)+1, where M*_{3.6}(z) is the absolute magnitude of the break in the galaxy luminosity function at the cluster redshift in the IRAC 3.6um bandpass. The cluster AGN fraction is 30 times greater than the 3sigma upper limit on the value for AGN of similar luminosity at z~0.25, as well as more than an order of magnitude greater than the AGN fraction at z~0.75. AGN with L_{X,H} >= 10^{43} erg/s exhibit similarly pronounced evolution with redshift. In contrast with the local universe, where the luminous AGN fraction is higher in the field than in clusters, the X-ray and MIR-selected AGN fractions in the field and clusters are consistent at 1<z<1.5. This is evidence that the cluster AGN population has evolved more rapidly than the field population from z~1.5 to the present. This environment-dependent AGN evolution mimics the more rapid evolution of star-forming galaxies in clusters relative to the field.
Two concepts, very different in nature, have proved to be useful in analytical and numerical studies of spectral stability: (i) the Krein signature of an eigenvalue, a quantity usually defined in terms of the relative orientation of certain subspaces
that is capable of detecting the structural instability of imaginary eigenvalues and hence their potential for moving into the right half-plane leading to dynamical instability under perturbation of the system, and (ii) the Evans function, an analytic function detecting the location of eigenvalues. One might expect these two concepts to be related, but unfortunately examples demonstrate that there is no way in general to deduce the Krein signature of an eigenvalue from the Evans function. The purpose of this paper is to recall and popularize a simple graphical interpretation of the Krein signature well-known in the spectral theory of polynomial operator pencils. This interpretation avoids altogether the need to view the Krein signature in terms of root subspaces and their relation to indefinite quadratic forms. To demonstrate the utility of this graphical interpretation of the Krein signature, we use it to define a simple generalization of the Evans function -- the Evans-Krein function -- that allows the calculation of Krein signatures in a way that is easy to incorporate into existing Evans function evaluation codes at virtually no additional computational cost. The graphical Krein signature also enables us to give elegant proofs of index theorems for linearized Hamiltonians in the finite dimensional setting: a general result implying as a corollary the generalized Vakhitov-Kolokolov criterion (or Grillakis-Shatah-Strauss criterion) and a count of real eigenvalues for linearized Hamiltonian systems in canonical form. These applications demonstrate how the simple graphical nature of the Krein signature may be easily exploited.
We report the discovery of 12 new fossil groups of galaxies, systems dominated by a single giant elliptical galaxy and cluster-scale gravitational potential, but lacking the population of bright galaxies typically seen in galaxy clusters. These fossi
l groups (FGs), selected from the maxBCG optical cluster catalog, were detected in snapshot observations with the Chandra X-ray Observatory. We detail the highly successful selection method, with an 80% success rate in identifying 12 FGs from our target sample of 15 candidates. For 11 of the systems, we determine the X-ray luminosity, temperature, and hydrostatic mass, which do not deviate significantly from expectations for normal systems, spanning a range typical of rich groups and poor clusters of galaxies. A small number of detected FGs are morphologically irregular, possibly due to past mergers, interaction of the intra-group medium (IGM) with a central AGN, or superposition of multiple massive halos. Two-thirds of the X-ray-detected FGs exhibit X-ray emission associated with the central BCG, although we are unable to distinguish between AGN and extended thermal galaxy emission using the current data. This sample, a large increase in the number of known FGs, will be invaluable for future planned observations to determine FG temperature, gas density, metal abundance, and mass distributions, and to compare to normal (non-fossil) systems. Finally, the presence of a population of galaxy-poor systems may bias mass function determinations that measure richness from galaxy counts. When used to constrain power spectrum normalization and {Omega}_m, these biased mass functions may in turn bias these results.
