Transaction services, inflation, and welfare

This paper is motivated by empirical observations on the comovements of currency velocity, inflation, and the relative size of the credit services sector. We document these comovements and incorporate into a monetary growth model a credit services sector that provides services that help people economize on money. Our model makes two new contributions. First, we show that direct evidence on the appropriately defined credit service sector for the United States is consistent with the welfare cost measured using an estimated money demand schedule. Second, we provide welfare cost of inflation estimates that have some new features.Inflation (Finance) ; Welfare

Spatial fluctuations of a surviving particle in the trapping reaction

We consider the trapping reaction, $A+B\to B$, where $A$ and $B$ particles have a diffusive dynamics characterized by diffusion constants $D_A$ and $D_B$. The interaction with $B$ particles can be formally incorporated in an effective dynamics for one $A$ particle as was recently shown by Bray {\it et al}. [Phys. Rev. E {\bf 67}, 060102 (2003)]. We use this method to compute, in space dimension $d=1$, the asymptotic behaviour of the spatial fluctuation, $^{1/2}$, for a surviving $A$ particle in the perturbative regime, $D_A/D_B\ll 1$, for the case of an initially uniform distribution of $B$ particles. We show that, for $t\gg 1$, $^{1/2} \propto t^{\phi}$ with $\phi=1/4$. By contrast, the fluctuations of paths constrained to return to their starting point at time $t$ grow with the larger exponent 1/3. Numerical tests are consistent with these predictions.Comment: 10 pages, 5 figure

The structure of one-relator relative presentations and their centres

Suppose that G is a nontrivial torsion-free group and w is a word in the alphabet G\cup\{x_1^{\pm1},...,x_n^{\pm1}\} such that the word w' obtained from w by erasing all letters belonging to G is not a proper power in the free group F(x_1,...,x_n). We show how to reduce the study of the relative presentation \^G= to the case n=1. It turns out that an "n-variable" group \^G can be constructed from similar "one-variable" groups using an explicit construction similar to wreath product. As an illustration, we prove that, for n>1, the centre of \^G is always trivial. For n=1, the centre of \^G is also almost always trivial; there are several exceptions, and all of them are known.Comment: 15 pages. A Russian version of this paper is at http://mech.math.msu.su/department/algebra/staff/klyachko/papers.htm . V4: the intoduction is rewritten; Section 1 is extended; a short introduction to Secton 5 is added; some misprints are corrected and some cosmetic improvements are mad

Invisibility and perfect absorption of all-dielectric metasurfaces originated from the transverse Kerker effect

Dielectric metasurfaces perform unique photonics effects and serve as the engine of nowadays light-matter technologies. Here, we suggest theoretically and demonstrate experimentally the realization of a high transparency effect in a novel type of all-dielectric metasurface, where each constituting meta-atom of the lattice presents the so-called transverse Kerker effect. In contrast to Huygens' metasurfaces, both phase and amplitude of the incoming wave remain unperturbed at the resonant frequency and, consequently, our metasurface totally operates in the invisibility regime. We prove experimentally, for the microwave frequency range, that both phase and amplitude of the transmitted wave from the metasurface remain almost unaffected. Finally, we demonstrate both numerically and experimentally and explain theoretically in detail a novel mechanism to achieve perfect absorption of the incident light enabled by the resonant response of the dielectric metasurfaces placed in the vicinity of a conducting substrate. In the subdiffractive limit, we show the aforementioned effects are mainly determined by the optical response of the constituting meta-atoms rather than the collective lattice contributions. With the spectrum scalability, our findings can be incorporated in engineering devices for energy harvesting, nonlinear phenomena and filters applications.Comment: 10 pages, 6 figure

Competing orders II: the doped quantum dimer model

We study the phases of doped spin S=1/2 quantum antiferromagnets on the square lattice, as they evolve from paramagnetic Mott insulators with valence bond solid (VBS) order at zero doping, to superconductors at moderate doping. The interplay between density wave/VBS order and superconductivity is efficiently described by the quantum dimer model, which acts as an effective theory for the total spin S=0 sector. We extend the dimer model to include fermionic S=1/2 excitations, and show that its mean-field, static gauge field saddle points have projective symmetries (PSGs) similar to those of `slave' particle U(1) and SU(2) gauge theories. We account for the non-perturbative effects of gauge fluctuations by a duality mapping of the S=0 dimer model. The dual theory of vortices has a PSG identical to that found in a previous paper (L. Balents et al., cond-mat/0408329) by a duality analysis of bosons on the square lattice. The previous theory therefore also describes fluctuations across superconducting, supersolid and Mott insulating phases of the present electronic model. Finally, with the aim of describing neutron scattering experiments, we present a phenomenological model for collective S=1 excitations and their coupling to superflow and density wave fluctuations.Comment: 22 pages, 10 figures; part I is cond-mat/0408329; (v2) changed title and added clarification

Consistent Batalin--Fradkin quantization of Infinitely Reducible First Class Constraints

We reconsider the problem of BRST quantization of a mechanics with infinitely reducible first class constraints. Following an earlier recipe [Phys. Lett. B 381, 105, (1996)], the original phase space is extended by purely auxiliary variables, the constraint set in the enlarged space being first stage of reducibility. The BRST charge involving only a finite number of ghost variables is explicitly constructed.Comment: 5 pages, LaTex. Minor corrections including the title. The version to appear in Phys. Rev.

WISE colours and star-formation in the host galaxies of radio-loud narrow-line Seyfert 1

We investigate the mid-infrared properties of the largest (42 objects) sample of radio-loud narrow-line Seyfert 1 (RL NLS1) collected to date, using data from the Wide-field Infrared Survey Explorer (WISE). We analyse the mid-IR colours of these objects and compare them to what is expected from different combinations of AGN and galaxy templates. We find that, in general, the host-galaxy emission gives an importan contribution to the observed mid-IR flux in particular at the longest wavelengths (W3, at 12micron, and W4, at 22micron). In about half of the sources (22 objects) we observe a very red mid-IR colour (W4-W3>2.5) that can be explained only using a starburst galaxy template (M82). Using the 22micron luminosities, corrected for the AGN contribution, we have then estimated the star-formation rate for 20 of these "red" RL NLS1, finding values ranging from 10 to 500 Msun/y. For the RL NLS1 showing bluer colours, instead, we cannot exclude the presence of a star-forming host galaxy although, on average, we expect a lower star-formation rate. Studying the radio (1.4GHz) to mid-IR (22micron) flux ratios of the RL NLS1 in the sample we found that in ~10 objects the star-forming activity could represent the most important component also at radio frequencies, in addition (or in alternative) to the relativistic jet. We conclude that both the mid-IR and the radio emission of RL NLS1 are a mixture of different components, including the relativistic jet, the dusty torus and an intense star-forming activity.Comment: Accepted for publication in MNRAS, 11 pages, 7 figures, 2 table