Particular Solutions in Bimetric Theory and Their Implications

Ghost-free bimetric theory can describe gravity in the presence of an extra spin-2 field. We study certain aspects of dynamics in this theory: (1) It is shown that if either of the metrics is an Einstein solution then the other is always forced to be Einstein, too. For a class of bimetric models this constraint is stronger and as soon as one metric is Einstein, the other metric is forced to be proportional to it. As a consequence, the models in this class avoid a branch of pathological solutions that exhibit determinant singularities or nonlinear ghosts. These constraints persists in a generalized form when sources are included, but are destroyed in the massive gravity limit of the theory. (2) For another class of bimetric models, we show the existence of solutions that do not admit a massive gravity limit. A bimetric model that could exhibit a nonlinear version of "partially massless" symmetry belongs to both these classes. It is argued that if such a model exits, its symmetry will not survive in the massive gravity limit.Comment: Latex, 18 pages. Published versio

Zintl Chemistry for Designing High Efficiency Thermoelectric Materials

Zintl phases and related compounds are promising thermoelectric materials; for instance, high zT has been found in Yb_(14)MnSb_(11), clathrates, and the filled skutterudites. The rich solid-state chemistry of Zintl phases enables numerous possibilities for chemical substitutions and structural modifications that allow the fundamental transport parameters (carrier concentration, mobility, effective mass, and lattice thermal conductivity) to be modified for improved thermoelectric performance. For example, free carrier concentration is determined by the valence imbalance using Zintl chemistry, thereby enabling the rational optimization of zT. The low thermal conductivity values obtained in Zintl thermoelectrics arise from a diverse range of sources, including point defect scattering and the low velocity of optical phonon modes. Despite their complex structures and chemistry, the transport properties of many modern thermoelectrics can be understood using traditional models for heavily doped semiconductors

Transport properties of the layered Zintl compound SrZnSb_2

Transport properties of the layered Zintl compound SrZnSb_2 have been characterized from room temperature to 725 K on polycrystalline samples. SrZnSb_2 samples were found to be p-type with a Hall carrier concentration of 5×10^(20) cm^(−3) at room temperature, and a small Seebeck coefficient and electrical resistivity are observed. A single band model predicts that, even with optimal doping, significant thermoelectric performance will not be achieved in SrZnSb_2. A relatively low lattice thermal conductivity is observed, κ_L~1.2 W m^(−1) K^(−1), at room temperature. The thermal transport of SrZnSb_2 is compared to that of the layered Zintl compounds AZn2Sb_2 (A=Ca,Yb,Sr,Eu), which have smaller unit cells and larger lattice thermal conductivity, κ_L~2 W m^(−1) K^(−1), at 300K. Ultrasonic measurements, in combination with kinetic theory and the estimated κ_L values, suggest that the lower κ_L of SrZnSb_2 is primarily the result of a reduction in the volumetric specific heat of the acoustic phonons due to the increased number of atoms per unit cell. Therefore, this work recommends that unit cell size should be considered when selecting Zintl compounds for potential thermoelectric application

Extended Weyl Invariance in a Bimetric Model and Partial Masslessness

We revisit a particular ghost-free bimetric model which is related to both partial masslessness (PM) and conformal gravity. Linearly, the model propagates six instead of seven degrees of freedom not only around de Sitter but also around flat spacetime. Nonlinearly, the equations of motion can be recast in the form of expansions in powers of curvatures, and exhibit a remarkable amount of structure. In this form, the equations are shown to be invariant under scalar gauge transformations, at least up to six orders in derivatives, the lowest order term being a Weyl scaling of the metrics. The terms at two-derivative order reproduce the usual PM gauge transformations on de Sitter backgrounds. At the four-derivative order, a potential obstruction that could destroy the symmetry is shown to vanish. This in turn guarantees the gauge invariance to at least six-orders in derivatives. This is equivalent to adding up to 10-derivative corrections to conformal gravity. More generally, we outline a procedure for constructing the gauge transformations order by order as an expansion in derivatives and comment on the validity and limitations of the procedure. We also discuss recent arguments against the existence of a PM gauge symmetry in bimetric theory and show that, at least in their present form, they are evaded by the model considered here. Finally, we argue that a bimetric approach to PM theory is more promising than one based on the existence of a fundamental PM field.Comment: Latex, 35 pages. Matches published versio

Species Abundance Patterns in Complex Evolutionary Dynamics

An analytic theory of species abundance patterns (SAPs) in biological networks is presented. The theory is based on multispecies replicator dynamics equivalent to the Lotka-Volterra equation, with diverse interspecies interactions. Various SAPs observed in nature are derived from a single parameter. The abundance distribution is formed like a widely observed left-skewed lognormal distribution. As the model has a general form, the result can be applied to similar patterns in other complex biological networks, e.g. gene expression.Comment: 4 pages, 3 figures. Physical Review Letters, in pres

Thermoelectric properties of p-type LiZnSb: Assessment of ab initio calculations

In response to theoretical calculations on the thermoelectric performance of LiZnSb, we report the pertinent transport properties between room temperature and 523 K. Nominal LiZnSb samples are found to be p-type, with a carrier concentration in the range (4–7)×10^(20) cm^(−3). The thermoelectric figure of merit (zT) is found to be 0.02–0.08 at 523 K. Analysis of material transport parameters and previously reported ab initio calculations demonstrates that even with optimal doping, p-type LiZnSb is unlikely to achieve zT>0.2 at 523 K. The accuracy of the high zT estimate (zT>2) for n-type compositions from ab initio calculations is discussed within the current synthetic limits