Chemical Hardness, Linear Response, and Pseudopotential Transferability

We propose a systematic method of analyzing pseudopotential transferability based on linear-response properties of the free atom, including self-consistent chemical hardness and polarizability. Our calculation of hardness extends the approach of Teter\cite{teter} not only by including self-consistency, but also by generalizing to non-diagonal hardness matrices, thereby allowing us to test for transferability to non-spherically symmetric environments. We apply the method to study the transferability of norm-conserving pseudopotentials for a variety of elements in the Periodic Table. We find that the self-consistent corrections are frequently significant, and should not be neglected. We prove that the partial-core correction improves the pseudopotential hardness of alkali metals considerably. We propose a quantity to represent the average hardness error and calculate this quantity for many representative elements as a function of pseudopotential cutoff radii. We find that the atomic polarizabilities are usually well reproduced by the norm-conserving pseudopotentials. Our results provide useful guidelines for making optimal choices in the pseudopotential generation procedure.Comment: Revtex (preprint style, 33 pages) + 9 postscript figures A version in two-column article style with embedded figures is available at http://electron.rutgers.edu/~dhv/preprints/index.html#l

Extreme nonlinear electrodynamics in metamaterials with very small linear dielectric permittivity

We consider a sub-wavelength periodic layered medium whose slabs are filled by arbitrary linear metamaterials and standard nonlinear Kerr media and we show that the homogenized medium behaves as a Kerr medium whose parameters can assume values not available in standard materials. Exploiting such a parameter availability, we focus on the situation where the linear relative dielectric permittivity is very small thus allowing the observation of the extreme nonlinear regime where the nonlinear polarization is comparable with or even greater than the linear part of the overall dielectric response. The behavior of the electromagnetic field in the extreme nonlinear regime is very peculiar and characterized by novel features as, for example, the transverse power flow reversing. In order to probe the novel regime, we consider a class of fields (transverse magnetic nonlinear guided waves) admitting full analytical description and we show that these waves are allowed to propagate even in media with $\epsilon0$ since the nonlinear polarization produces a positive overall effective permittivity. The considered nonlinear waves exhibit, in addition to the mentioned features, a number of interesting properties like hyper-focusing induced by the phase difference between the field components.Comment: 12 pages, 7 figure

Entropy of the FRW universe based on the generalized uncertainty principle

The statistical entropy of the FRW universe described by time-dependent metric is newly calculated using the brick wall method based on the general uncertainty principle with the minimal length. We can determine the minimal length with the Plank scale to obtain the entropy proportional to the area of the cosmological apparent horizon.Comment: 10 pages, accepted in Modern Physics Letters

Novel Scaling Behavior for the Multiplicity Distribution under Second-Order Quark-Hadron Phase Transition

Deviation of the multiplicity distribution $P_q$ in small bin from its Poisson counterpart $p_q$ is studied within the Ginzburg-Landau description for second-order quark-hadron phase transition. Dynamical factor $d_q\equiv P_q/p_q$ for the distribution and ratio $D_q\equiv d_q/d_1$ are defined, and novel scaling behaviors between $D_q$ are found which can be used to detect the formation of quark-gluon plasma. The study of $d_q$ and $D_q$ is also very interesting for other multiparticle production processes without phase transition.Comment: 4 pages in revtex, 5 figures in eps format, will be appeared in Phys. Rev.

Late acceleration and w=−1w=-1 crossing in induced gravity

We study the cosmological evolution on a brane with induced gravity within a bulk with arbitrary matter content. We consider a Friedmann-Robertson-Walker brane, invariantly characterized by a six-dimensional group of isometries. We derive the effective Friedmann and Raychaudhuri equations. We show that the Hubble expansion rate on the brane depends on the covariantly defined integrated mass in the bulk, which determines the energy density of the generalized dark radiation. The Friedmann equation has two branches, distinguished by the two possible values of the parameter \ex=\pm 1. The branch with \ex=1 is characterized by an effective cosmological constant and accelerated expansion for low energy densities. Another remarkable feature is that the contribution from the generalized dark radiation appears with a negative sign. As a result, the presence of the bulk corresponds to an effective negative energy density on the brane, without violation of the weak energy condition. The transition from a period of domination of the matter energy density by non-relativistic brane matter to domination by the generalized dark radiation corresponds to a crossing of the phantom divide $w=-1$.Comment: 7 pages, no figures, RevTex 4.0; (v2) new references are added, minor corrections and expanded discussion; (v3) additional comments at the end of section III, minor corrections and several new references are added, to match published version in Phys. Rev.

Exact equqations and scaling relations for f-avalanche in the Bak-Sneppen evolution model

Infinite hierarchy of exact equations are derived for the newly-observed f-avalanche in the Bak-Sneppen evolution model. By solving the first order exact equation, we found that the critical exponent which governs the divergence of the average avalanche size, is exactly 1 (for all dimensions), confirmed by the simulations. Solution of the gap equation yields another universal exponent, denoting the the relaxation to the attractor, is exactly 1. We also establish some scaling relations among the critical exponents of the new avalanche.Comment: 5 pages, 1 figur