Effect of quantum fluctuations on structural phase transitions in SrTiO_3 and BaTiO_3

Using path-integral Monte Carol simulations and an ab initio effective Hamiltonian, we study the effects of quantum fluctuations on structural phase transitions in the cubic perovskite compounds SrTiO3 and BaTiO3. We find quantum fluctuations affect ferroelectric (FE) transitions more strongly than antiferrodistortive (AFD) ones, even though the effective mass of a single FE local mode is larger. For SrTiO3 we find that the quantum fluctuations suppress the FE transition completely, and reduce the AFD transition temperature from 130K to 110K. For BaTiO3, quantum fluctuations do not affect the order of the transition, but do reduce the transition temperature by 35-50 K. The implications of the calculations are discussed.Comment: Revtex (preprint style, 14 pages) + 2 postscript figures. A version in two-column article style with embedded figures is available at http://electron.rutgers.edu/~dhv/preprints/index.html#wz_qs

First-principles investigation of 180-degree domain walls in BaTiO_3

We present a first-principles study of 180-degree ferroelectric domain walls in tetragonal barium titanate. The theory is based on an effective Hamiltonian that has previously been determined from first-principles ultrasoft-pseudopotential calculations. Statistical properties are investigated using Monte Carlo simulations. We compute the domain-wall energy, free energy, and thickness, analyze the behavior of the ferroelectric order parameter in the interior of the domain wall, and study its spatial fluctuations. An abrupt reversal of the polarization is found, unlike the gradual rotation typical of the ferromagnetic case.Comment: Revtex (preprint style, 13 pages) + 3 postscript figures. A version in two-column article style with embedded figures is available at http://electron.rutgers.edu/~dhv/preprints/index.html#pad_wal

Solutions of the Yang-Baxter Equation with Extra Non-Additive Parameters II: Uq(gl(m∣n))U_q(gl(m|n))}

The type-I quantum superalgebras are known to admit non-trivial one-parameter families of inequivalent finite dimensional irreps, even for generic $q$. We apply the recently developed technique to construct new solutions to the quantum Yang-Baxter equation associated with the one-parameter family of irreps of $U_q(gl(m|n))$, thus obtaining R-matrices which depend not only on a spectral parameter but in addition on further continuous parameters. These extra parameters enter the Yang-Baxter equation in a similar way to the spectral parameter but in a non-additive form.Comment: 10 pages, LaTex file (some errors in the Casimirs corrected

On Type-I Quantum Affine Superalgebras

The type-I simple Lie-superalgebras are $sl(m|n)$ and $osp(2|2n)$. We study the quantum deformations of their untwisted affine extensions $U_q(sl(m|n)^{(1)})$ and $U_q(osp(2|2n)^{(1)})$. We identify additional relations between the simple generators (``extra $q$-Serre relations") which need to be imposed to properly define \uqgh and $U_q(osp(2|2n)^{(1)})$. We present a general technique for deriving the spectral parameter dependent R-matrices from quantum affine superalgebras. We determine the R-matrices for the type-I affine superalgebra $U_q(sl(m|n)^{(1)})$ in various representations, thereby deriving new solutions of the spectral-dependent Yang-Baxter equation. In particular, because this algebra possesses one-parameter families of finite-dimensional irreps, we are able to construct R-matrices depending on two additional spectral-like parameters, providing generalizations of the free-fermion model.Comment: 23 page

Optimization of robustness of scale-free network to random and targeted attacks

The scale-fee networks, having connectivity distribution $P(k)\sim k^{-\alpha}$ (where $k$ is the site connectivity), is very resilient to random failures but fragile to intentional attack. The purpose of this paper is to find the network design guideline which can make the robustness of the network to both random failures and intentional attack maximum while keeping the average connectivity per node constant. We find that when $=3$ the robustness of the scale-free networks reach its maximum value if the minimal connectivity $m=1$, but when is larger than four, the networks will become more robust to random failures and targeted attacks as the minimal connectivity $m$ gets larger

Nuclear Modification to Parton Distribution Functions and Parton Saturation

We introduce a generalized definition of parton distribution functions (PDFs) for a more consistent all-order treatment of power corrections. We present a new set of modified DGLAP evolution equations for nuclear PDFs, and show that the resummed $\alpha_s A^{1/3}/Q^2$-type of leading nuclear size enhanced power corrections significantly slow down the growth of gluon density at small-$x$. We discuss the relation between the calculated power corrections and the saturation phenomena.Comment: 4 pages, to appear in the proceedings of QM200

Generarized Cubic Model for BaTiO3_3-like Ferroelectric Substance

We propose an order-disorder type microscopic model for BaTiO$_3$-like Ferroelectric Substance. Our model has three phase transitions and four phases. The symmetry and directions of the polarizations of the ordered phases agree with the experimental results of BaTiO$_3$. The intermediate phases in our model are known as an incompletely ordered phase, which appears in a generalized clock model.Comment: 6 pages, 4figure

Nonlocality of Kohn-Sham exchange-correlation fields in dielectrics

The theory of the macroscopic field appearing in the Kohn-Sham exchange-correlation potential for dielectric materials, as introduced by Gonze, Ghosez and Godby, is reexamined. It is shown that this Kohn-Sham field cannot be determined from a knowledge of the local state of the material (local crystal potential, electric field, and polarization) alone. Instead, it has an intrinsically nonlocal dependence on the global electrostatic configuration. For example, it vanishes in simple transverse configurations of a polarized dielectric, but not in longitudinal ones.Comment: 4 pages, two-column style with 2 postscript figures embedded. Uses REVTEX and epsf macros. Also available at http://www.physics.rutgers.edu/~dhv/preprints/index.html#dv_gg

Quantum Creation of Topological Black Hole

The constrained instanton method is used to study quantum creation of a vacuum or charged topological black hole. At the $WKB$ level, the relative creation probability is the exponential of a quarter sum of the horizon areas associated with the seed instanton.Comment: Report-no change onl