Search on a fractal lattice using a quantum random walk

The spatial search problem on regular lattice structures in integer number of dimensions d >= 2 has been studied extensively, using both coined and coinless quantum walks. The relativistic Dirac operator has been a crucial ingredient in these studies. Here, we investigate the spatial search problem on fractals of noninteger dimensions. Although the Dirac operator cannot be defined on a fractal, we construct the quantum walk on a fractal using the flip-flop operator that incorporates a Klein-Gordon mode. We find that the scaling behavior of the spatial search is determined by the spectral (and not the fractal) dimension. Our numerical results have been obtained on the well-known Sierpinski gaskets in two and three dimensions.

Activation of Lattice Oxygen of TiO2 by Pd2+ Ion: Correlation of Low-Temperature CO and Hydrocarbon Oxidation with Structure of Ti1-xPdxO2-x (x=0.01-0.03)

Lattice oxygen of TiO2 is activated by the substitution of Pd ion in its lattice. Ti1-xPdxO2-x (x = 0.01-0.03) have been synthesized by solution combustion method crystallizing in anatase TiO2 structure. Pd is in +2 oxidation state and Ti is in +4 oxidation state in the catalyst. Pd is more ionic in TiO2 lattice compared to Pd in PdO. Oxygen storage capacity defined by ``amount of oxygen that is used reversibly to oxidize CO'' is as high as 5100 mu mol/g of Ti0.97Pd0.03O1.97. Oxygen is extracted by CO to CO2 in absence of feed oxygen even at room temperature which is more than 20 times compared to pure TiO2. Rate of CO oxidation is 2.75 mu mol g(-1) s(-1) at 60 degrees C over Ti0.97Pd0.03O1.97 and C2H2 gets oxidized to CO2 and H2O at room temperature. Catalyst is not poisoned on long time operation of the reactor. Such high catalytic activity is due to activated lattice oxygen created by the substitution of Pd ion as seen from first-principles density functional theory (DFT) calculations with 96 atom supercells of Ti32O64, Ti31Pd1O63, Ti30Pd2O62, and Ti29Pd3O61. The compounds crystallize in anatase TiO2 structure with Pd2+ ion in nearly square planar geometry and TiO6 octahedra are distorted by the creation of weakly bound oxygens. Structural analysis of Ti31Pd1O63 which is close to 3% Pd ion substituted TiO2 shows that oxygens associated with both Ti and Pd ions in the lattice show bond valence sum of 1.87, a low value characteristic of weak oxygen in the lattice compared to oxygens with valence 2 and above in the same lattice. Exact positions of activated oxygens have been identified in the lattice from DFT calculations.

Perturbative expansion of the QCD Adler function improved by renormalization-group summation and analytic continuation in the Borel plane

We examine the large-order behavior of a recently proposed renormalization-group-improved expansion of the Adler function in perturbative QCD, which sums in an analytically closed form the leading logarithms accessible from renormalization-group invariance. The expansion is first written as an effective series in powers of the one-loop coupling, and its leading singularities in the Borel plane are shown to be identical to those of the standard ``contour-improved'' expansion. Applying the technique of conformal mappings for the analytic continuation in the Borel plane, we define a class of improved expansions, which implement both the renormalization-group invariance and the knowledge about the large-order behavior of the series. Detailed numerical studies of specific models for the Adler function indicate that the new expansions have remarkable convergence properties up to high orders. Using these expansions for the determination of the strong coupling from the hadronic width of the tau lepton we obtain, with a conservative estimate of the uncertainty due to the nonperturbative corrections, alpha(s)(M-tau(2)) = 0.3189(-0.0151)(+0.0173), which translates to alpha(s)(M-Z(2)) = 0.1184(-0.0018)(+0.0021). DOI: 10.1103/PhysRevD.87.014008

Correlation between enhanced lattice polarizability and high piezoelectric response in BiScO3-PbTiO3

Piezoelectric and ex situ electric-field induced structural studies were carried out on closely spaced compositions in the morphotropic phase boundary region of (1 - x) PbTiO3-(x)BiScO3. While the common approach of zero field structural analysis failed to provide a unique relationship between the anomalous piezoresponse of x = 0.3725 and structural factor(s), ex situ study of electric-field induced structural changes revealed that the composition exhibiting the highest piezoelectric response is the one which also exhibits significantly enhanced polarizability of the lattices of both coexisting (monoclinic and tetragonal) phases. The enhanced lattice polarizability manifests as a significant fraction of the monoclinic phase transforming irreversibly to the tetragonal phase after electric poling. DOI: 10.1103/PhysRevB.87.064106

Renormalization of noncommutative quantum field theories

We report on a comprehensive analysis of the renormalization of noncommutative phi(4) scalar field theories on the Groenewold-Moyal plane. These scalar field theories are twisted Poincare invariant. Our main results are that these scalar field theories are renormalizable, free of UV/IR mixing, possess the same fixed points and beta-functions for the couplings as their commutative counterparts. We also argue that similar results hold true for any generic noncommutative field theory with polynomial interactions and involving only pure matter fields. A secondary aim of this work is to provide a comprehensive review of different approaches for the computation of the noncommutative S-matrix: noncommutative interaction picture and noncommutative Lehmann-Symanzik-Zimmermann formalism. DOI: 10.1103/PhysRevD.87.064014

Chapman-Enskog analysis for finite-volume formulation of lattice Boltzmann equation

The classical Chapman-Enskog expansion is performed for the recently proposed finite-volume formulation of lattice Boltzmann equation (LBE) method D.V. Patil, K.N. Lakshmisha, Finite volume TVD formulation of lattice Boltzmann simulation on unstructured mesh, J. Comput. Phys. 228 (2009) 5262-5279]. First, a modified partial differential equation is derived from a numerical approximation of the discrete Boltzmann equation. Then, the multi-scale, small parameter expansion is followed to recover the continuity and the Navier-Stokes (NS) equations with additional error terms. The expression for apparent value of the kinematic viscosity is derived for finite-volume formulation under certain assumptions. The attenuation of a shear wave, Taylor-Green vortex flow and driven channel flow are studied to analyze the apparent viscosity relation.

Chiral Mott insulator with staggered loop currents in the fully frustrated Bose-Hubbard model

Motivated by experiments on Josephson junction arrays in a magnetic field and ultracold interacting atoms in an optical lattice in the presence of a ``synthetic'' orbital magnetic field, we study the ``fully frustrated'' Bose-Hubbard model and quantum XY model with half a flux quantum per lattice plaquette. Using Monte Carlo simulations and the density matrix renormalization group method, we show that these kinetically frustrated boson models admit three phases at integer filling: a weakly interacting chiral superfluid phase with staggered loop currents which spontaneously break time-reversal symmetry, a conventional Mott insulator at strong coupling, and a remarkable ``chiral Mott insulator'' (CMI) with staggered loop currents sandwiched between them at intermediate correlation. We discuss how the CMI state may be viewed as an exciton condensate or a vortex supersolid, study a Jastrow variational wave function which captures its correlations, present results for the boson momentum distribution across the phase diagram, and consider various experimental implications of our phase diagram. Finally, we consider generalizations to a staggered flux Bose-Hubbard model and a two-dimensional (2D) version of the CMI in weakly coupled ladders.

Quantum phases and phase transitions of frustrated hard-core bosons on a triangular ladder

Kinetically frustrated bosons at half filling in the presence of a competing nearest-neighbor repulsion support a wide supersolid regime on the two-dimensional triangular lattice. We study this model on a two-leg ladder using the finite-size density-matrix renormalization-group method, obtaining a phase diagram which contains three phases: a uniform superfluid (SF), an insulating charge density wave (CDW) crystal, and a bond ordered insulator (BO). We show that the transitions from SF to CDW and SF to BO are continuous in nature, with critical exponents varying continuously along the phase boundaries, while the transition from CDW to BO is found to be first order. The phase diagram is also found to contain an exactly solvable Majumdar Ghosh point, and reentrant SF to CDW phase transitions.

Cl-35 NQR frequency and spin lattice relaxation time in 3,4-dichlorophenol as a function of pressure and temperature

The pressure dependences of Cl-35 nuclear quadrupole resonance (NQR) frequency, temperature and pressure variation of spin lattice relaxation time (T-1) were investigated in 3,4-dichlorophenol. T-1 was measured in the temperature range 77-300 K. Furthermore, the NQR frequency and T-1 for these compounds were measured as a function of pressure up to 5 kbar at 300 K. The temperature dependence of the average torsional lifetimes of the molecules and the transition probabilities W-1 and W-2 for the Delta m = +/- 1 and Delta m = +/- 2 transitions were also obtained. A nonlinear variation of NQR frequency with pressure has been observed and the pressure coefficients were observed to be positive. A thermodynamic analysis of the data was carried out to determine the constant volume temperature coefficients of the NQR frequency. An attempt is made to compare the torsional frequencies evaluated from NQR data with those obtained by IR spectra. On selecting the appropriate mode from IR spectra, a good agreement with torsional frequency obtained from NQR data is observed. The previously mentioned approach is a good illustration of the supplementary nature of the data from IR studies, in relation to NQR studies of compounds in solid state.

DETERMINATION OF THE STRONG COUPLING FROM HADRONIC TAU DECAYS USING RENORMALIZATION GROUP SUMMED PERTURBATION THEORY

Be the strong coupling constant alpha(s) from the tau hadronn width using a renormalization group summed (RGS) expansion of the QCD Adler lunction. The main theoretical uncertainty in the extraction of as is due to the manner in which renormalization group invariance is implemented, and the as yet uncalculated higher order terms in the QCD perturbative series. We show that new expansion exhibits good renormalization group improvement and the behavior of the series is similar to that of the standard RGS expansion. The value of the strong coupling in (MS) over bar scheme obtained with the RCS expansion is alpha(s) (M-tau(2)) = 0.338 +/- 0.010. The convergence properties of the new expansion can be improved by Bond transformation and analytic continuation in t he Bond plane. This is discussed elsewhere in these issues.

Gap renormalization of molecular crystals from density-functional theory

Fundamental gap renormalization due to electronic polarization is a basic phenomenon in molecular crystals. Despite its ubiquity and importance, all conventional approaches within density-functional theory completely fail to capture it, even qualitatively. Here, we present a new screened range-separated hybrid functional, which, through judicious introduction of the scalar dielectric constant, quantitatively captures polarization-induced gap renormalization, as demonstrated on the prototypical organic molecular crystals of benzene, pentacene, and C-60. This functional is predictive, as it contains system-specific adjustable parameters that are determined from first principles, rather than from empirical considerations.

Strong-coupling expansion for ultracold bosons in an optical lattice at finite temperatures in the presence of superfluidity

We develop a strong-coupling (t << U) expansion technique for calculating the density profile for bosonic atoms trapped in an optical lattice with an overall harmonic trap at finite temperature and finite on-site interaction in the presence of superfluid regions. Our results match well with quantum Monte Carlo simulations at finite temperature. We also show that the superfluid order parameter never vanishes in the trap due to the proximity effect. Our calculations for the scaled density in the vacuum-to-superfluid transition agree well with the experimental data for appropriate temperatures. We present calculations for the entropy per particle as a function of temperature which can be used to calibrate the temperature in experiments. We also discuss issues connected with the demonstration of universal quantum critical scaling in the experiments.

Atomic Structure of Quantum Gold Nanowires: Quantification of the Lattice Strain

Theoretical studies exist to compute the atomic arrangement in gold nanowires and the influence on their electronic behavior with decreasing diameter. Experimental studies, e.g., by transmission electron microscopy, on chemically synthesized ultrafine wires are however lacking owing to the unavailability of suitable protocols for sample preparation and the stability of the wires under electron beam irradiation. In this work, we present an atomic scale structural investigation on quantum single crystalline gold nanowires of 2 nm diameter, chemically prepared on a carbon film grid. Using low dose aberration-corrected high resolution (S)TEM, we observe an inhomogeneous strain distribution in the crystal, largely concentrated at the twin boundaries and the surface along with the presence of facets and surface steps leading to a noncircular cross section of the wires. These structural aspects are critical inputs needed to determine their unique electronic character and their potential as a suitable catalyst material. Furthermore, electron-beam-induced structural changes at the atomic scale, having implications on their mechanical behavior and their suitability as interconnects, are discussed.

Simulation of inhomogeneous distributions of ultracold atoms in an optical lattice via a massively parallel implementation of nonequilibrium strong-coupling perturbation theory

We present a nonequilibrium strong-coupling approach to inhomogeneous systems of ultracold atoms in optical lattices. We demonstrate its application to the Mott-insulating phase of a two-dimensional Fermi-Hubbard model in the presence of a trap potential. Since the theory is formulated self-consistently, the numerical implementation relies on a massively parallel evaluation of the self-energy and the Green's function at each lattice site, employing thousands of CPUs. While the computation of the self-energy is straightforward to parallelize, the evaluation of the Green's function requires the inversion of a large sparse 10(d) x 10(d) matrix, with d > 6. As a crucial ingredient, our solution heavily relies on the smallness of the hopping as compared to the interaction strength and yields a widely scalable realization of a rapidly converging iterative algorithm which evaluates all elements of the Green's function. Results are validated by comparing with the homogeneous case via the local-density approximation. These calculations also show that the local-density approximation is valid in nonequilibrium setups without mass transport.

Electrostatic modulation of periodic potentials in a two-dimensional electron gas: from antidot lattice to quantum dot lattice

We use a dual gated device structure to introduce a gate-tuneable periodic potential in a GaAs/AlGaAs two dimensional electron gas (2DEG). Using only a suitable choice of gate voltages we can controllably alter the potential landscape of the bare 2DEG, inducing either a periodic array of antidots or quantum dots. Antidots are artificial scattering centers, and therefore allow for a study of electron dynamics. In particular, we show that the thermovoltage of an antidot lattice is particularly sensitive to the relative positions of the Fermi level and the antidot potential. A quantum dot lattice, on the other hand, provides the opportunity to study correlated electron physics. We find that its current-voltage characteristics display a voltage threshold, as well as a power law scaling, indicative of collective Coulomb blockade in a disordered background.