Search on a hypercubic lattice using a quantum random walk. I. d > 2

Random walks describe diffusion processes, where movement at every time step is restricted to only the neighboring locations. We construct a quantum random walk algorithm, based on discretization of the Dirac evolution operator inspired by staggered lattice fermions. We use it to investigate the spatial search problem, that is, to find a marked vertex on a d-dimensional hypercubic lattice. The restriction on movement hardly matters for d > 2, and scaling behavior close to Grover's optimal algorithm (which has no restriction on movement) can be achieved. Using numerical simulations, we optimize the proportionality constants of the scaling behavior, and demonstrate the approach to that for Grover's algorithm (equivalent to the mean-field theory or the d -> infinity limit). In particular, the scaling behavior for d = 3 is only about 25% higher than the optimal d -> infinity value.

Search on a hypercubic lattice using a quantum random walk. II. d = 2

We investigate the spatial search problem on the two-dimensional square lattice, using the Dirac evolution operator discretized according to the staggered lattice fermion formalism. d = 2 is the critical dimension for the spatial search problem, where infrared divergence of the evolution operator leads to logarithmic factors in the scaling behavior. As a result, the construction used in our accompanying article A. Patel and M. A. Rahaman, Phys. Rev. A 82, 032330 (2010)] provides an O(root N ln N) algorithm, which is not optimal. The scaling behavior can be improved to O(root N ln N) by cleverly controlling the massless Dirac evolution operator by an ancilla qubit, as proposed by Tulsi Phys. Rev. A 78, 012310 (2008)]. We reinterpret the ancilla control as introduction of an effective mass at the marked vertex, and optimize the proportionality constants of the scaling behavior of the algorithm by numerically tuning the parameters.

Variational calculation for the spin-(1/2 Heisenberg antiferromagnet on a square lattice

The ground-state properties of the spin-(1/2 Heisenberg antiferromagnet on a square lattice are studied by using a simple variational wave function that interpolates continuously between the Néel state and short-range resonating-valence-bond states. Exact calculations of the variational energy for small systems show that the state with the lowest energy has long-range antiferromagnetic order. The staggered magnetization in this state is approximately 70% of its maximum possible value. The variational estimate of the ground-state energy is substantially lower than the value obtained for the nearest-neighbor resonating-valence-bond wave function.

Enhanced Pair Hydrophobicity in the Water-Dimethylsulfoxide (DMSO) Binary Mixture at Low DMSO Concentrations

We observe a surprisingly sharp increase in the pair hydrophobicity in the water climethylsulfoxide (DMSO) binary mixture at small DMSO concentrations, with the mole fraction of DMSO (x(D)) in the range 0.12-0.16. The increase in pair hydrophobicity is measured by an increase in the depth of the first minimum in the potential of mean force (PMF) between two methane molecules. However, this enhanced hydrophobicity again weakens at higher DMSO concentrations. We find markedly unusual behavior of the pure binary mixture (in the same composition range) in the diffusion coefficient of DMSO and in the local composition fluctuation of water, We find that, in the said composition range, the average coordination number of the methyl groups (of distinct DMSO) varies between 2.4 and 2.6, indicating the onset of the formation of a chain-like extended connectivity in an otherwise stable tetrahedral network comprising of water and DMSO molecules. We propose that the enhanced pair hydrophobicity of the binary mixture at low DMSO concentrations is due to the participation of the two methane molecules in the local structural order and the emerging molecular associations in the water-DMSO mixture.

Interdiffusion study in binary gold-tin system

Solid state reactive diffusion in binary Au-Sn system has been studied using the diffusion couple consisting of pure elements Au and Sn annealed in the temperature range of 180-100 degrees C for 25 h Interdiffusion zone consists of four intermetallic phases Au5Sn, AuSn, AuSn2, and AuSn4 Activation energy for parabolic growth constant and integrated diffusivity for each phase has been calculated to indicate about the possible mechanism for diffusion controlled growth process Parabolic growth constant of individual phases has also been compared Kirkendall marker plane position has been indicated in the interdiffusion zone and furthermore the ratio of intrinsic diffusivities of species has also been determined. (C) 2010 Elsevier Ltd. All rights reserved.

Diffusion coefficients for selected binary liquid systems: cyclohexanes and n-alkyl alcohols

In the present work the integral diffusion coefficients are estimated by using the diaphragm cell technique. The diffusion coefficients are measured at various compositions for two sets binary systems: one of cyclohexane and n-paraffinic alcohols and the other of methylcyclohexane and n-paraffinic alcohols. The alcohols used are seven members of homologous series of n-paraffinic alcohols from ethanol to octanol. The maximum possible error in the experimental diffusion coefficient could be 8% for both the cyclohexane-n-alkyl alcohol system and methylcyclohexane-n-alkyl alcohol system. A correlation for each of the two sets of binary systems is given. The maximum deviation in the correlations was less than 6.5 and 3.5% for cyclohexane-n-alkyl alcohols and methylcyclohexane-n-alkyl alcohols, respectively.

Theoretical gain‐optimization studies in CO2–N2 gasdynamic lasers. II. Results of parametric study

Based on a method presented in detail in a previous work by the authors, similar solutions have been obtained for the steady inviscid quasi‐one‐dimensional nonreacting flow in the supersonic nozzle of a CO2–N2 gasdynamic laser system, with either H2O or He as the catalyst. It has been demonstrated how these solutions could be used to optimize the small‐signal gain coefficient on a specified vibrational‐rotational transition. Results presented for a wide range of mixture compositions include optimum values for the small‐signal gain, area ratio, reservoir temperature, and a binary scaling parameter, which is the product of reservoir pressure and nozzle shape factor.

Exploring glueball wave functions on the lattice

We calculate the string tension and 0++ and 2++ glueball masses in pure gauge QCD using an improved lattice action. We compare various smearing methods, and find that the best glueball signal is obtained using smeared Wilson loops of a size of about 0.5 fm. Our results for mass ratios m0++/√σ=3.5(3) and m2++/m0++=1.6(2) are consistent with those computed with the simple plaquette action.

Communication: Unusual dynamics of hybrid nanoparticles and their binary mixtures

We present the results on the evolution of microscopic dynamics of hybrid nanoparticles and their binary mixtures as a function of temperature and wave vector. We find unexpectedly a nonmonotonic dependence of the structural relaxation time of the nanoparticles as a function of the morphology. In binary mixtures of two of the largest nanoparticles studied, we observe re-entrant vitrification as a function of the volume fraction of the smaller nanoparticle, which is unusual for such high diameter ratio. Possible explanation for the observed behavior is provided. (C) 2010 American Institute of Physics. doi:10.1063/1.3495480]

Structural synthesis by transformation of binary chains Strukturelle synthese durch umwandlung binaerer ketten

The paper presents a general method of structural synthesis which can be used to derive all possible simple- and multiple-jointed chains of positive, zero or negative degree-of-freedom. In this method all possible chains with N links and F degrees-of-freedom are derived by the transformation of the corresponding “binary chains” with N binary links and F degrees-of-freedom. The method is illustrated by applying to the case of chains with degrees-of-freedom 1,2,0 and −1.

Metal-Insulator Transition in the Hubbard Model on a Triangular Lattice

We discuss the results of an extensive mean-field investigation of the half-filled Hubbard model on a triangular lattice at zero temperature. At intermediate U we find a first-order metal-insulator transition from an incommensurate spiral magnetic metal to a semiconducting state with a commensurate linear spin density wave ordering stabilized by the competition between the kinetic energy and the frustrated nature of the magnetic interaction. At large U the ground state is that of a classical triangular antiferromagnet within our approximation. In the incommensurate spiral metallic phase the Fermi surface has parts in which the wave function renormalization Z is extremely small. The evolution of the Fermi surface and the broadening of the quasi-particle band along with the variation of the plasma frequency and a charge stiffness constant with U/t are discussed.

Molecular theory of dielectric relaxation in a dense binary dipolar liquid

A molecular theory of dielectric relaxation in a dense binary dipolar liquid is presented. The theory takes into account the effects of intra- and interspecies intermolecular interactions. It is shown that the relaxation is, in general, nonexponential. In certain limits, we recover the biexponential form traditionally used to analyze the experimental data of dielectric relaxation in a binary mixture. However, the relaxation times are widely different from the prediction of the noninteracting rotational diffusion model of Debye for a binary system. Detailed numerical evaluation of the frequency-dependent dielectric function epsilon-(omega) is carried out by using the known analytic solution of the mean spherical approximation (MSA) model for the two-particle direct correlation function for a polar mixture. A microscopic expression for both wave vector (k) and frequency (omega) dependent dielectric function, epsilon-(k,omega), of a binary mixture is also presented. The theoretical predictions on epsilon-(omega) (= epsilon-(k = 0, omega)) have been compared with the available experimental results. In particular, the present theory offers a molecular explanation of the phenomenon of fusing of the two relaxation channels of the neat liquids, observed by Schallamach many years ago.

Mutual diffusion coefficients of some binary liquid systems: benzene-n-alkyl alcohol

The mutual diffusion coefficients for binary liquid systems of benzene-n-alkyl alcohol at various compositions have been determined by the diaphragm cell method at 28-degrees-C. The alcohols used were the members of n-paraffinic alcohols ranging from C1 to C8. The maximum possible experimental error is 14%. The data were fitted with a generalized correlation, giving the deviation from the experimental data to within 2.75%, on average.

Sign Of The Order Parameter In Oriented Systems And Its Utility In The Study Of The Dynamic Properties Of Molecules

Novel one and two dimensional NMR techniques are proposed and utilized for the determination of the signs of the order parameters used for the study of the mobility of the fatty acid chains. The experiments designed to extract this information involve the use of the intensities of the side bands in the spectra of oriented systems spinning at the magic angle. Advantages of the two dimensional technique over the one dimensional method are discussed. The utility of the method in the study of the dynamic properties of membranes and model systems is pointed out.

Spiral states in the square-lattice Hubbard model

We present a variety of physical implications of a mean-field theory for spiral spin-density-wave states in the square-lattice Hubbard model for small deviations from half filling. The phase diagram with the paramagnetic metal, two spiral (semimetallic) states, and ferromagnet is calculated. The momentum distribution function and the (quasiparticle) density of states are discussed. There is a significant broadening of the quasiparticle bands when the antiferromagnetic insulator is doped. The evolution of the Fermi surface and the variation of the plasma frequency and a charge-stiffness constant with U/t and δ are calculated. The connection to results based on the Schwinger-boson-slave-fermion formalism is made.