Conformal invariance and scalar-tensor theories

A new generalisation of Einstein’s theory is proposed which is invariant under conformal mappings. Two scalar fields are introduced in addition to the metric tensor field, so that two special choices of gauge are available for physical interpretation, the ‘Einstein gauge’ and the ‘atomic gauge’. The theory is not unique but contains two adjustable parameters ζ anda. Witha=1 the theory viewed from the atomic gauge is Brans-Dicke theory (ω=−3/2+ζ/4). Any other choice ofa leads to a creation-field theory. In particular the theory given by the choicea=−3 possesses a cosmological solution satisfying Dirac’s ‘large numbers’ hypothesis.

Long-range Coulomb interactions and nanoscale electronic inhomogeneities in correlated oxides

Electronic, magnetic, or structural inhomogeneities ranging in size from nanoscopic to mesoscopic scales seem endemic and are possibly generic to colossal magnetoresistance manganites and other transition metal oxides. They are hence of great current interest and understanding them is of fundamental importance. We show here that an extension, to include long-range Coulomb interactions, of a quantum two-fluid l-b model proposed recently for manganites [Phys. Rev. Lett. 92, 157203 (2004)] leads to an excellent description of such inhomogeneities. In the l-b model two very different kinds of electronic states, one localized and polaronic (l) and the other extended or broad band (b) coexist. For model parameters appropriate to manganites and even within a simple dynamical mean-field theory (DMFT) framework, it describes many of the unusual phenomena seen in manganites, including colossal magnetoresistance (CMR), qualitatively and quantitatively. However, in the absence of long-ranged Coulomb interaction, a system described by such a model would actually phase separate, into macroscopic regions of l and b electrons, respectively. As we show in this paper, in the presence of Coulomb interactions, the macroscopic phase separation gets suppressed and instead nanometer scale regions of polarons interspersed with band electron puddles appear, constituting a kind of quantum Coulomb glass. We characterize the size scales and distribution of the inhomogeneity using computer simulations. For realistic values of the long-range Coulomb interaction parameter V-0, our results for the thresholds for occupancy of the b states are in agreement with, and hence support, the earlier approach mentioned above based on a configuration averaged DMFT treatment which neglects V-0; but the present work has features that cannot be addressed in the DMFT framework. Our work points to an interplay of strong correlations, long-range Coulomb interaction, and dopant ion disorder, all inevitably present in transition metal oxides as the origin of nanoscale inhomogeneities rather than disorder frustrated phase competition as is generally believed. As regards manganites, it argues against explanations for CMR based on disorder frustrated phase separation and for an intrinsic origin of CMR. Based on this, we argue that the observed micrometer (meso) scale inhomogeneities owe their existence to extrinsic causes, e.g., strain due to cracks and defects. We suggest possible experiments to validate our speculation.

Influence of spatial variability of permeability property on steady state seepage flow and slope stability analysis

In recent years, spatial variability modeling of soil parameters using random field theory has gained distinct importance in geotechnical analysis. In the present Study, commercially available finite difference numerical code FLAC 5.0 is used for modeling the permeability parameter as spatially correlated log-normally distributed random variable and its influence on the steady state seepage flow and on the slope stability analysis are studied. Considering the case of a 5.0 m high cohesive-frictional soil slope of 30 degrees, a range of coefficients of variation (CoV%) from 60 to 90% in the permeability Values, and taking different values of correlation distance in the range of 0.5-15 m, parametric studies, using Monte Carlo simulations, are performed to study the following three aspects, i.e., (i) effect ostochastic soil permeability on the statistics of seepage flow in comparison to the analytic (Dupuit's) solution available for the uniformly constant permeability property; (ii) strain and deformation pattern, and (iii) stability of the given slope assessed in terms of factor of safety (FS). The results obtained in this study are useful to understand the role of permeability variations in slope stability analysis under different slope conditions and material properties. (C) 2009 Elsevier B.V. All rights reserved.

Improved procedures for static and dynamic analyses of wrinkled membranes

An analysis of large deformations of flexible membrane structures within the tension field theory is considered. A modification-of the finite element procedure by Roddeman et al. (Roddeman, D. G., Drukker J., Oomens, C. W J., Janssen, J. D., 1987, ASME J. Appl. Mech. 54, pp. 884-892) is proposed to study the wrinkling behavior of a membrane element. The state of stress in the element is determined through a modified deformation gradient corresponding to a fictive nonwrinkled surface. The new model uses a continuously modified deformation gradient to capture the location orientation of wrinkles more precisely. It is argued that the fictive nonwrinkled surface may be looked upon as an everywhere-taut surface in the limit as the minor (tensile) principal stresses over the wrinkled portions go to zero. Accordingly, the modified deformation gradient is thought of as the limit of a sequence of everywhere-differentiable tensors. Under dynamic excitations, the governing equations are weakly projected to arrive at a system of nonlinear ordinary differential equations that is solved using different integration schemes. It is concluded that, implicit integrators work much better than explicit ones in the present context.

Giant magnons in the D1-D5 system

We study giant magnons in the the D1-D5 system from both the boundary CFT and as classical solutions of the string sigma model in AdS(3) x S-3 x T-4. Re-examining earlier studies of the symmetric product conformal field theory we argue that giant magnons in the symmetric product are BPS states in a centrally extended SU(1 vertical bar 1) x SU(1 vertical bar 1) superalgebra with two more additional central charges. The magnons carry these additional central charges locally but globally they vanish. Using a spin chain description of these magnons and the extended superalgebra we show that these magnons obey a dispersion relation which is periodic in momentum. We then identify these states on the string theory side and show that here too they are BPS in the same centrally extended algebra and obey the same dispersion relation which is periodic in momentum. This dispersion relation arises as the BPS condition for the extended algebra and is similar to that of magnons in N = 4 Yang-Mills Yang-Mills.

Low energy properties of the SU(m|n) supersymmetric Haldane–Shastry spin chain

The ground state and low energy excitations of the SU(m|n) supersymmetric Haldane–Shastry spin chain are analyzed. In the thermodynamic limit, it is found that the ground state degeneracy is finite only for the SU(m|0) and SU(m|1) spin chains, while the dispersion relation for the low energy and low momentum excitations is linear for all values of m and n. We show that the low energy excitations of the SU(m|1) spin chain are described by a conformal field theory of m non-interacting Dirac fermions which have only positive energies; the central charge of this theory is m/2. Finally, for ngreater-or-equal, slanted1, the partition functions of the SU(m|n) Haldane–Shastry spin chain and the SU(m|n) Polychronakos spin chain are shown to be related in a simple way in the thermodynamic limit at low temperatures.

Sound Velocity Anomaly at the Mott Transition: Application to Organic Conductors and V2O3

Close to the Mott transition, lattice degrees of freedom react to the softening of electron degrees of freedom. This results in a change of lattice spacing, a diverging compressibility, and a critical anomaly of the sound velocity. These effects are investigated within a simple model, in the framework of dynamical mean-field theory. The results compare favorably to recent experiments on the layered organic-conductor kappa-(BEDT-TTF)(2)Cu[N(CN)(2)]Cl. We predict that effects of a similar magnitude are expected for V2O3, despite the much larger value of the elastic modulus of this material.

Potentiometric and spectrophotometric investigation of nickel-monoethanol-amine complexes

A detailed study of nickel-monoethanolamine complexes has been made employing potentiometric and spectrophotometric methods. The conditions for the formation of mono as well as polynuclear complexes have been investigated by potentiometric method. Evidence is presented for the formation of the following complexes and their stability constants are determined: NiA2+, Ni22+, Ni32+, NiA42+, NiA52+, NiA22+, Ni2A24+ and Ni3A36+. Combining potentiometric data with the spectrophotometric data, absorption spectra of the pure mononuclear complexes NiA2+ to NiA42+ and NiA2+6 have been computed. The absorption spectrum of NiA2+6 has been discussed on the basis of ligand field and molecular orbital theories. The absorption spectra of intermediate complexes have been interpreted on the basis of average ligand field theory. There has been good agreement between the experimental (10,400 cm-1) value of 10 Dq of NiA2+6 and the calculated value of 10 Dq (11,400 cm-1) on the basis of M.O. theory.

Potentiometric and spectrophotometric investigations of nickel-triethanolamine complexes

A detailed study of nickel-triethanolamine complexes has been made employing potentiometric and spectrophotometric methods. The potentiometric method has been used to investigate the conditions for the formation of both mono- and polynuclear complexes. The formulae and the stability constants of the following complexes have been determined Ni(TEA)2+, Ni(TEA)22+, and Ni2(TEA)24+. Absorption spectra of pure mononuclear complexes have been computed by the combination of potentiometric and spectrophotometric methods. The results are discussed on the basis of ligand field theory. Comparison of the step constants of the nickel-ethanolamines (mono-, di- and tri-) shows a slight chelate effect in these complexes due to coordination through hydroxyl oxygen. In the case of polynuclear complexes it is likely that bridging occurs through hydroxyl oxygen.

Fate of the superconducting ground state on the Moyal plane

It is known that Berry curvature of the band structure of certain crystals can lead to effective noncommutativity between spatial coordinates. Using the techniques of twisted quantum field theory, we investigate the question of the formation of a paired state of twisted fermions in such a system. We find that to leading order in the noncommutativity parameter, the gap between the non-interacting ground state and the paired state is smaller compared to its commutative counterpart. This suggests that BCS type superconductivity, if present in such systems, is more fragile and easier to disrupt. (C) 2010 Elsevier B.V. All rights reserved.

Fractional quantum Hall edge: Effect of nonlinear dispersion and edge roton

According to Wen's theory, a universal behavior of the fractional quantum Hall edge is expected at sufficiently low energies, where the dispersion of the elementary edge excitation is linear. A microscopic calculation shows that the actual dispersion is indeed linear at low energies, but deviates from linearity beyond certain energy, and also exhibits an "edge roton minimum." We determine the edge exponent from a microscopic approach, and find that the nonlinearity of the dispersion makes a surprisingly small correction to the edge exponent even at energies higher than the roton energy. We explain this insensitivity as arising from the fact that the energy at maximum spectral weight continues to show an almost linear behavior up to fairly high energies. We also study, in an effective-field theory, how interactions modify the exponent for a reconstructed edge with multiple edge modes. Relevance to experiment is discussed.

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.

Uniformly accelerated observer in Moyal spacetime

In Minkowski space, an accelerated reference frame may be defined as one that is related to an inertial frame by a sequence of instantaneous Lorentz transformations. Such an accelerated observer sees a causal horizon, and the quantum vacuum of the inertial observer appears thermal to the accelerated observer, also known as the Unruh effect. We argue that an accelerating frame may be similarly defined (i.e. as a sequence of instantaneous Lorentz transformations) in noncommutative Moyal spacetime, and discuss the twisted quantum field theory appropriate for such an accelerated observer. Our analysis shows that there are several new features in the case of noncommutative spacetime: chiral massless fields in (1 + 1) dimensions have a qualitatively different behavior compared to massive fields. In addition, the vacuum of the inertial observer is no longer an equilibrium thermal state of the accelerating observer, and the Bose-Einstein distribution acquires.-dependent corrections.

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.

Long range interactions between some charged solitons

A procedure is offered for evaluating the forces between classical, charged solitons at large distances. This is employed for the solitons of a complex, scalar two-dimensional field theory with a U(1) symmetry, that leads to a conserved chargeQ. These forces are the analogues of the strong interaction forces. The potential,U(Q, R), is found to be attractive, of long range, and strong when the coupling constants in the theory are small. The dependence ofU(Q, R) onQ, the sum of the charges of the two interacting solitons (Q will refer to isospin in the SU(2) generalisation of the U(1) symmetric theory) is of importance in the theory of strong interactions; group theoretical considerations do not give such information. The interaction obtained here will be the leading term in the corresponding quantum field theory when the coupling-constants are small.