Phases and transitions in the spin-1 Bose-Hubbard model: Systematics of a mean-field theory

We generalize the mean-field theory for the spinless Bose-Hubbard model to account for the different types of superfluid phases that can arise in the spin-1 case. In particular, our mean-field theory can distinguish polar and ferromagnetic superfluids, Mott insulator, that arise at integer fillings at zero temperature, and normal Bose liquids into which the Mott insulators evolve at finite temperatures. We find, in contrast to the spinless case, that several of the superfluid-Mott insulator transitions are of first order at finite temperatures. Our systematic study yields rich phase diagrams that include first-order and second-order transitions and a variety of tricritical points. We discuss the possibility of realizing such phase diagrams in experimental systems.

Theory of the unusual doping and temperature dependence of photoemission spectra in manganites

A recent, major, puzzle in the core-level photoemission spectra of doped manganites is the observation of a 1–2 eV wide shoulder with intensity varying with temperature T as the square of the magnetization over a T scale of order 200 K, an order of magnitude less than electronic energies. This is addressed and resolved here, by extending a recently proposed two-fluid polaron–mobile electron model for these systems to include core-hole effects. The position of the shoulder is found to be determined by Coulomb and Jahn-Teller energies, while its spectral weight is determined by the mobile electron energetics which is strongly T and doping dependent, due to annealed disorder scattering from the polarons and the t2g core spins. Our theory accounts quantitatively for the observed T dependence of the difference spectra, and furthermore, explains the observed correspondence between spectral changes due to increasing doping and decreasing T.

Simplified theory of optical nonlinearities in spin-polarized bulk GaAs

Apart from their intrinsic physical interest, spin-polarized many-body effects are expected to be important to the working of spintronic devices. A vast literature exists on the effects of a spin-unpolarized electron-hole plasma on the optical properties of a semiconductor. Here, we include the spin degree of freedom to model optical absorption of circularly polarized light by spin-polarized bulk GaAs. Our model is easy to implement and does not require elaborate numerics, since it is based on the closed-form analytical pair-equation formula that is valid in 3d. The efficacy of our approach is demonstrated by a comparison with recent experimental data.

Modified density matrix renormalization group algorithm for the zigzag spin-1/2 chain with frustrated antiferromagnetic exchange: Comparison with field theory at large J(2)/J(1)

A modified density matrix renormalization group (DMRG) algorithm is applied to the zigzag spin-1/2 chain with frustrated antiferromagnetic exchange J(1) and J(2) between first and second neighbors. The modified algorithm yields accurate results up to J(2)/J(1) approximate to 4 for the magnetic gap Delta to the lowest triplet state, the amplitude B of the bond order wave phase, the wavelength lambda of the spiral phase, and the spin correlation length xi. The J(2)/J(1) dependences of Delta, B, lambda, and xi provide multiple comparisons to field theories of the zigzag chain. The twist angle of the spiral phase and the spin structure factor yield additional comparisons between DMRG and field theory. Attention is given to the numerical accuracy required to obtain exponentially small gaps or exponentially long correlations near a quantum phase transition.

Anomalous temperature dependence of Fermi-edge singularity in modulation-doped AlGaAs/InGaAs/GaAs hetero-structures

The temperature and power dependence of Fermi-edge singularity (FES) in high-density two-dimensional electron gas, specific to pseudomorphic AlxGa1-xAs/InGa1-yAs/GaAs heterostructures is studied by photoluminescence (PL). In all these structures, there are two prominent transitions E-11 and E-21 considered to be the result of electron-hole recombination from first and second electron sub-bands with that of first heavy-hole sub-band. FES is observed approximately 5-10 meV below the E-21 transition. At 4.2 K, FES appears as a lower energy shoulder to the E-21 transition. The PL intensity of all the three transitions E-11, FES and E-21 grows linearly with excitation power. However, we observe anomalous behavior of FES with temperature. While PL intensity of E-11 and E-21 decrease with increasing temperature, FES transition becomes stronger initially and then quenches-off slowly (till 40K). Though it appears as a distinct peak at about 20 K, its maximum is around 7 - 13 K.

Simplified theory of optical nonlinearities in spin-polarized bulk GaAs

Apart from their intrinsic physical interest, spin-polarized many-body effects are expected to be important to the working of spintronic devices. A vast literature exists on the effects of a spin-unpolarized electron-hole plasma on the optical properties of a semiconductor. Here, we include the spin degree of freedom to model optical absorption of circularly polarized light by spin-polarized bulk GaAs. Our model is easy to implement and does not require elaborate numerics, since it is based on the closed-form analytical pair-equation formula that is valid in 3d. The efficacy of our approach is demonstrated by a comparison with recent experimental data.

Non-Fermi liquid theory of quantum hall effects

Within the Grassmannian U(2N)/U(N) x U(N) nonlinear sigma-model representation of localization, one can study the low-energy dynamics of both a free and interacting electron gas. We study the crossover between these two fundamentally different physical problems. We show how the topological arguments for the exact quantization of the Hall conductance are extended to include the Coulomb interaction problem. We discuss dynamical scaling and make contact with the theory of variable range hopping. (C) 2005 Pleiades Publishing, Inc.

Surface instability of confined elastic bilayers: Theory and simulations

The surface of a soft elastic film becomes unstable and forms a self-organized undulating pattern because of adhesive interactions when it comes in contact proximity with a rigid surface. For a single film, the pattern length scale lambda, which is governed by the minimization of the elastic stored energy, gives lambda similar to 3h, where h is the film thickness. Based on a linear stability analysis and simulations of adhesion and debonding, we consider the contact instability of an elastic bilayer, which provides greater flexibility in the morphological control of interfacial instability. Unlike the case of a single film, the morphology of the contact instability patterns, debonding distance, and debonding force in a bilayer can be controlled in a nonlinear way by varying the thicknesses and shear moduli of the films. Interestingly, the pattern wavelength in a bilayer can be greatly increased or decreased compared to a single film when the adhesive contact is formed by the stiffer or the softer of the two films, respectively. In particular, lambda as small as 0.5h can be obtained. This indicates a new strategy for pattern miniaturization in elastic contact lithography.

Theory of laminar flame propagation with non-normal diffusion.

A study has been made of the problem of steady, one-dimensional, laminar flame propagation in premixed gases, with the Lewis number differing from (and equal to) unity. Analytical solutions, using the method of matched asymptotic expansions, have been obtained for large activation energies. Numerical solutions have been obtained for a wide range of the reduced activation temperature parameter (n {geometrically equal to} E/RTb), and the Lewis number δ. The studies reveal that the flame speed eigenvalue is linear in Lewis number for first order and quadratic in Lewis number for second order reactions. For a quick determination of flame speeds, with reasonable accuracy, a simple rule, expressing the flame speed eigenvalue as a function of the Lewis number and the centroid of the reaction rate function, is proposed. Comparisons have been made with some of the earlier works, for both first and second order reactions.

A generalized mathematical theory and experimental verification of proportional notches

A theory and generalized synthesis procedure is advocated for the design of weir notches and orifice-notches having a base in any given shape, to a depth a, such that the discharge through it is proportional to any singular monotonically-increasing function of the depth of flow measured above a certain datum. The problem is reduced to finding an exact solution of a Volterra integral equation in Abel form. The maximization of the depth of the datum below the crest of the notch is investigated. Proof is given that for a weir notch made out of one continuous curve, and for a flow proportional to the mth power of the head, it is impossible to bring the datum lower than (2m − 1)a below the crest of the notch. A new concept of an orifice-notch, having discontinuity in the curve and a division of flow into two distinct portions, is presented. The division of flow is shown to have a beneficial effect in reducing the datum below (2m − 1)a from the crest of the weir and still maintaining the proportionality of the flow. Experimental proof with one such orifice-notch is found to have a constant coefficient of discharge of 0.625. The importance of this analysis in the design of grit chambers is emphasized.

Moment methods and "restricted variation" in kinetic theory

It is shown that there is a strict one-to-one correspondence between results obtained by the use of "restricted" variational principles and those obtained by a moment method of the Mott-Smith type for shock structure.

On the theory of the indentation test for the measurement of tensile strength of brittle materials

A theoretical solution has been obtained for the state of stress in a rectangular plate under a pair of symmetrically placed rigid indenters. The stress distributions along the two central axes have been calculated for a square plate assuming the pressure distribution under the indenters as uniform, parabolic and one resulting from 'constant displacement' on a semiinfinite boundary, for different ratios of indenter-width to side of square. The results are compared with those of photoelastic analysis of Berenbaum and Brodie and the validity of the solution is discussed. The solution has been extended to orthotropic materials and numerical results for one type of coal are given.

A nonlinear theory of wake development

A simple new series, using an expansion of the velocity profile in parabolic cylinder functions, has been developed to describe the nonlinear evolution of a steady, laminar, incompressible wake from a given arbitrary initial profile. The first term in this series is itself found to provide a very satisfactory prediction of the decay of the maximum velocity defect in the wake behind a flat plate or aft of the recirculation zone behind a symmetric blunt body. A detailed analysis, including higher order terms, has been made of the flat plate wake with a Blasius profile at the trailing edge. The same method yields, as a special case, complete results for the development of linearized wakes with arbitrary initial profile under the influence of arbitrary pressure gradients. Finally, for purposes of comparison, a simple approximate solution is obtained using momentum integral methods, and found to predict satisfactorily the decay of the maximum velocity defect. © 1970 Wolters-Noordhoff Publishing.

Simplified theory of carrier back-scattering in semiconducting carbon nanotubes: A Kane's model approach

We present a simplified yet analytical formulation of the carrier backscattering coefficient for zig-zag semiconducting single walled carbon nanotubes under diffusive regime. The electron-phonon scattering rate for longitudinal acoustic, optical, and zone-boundary phonon emissions for both inter- and intrasubband transition rates have been derived using Kane's nonparabolic energy subband model.The expressions for the mean free path and diffusive resistance have been formulated incorporating the aforementioned phonon scattering. Appropriate overlap function in Fermi's golden rule has been incorporated for a more general approach. The effect of energy subbands on low and high bias zones for the onset of longitudinal acoustic, optical, and zone-boundary phonon emissions and absorption have been analytically addressed. 90% transmission of the carriers from the source to the drain at 400 K for a 5 mu m long nanotube at 105 V m(-1) has been exhibited. The analytical results are in good agreement with the available experimental data. (c) 2010 American Institute of Physics.