arXiv subjects
Publications and source records attributed to A. R. Bishop.
The effect of the powder average on the peak shapes and positions in neutron pair distribution functions of polycrystalline materials is examined. It is shown that for highly anisotropic crystals, the powder average leads to shifts in peak positions and to non-Gaussian peak shapes. The peak shifts can be as large as several percent of the lattice spacing.
We present a minimal model for cuprate superconductors. At the unrestricted mean-field level, the model produces homogeneous superconductivity at large doping, striped superconductivity in the underdoped regime and various antiferromagnetic phases at low doping and for high temperatures. On the underdoped side, the superconductor is intrinsically inhomogeneous and global phase coherence is achieved through Josephson-like coupling of the superconducting stripes. The model is applied to calculate experimentally measurable ARPES spectra.
We study thermal relaxation in ordered arrays of coupled nonlinear elements with external driving. We find, that our model exhibits dynamic self-organization manifested in a universal stretched-exponential form of relaxation. We identify two types of self-organization, cooperative and anti-cooperative, which lead to fast and slow relaxation, respectively. We give a qualitative explanation for the behavior of the stretched exponent in different parameter ranges. We emphasize that this is a system exhibiting stretched-exponential relaxation without explicit disorder or frustration.
We investigate the electronic dynamics in the underdoped cuprates focusing on the effects of one-dimensional charge stripes. We address recent experimental Angular-Resolved Photoemission Spectra results on (La$_{1.28}$Nd$_{0.6}$Sr$_{0.12}$)CuO$_4$. We find that various inhomogeneous models can account for the distribution of quasiparticle weights close to momentum ${\bf k}=(π,0)$ and symmetry related points. The observed flat dispersion region around the same ${\bf k}$ point can only be addressed by certain classes of those inhomogeneous models which locally break spin symmetry. Homogeneous models including hopping elements up to second neighbors cannot reproduce the experimental quasiparticle weight, since most of it is centered around ${\bf k}=(\frac π{2},\frac π {2})$.
Positions of protons in DNA hydrogen bonds are fundamental for the fidelity of the replication process. Because the hydrogen bond is partially covalent the electronic structure of DNA plays an important role in the replication process. Current studies of electron transfer in DNA have shown that simple pictures based on independent electron physics are not sufficient to account for the experimental data. In this paper we propose a model for electron-proton interaction in DNA and its relationship to mutagenesis. We argue that mutations will be more frequent in DNA sequences where electron delocalization occurs. To test our theory we calculate the heat capacity of DNA at low temperatures and compare with the available experimental data in hydrated DNA. We find that our model is in good agreement with the data. We also propose new measurements of infrared absorption which would further test our ideas.
We present a comparative numerical study of the ordered and the random two-dimensional sine-Gordon models on a lattice. We analytically compute the main features of the expected high temperature phase of both models, described by the Edwards-Wilkinson equation. We then use those results to locate the transition temperatures of both models in our Langevin dynamics simulations. We show that our results reconcile previous contradictory numerical works concerning the superroughening transition in the random sine-Gordon model. We also find evidence supporting the existence of two different low temperature phases for the disordered model. We discuss our results in view of the different analytical predictions available and comment on the nature of these two putative phases.
The problems of charge stripe formation, spin-charge separation, and stability of the antiphase domain wall (ADW) associated with a stripe are addressed using an analytical approach to the t-J_z model. We show that a metallic stripe together with its ADW is the ground state of the problem in the low doping regime. The stripe is described as a system of spinons and magnetically confined holons strongly coupled to the two dimensional (2D) spin environment with holon-spin-polaron elementary excitations filling a one-dimensional band.
We generalize recent work on parametric resonances for nonlinear Schr{ö}dinger (NLS) type equations to the case of three dimensional Bose-Einstein condensates at zero temperatures. We show the possibility of such resonances in the three-dimensional case, using a moment method and numerical simulations.
We demonstrate the spontaneous formation of spatial patterns in a damped, ac-driven cubic Klein-Gordon lattice. These patterns are composed of arrays of intrinsic localized modes characteristic for nonlinear lattices. We analyze the modulation instability leading to this spontaneous pattern formation. Our calculation of the modulational instability is applicable in one and two-dimensional lattices, however in the analyses of the emerging patterns we concentrate particularly on the two-dimensional case.
We present a minimal model of a doped Mott insulator that simultaneously supports antiferromagnetic stripes and d-wave superconductivity. We explore the implications for the global phase diagram of the superconducting cuprates. At the unrestricted mean-field level, the various phases of the cuprates, including weak and strong pseudogap phases, and two different types of superconductivity in the underdoped and the overdoped regimes, find a natural interpretation. We argue that on the underdoped side, the superconductor is intrinsically inhomogeneous -- striped coexistence of of superconductivity and magnetism -- and global phase coherence is achieved through Josephson-like coupling of the superconducting stripes. On the overdoped side, the state is overall homogeneous and the superconductivity is of the classical BCS type.
We argue that the superconducting state found in high-$T_c$ cuprates is inhomogeneous with a corresponding inhomogeneous superfluid density. We introduce two classes of microscopic models which capture the magnetic and superconducting properties of these strongly correlated materials. We start from a generalized t-J model, in which appropriate inhomogeneous terms mimic stripes. We find that inhomogeneous interactions that break magnetic symmetries are essential to induce substantial pair binding of holes in the thermodynamic limit. We argue that this type of model reproduces the ARPES and neutron scattering data seen experimentally.
A t-J-like model for inhomogeneous superconductivity of cuprate oxides is presented, in which local anisotropic magnetic terms are essential. We show that this model predicts pairing, consistent with experiments, and argue how the macroscopic phase-coherent state gradually grows upon lowering of the temperature. We show that appropriate inhomogeneities are essential in order to have significant pair binding in the thermodynamic limit. Particularly, {\it local} breaking of SU(2) spin symmetry is an efficient mechanism for inducing pairing of two holes, as well as explaining the magnetic scattering properties. We also discuss the connection of the resulting inhomogeneity-induced superconductivity to recent experimental evidence for a linear relation between magnetic incommensurability and the superconducting transition temperature, as a function of doping.
The competition between long-range and short-range interactions among holes moving in an antiferromagnet (AF), is studied within a model derived from the spin density wave picture of layered transition metal oxides. A novel numerical approach is developed which allows one to solve the problem at finite hole densities in very large systems (of order hundreds of lattice spacings), albeit in a quasiclassical limit, and to correctly incorporate the long-range part of the Coulomb interaction. The focus is on the problem of charge ordering and the charge phase diagram: at low temperatures four different phases are found, depending on the strength of the magnetic (dipolar) interaction generated by the spin-wave exchange, and the density of holes. The four phases are the Wigner crystal, diagonal stripes, a grid phase (horizontal-vertical stripe loops) and a glassy-clumped phase. In the presence of both in-plane and out-of-plane charged impurities the stripe ordering is suppressed, although finite stripe segments persist. At finite temperatures multiscale (intermittency) dynamics is found, reminiscent of that in glasses. The dynamics of stripe melting and its implications for experiments is discussed.
We propose a new optimized phonon approach for the numerical diagonalization of interacting electron-phonon systems combining density-matrix and Lanczos algorithms. We demonstrate the reliablity of this approach by calculating the phase diagram for bi-polaron formation in the one-dimensional Holstein-Hubbard model, and the Luttinger parameters for the metallic phase of the half-filled one-dimensional Holstein model of spinless fermions.
The in-plane oxygen vibrations in La2NiO4 are investigated for several hole-doping concentrations both theoretically and experimentally via inelastic neutron scattering. Using an inhomogeneous Hartree-Fock plus RPA numerical method in a two-dimensional Peierls-Hubbard model, it is found that the doping induces stripe ordering of localized charges, and that the strong electron-lattice coupling causes the in-plane oxygen modes to split into two subbands. This result agrees with the phonon band splitting observed by inelastic neutron scattering in La2-xSrxNiO4. Predictions of strong electron-lattice coupling in La2NiO4, the proximity of both oxygen-centered and nickel-centered charge ordering, and the relation between charged stripe ordering and the splitting of the in-plane phonon band upon doping are emphasized.
Starting from a t-J model, we introduce inhomogeneous terms to mimic stripes. We find that if the inhomogeneous terms break the SU(2) spin symmetry the binding between holes is tremendously enhanced in the thermodynamic limit. In any other model (including homogeneous models) the binding in the thermodynamic limit is small or neglible. By including these inhomogeneous terms we can reproduce experimental neutron scattering data. We also discuss the connection of the resulting inhomogeneity-induced superconductivity to recent experimental evidence for a linear relation between magnetic incommensurability and the superconducting transition temperature, as a function of doping.
We show how the St.Venant compatibility relations for strain in three dimensions lead to twinning for the cubic to tetragonal transition in martensitic materials within a Ginzburg-Landau model in terms of the six components of the symmetric strain tensor. The compatibility constraints generate an anisotropic long-range interaction in the order parameter (deviatoric strain) components. In contrast to two dimensions, the free energy is characterized by a "landscape" of competing metastable states. We find a variety of textures, which result from the elastic frustration due to the effects of compatibility. Our results are also applicable to structural phase transitions in improper ferroelastics such as ferroelectrics and magnetoelastics, where strain acts as a secondary order parameter.
We analyze numerically the ground-state and spectral properties of the three-quarter filled Peierls-Hubbard Hamiltonian. Various charge- and spin-ordered states are identified. In the strong-coupling regime, we find clear signatures of local lattice distortions accompanied by intrinsic multi-phonon localization. The results are discussed in relation to recent experiments on MX chain [-PtCl-] complexes. In particular we are able to reproduce the observed red shift of the overtone resonance Raman spectrum.