A. R. Bishop

Strain-induced metal-insulator phase coexistence in perovskite manganites

The coexistence of distinct metallic and insulating electronic phases within the same sample of a perovskite manganite, such as La1-x-yPryCaxMnO3, presents researchers with a tool for tuning the electronic properties in materials. In particular, colossal magnetoresistance in these materials—the dramatic reduction of resistivity in a magnetic field—is closely related to the observed texture owing to nanometre- and micrometre-scale inhomogeneities. Despite accumulated data from various high-resolution probes, a theoretical understanding for the existence of such inhomogeneities has been lacking. Mechanisms invoked so far, usually based on electronic mechanisms and chemical disorder, have been inadequate to describe the multiscale, multiphase coexistence within a unified picture. Moreover, lattice distortions and long-range strains are known to be important in the manganites. Here we show that the texturing can be due to the intrinsic complexity of a system with strong coupling between the electronic and elastic degrees of freedom. This leads to local energetically favourable configurations and provides a natural mechanism for the self-organized inhomogeneities over both nanometre and micrometre scales. The framework provides a physical understanding of various experimental results and a basis for engineering nanoscale patterns of metallic and insulating phases.

THE DISCRETE NONLINEAR SCHRÖDINGER EQUATION: A SURVEY OF RECENT RESULTS

In this paper we review a number of recent developments in the study of the Discrete Nonlinear Schrodinger (DNLS) equation. Results concerning ground and excited states, their construction, stability and bifurcations are presented in one and two spatial dimensions. Combinations of such steady states lead to the study of coherent structure bound states. A special case of such structures are the so-called twisted modes and their two-dimensional discrete vortex generalization. The ideas on such multi-coherent structures and their interactions are also useful in treating finite system effects through the image method. The statistical mechanics of the system is also analyzed and the partition function calculated in one spatial dimension using the transfer integral method. Finally, a number of open problems and future directions in the field are proposed.

Weakly-pinned Froehlich-charge-density-wave condensates: a new, nonlinear, current-carrying elementary excitation

New, nonlinear, charged elementary excitations are predicted to occur for weakly-pinned Froehlich-charge-density-wave condensates at low temperatures.

Solitons in condensed matter: A paradigm

Abstract For this new journal dealing with nonlinear phenomena we review the setting of several important current problems in the physics of condensed matter (solids, liquids). We show how the concepts embodied in the mathematical analysis of solitons provide systematic new insight (i.e., a paradigm) into a central question: what are the important physical configurations in nonlinear condensed systems? Following these general issues we summarize the analysis of the dynamics and equilibrium thermodynamics (i.e., statistical mechanics) of non-linear one-dimensional model systems, and we indicate how the solitonic configurational phenomenology provides a basis for dynamic effects which are seen both experimentally and in molecular dynamics computer simulations. Many problems in condensed matter differ from the more familiar nonlinear mechanical or hydrodynamic applications in that finite temperature thermal fluctuations must be considered along with systematic dynamics.

Dynamical superfluid-insulator transition in a chain of weakly coupled bose-Einstein condensates.

We predict a dynamical classical superfluid-insulator transition in a Bose-Einstein condensate trapped in an optical and a magnetic potential. In the tight-binding limit, this system realizes an array of weakly coupled condensates driven by an external harmonic field. For small displacements of the parabolic trap about the equilibrium position, the condensates coherently oscillate in the array. For large displacements, the condensates remain localized on the side of the harmonic trap with a randomization of the relative phases. The superfluid-insulator transition is due to a discrete modulational instability, occurring when the condensate center of mass velocity is larger than a critical value.

Soliton Excitations in Polyacetylene and Relativistic Field Theory Models

A continuum model of a Peierls-dimerized chain, as described generally by Brazovskii and discussed for the case of polyacetylene by Takayama, Lin-Liu and Maki (TLM), is considered. The continuum (Bogliubov-de Gennes) equations arising in this model of interacting electrons and phonons are shown to be equivalent to the static, semiclassical equations for a solvable model field theory of self-coupled fermions-the N = 2 Gross-Neveu model. Based on this equivalence we note the existence of soliton defect states in polyacetylene that are additional to, and qualitatively different from, the amplitude “kinks” commonly discussed. The new solutions do not have the topological stability of kinks but are essentially conventional strong-coupling polarons in the dimerized chain. They carry spin (12) and charge (±e). In addition, we discuss further areas in which known field theory results may apply to a Peierls-dimerized chain, including relations between phenomenological φ4 and continuum electron-phonon models, and the structure of the fully quantum versus mean field theories.

Nonlinear dynamics and the problem of slip at material interfaces

Abstract The problem of dry friction between two metallic interfaces is discussed from the perspective of large scale molecular dynamics (MD) simulations. For flat interfaces between identical metals, two-dimensional MD simulations using embedded-atom-method potentials for copper have shown a variety of phenomena associated with a velocity weakening of the tangential force at high relative velocities (approaching significant fractions of the transverse sound speed). These include dislocation generation, dislocation motion both parallel and normal to the sliding interface, large plastic deformation, nucleation of microstructure, diffusive coarsening of microstructure, and material mixing. The early time behavior of a flat sliding interface is dominated by dislocation motion parallel to the interface. For this early stage, lower-dimensional models are useful in interpreting some of the simulation data. A two-chain forced Frenkel-Kontorova model reproduces some of the behavior of the larger scale simulations when the phenomenological damping is taken to be consistent with the MD simulations. This model exhibits four velocity regimes of steady state flow which will be discussed. Some of the implications for the nucleation of microstructure will be addressed.

Superconductivity in oxides: toward a unified picture

We present a combined overview of current experimental knowledge and theoretical understanding of high temperature superconductivity based on the charge transfer excitation model. Our model is capable of rationalizing a great variety of experimental information and suggests directions to follow in designing even higherTc materials.

A quasi-periodic route to chaos in a near-integrable pde

Abstract Pattern formation and transitions to chaos are described for the damped, ac-driven, one-dimensional, periodic sine-Gordon equation. In a nonlinear Schrodinger regime, a generic quasi-periodic route to intermittent chaos is exhibited in detail using a range of dynamical systems diagnostics. In addition, a nonlinear spectral transform is exploited: (i) to identify and quantify coordinates of space-time attractors in terms of a small number of soliton modes of the underlying integrable system; (ii) to use these analytic coordinates to identify homoclinic orbits as possible sources of chaos; and (iii) to demonstrate the significance of energy transfer between coherent and extended states in this chaotic system.

DNA breathing dynamics in the presence of a terahertz field

We consider the influence of a terahertz field on the breathing dynamics of double-stranded DNA. We model the spontaneous formation of spatially localized openings of a damped and driven DNA chain, and find that linear instabilities lead to dynamic dimerization, while true local strand separations require a threshold amplitude mechanism. Based on our results we argue that a specific terahertz radiation exposure may significantly affect the natural dynamics of DNA, and thereby influence intricate molecular processes involved in gene expression and DNA replication.