arXiv subjects

A. R. Bishop

Publications and source records attributed to A. R. Bishop.

At least 55 records · Page 3Linked to original sources

arXiv2009

Localized structures in Kagome lattices

We investigate the existence and stability of gap vortices and multi-pole gap solitons in a Kagome lattice with a defocusing nonlinearity both in a discrete case and in a continuum one with periodic external modulation. In particular, predictions are made based on expansion around a simple and analytically tractable anti-continuum (zero coupling) limit. These predictions are then confirmed for a continuum model of an optically-induced Kagome lattice in a photorefractive crystal obtained by a continuous transformation of a honeycomb lattice.

nlin.PS↗

arXiv2008

Discrete solitons and vortices in hexagonal and honeycomb lattices: Existence, stability, and dynamics

We consider a prototypical dynamical lattice model, namely, the discrete nonlinear Schroedinger equation on nonsquare lattice geometries. We present a systematic classification of the solutions that arise in principal six-lattice-site and three-lattice-site contours in the form of both discrete multipole solitons and discrete vortices. Additionally to identifying the possible states, we analytically track their linear stability both qualitatively and quantitatively. We find that among the six-site configurations, the hexapole of alternating phases, as well as the vortex of topological charge S=2 have intervals of stability; among three-site states, only the vortex of topological charge S=1 may be stable in the case of focusing nonlinearity. These conclusions are confirmed both for hexagonal and for honeycomb lattices by means of detailed numerical bifurcation analysis of the stationary states from the anticontinuum limit, and by direct simulations to monitor the dynamical instabilities, when the latter arise. The dynamics reveal a wealth of nonlinear behavior resulting not only in single-site solitary wave forms, but also in robust multisite breathing structures.

nlin.PS↗

arXiv2008

Pressure-induced phase transition to a novel spin state in striped nickelates

We analyze pressure effects on stripe states within a selfconsistent Hartree-Fock calculation for a model of a striped nickelates. The results show a transition induced by high pressure and predict possible new spin states. We describe characteristics in the phonon excitations at the predicted transition, based on a real-space random phase approximation.

cond-mat.str-el↗

arXiv2008

Polaron Coherence as Origin of the Pseudogap Phase in High Temperature Superconducting Cuprates

Within a two component approach to high Tc copper oxides including polaronic couplings, we identify the pseudogap phase as the onset of polaron ordering. This ordering persists in the superconducting phase. A huge isotope effect on the pseudogap onset temperature is predicted and in agreement with experimental data. The anomalous temperature dependence of the mean square copper oxygen ion displacement observed above, at and below Tc stems from an s-wave superconducting component of the order parameter, whereas a pure d-wave order parameter alone can be excluded.

cond-mat.supr-con↗

arXiv2008

Matter-wave solitons with a periodic, piecewise-constant nonlinearity

Motivated by recent proposals of ``collisionally inhomogeneous'' Bose-Einstein condensates (BECs), which have a spatially modulated scattering length, we study the existence and stability properties of bright and dark matter-wave solitons of a BEC characterized by a periodic, piecewise-constant scattering length. We use a ``stitching'' approach to analytically approximate the pertinent solutions of the underlying nonlinear Schrödinger equation by matching the wavefunction and its derivatives at the interfaces of the nonlinearity coefficient. To accurately quantify the stability of bright and dark solitons, we adapt general tools from the theory of perturbed Hamiltonian systems. We show that solitons can only exist at the centers of the constant regions of the piecewise-constant nonlinearity. We find both stable and unstable configurations for bright solitons and show that all dark solitons are unstable, with different instability mechanisms that depend on the soliton location. We corroborate our analytical results with numerical computations.

nlin.PS↗

arXiv2008

Kondo Stripes in an Anderson-Heisenberg Model of Heavy Fermion Systems

We study the interplay between the spin-liquid and Kondo physics, as related to the non-magnetic part of the phase diagram of heavy fermion materials. Within the unrestricted mean-field treatment of the infinite-$U$ 2D Anderson-Heisenberg model, we find that there are two topologically distinct non-degenerate uniform heavy Fermi liquid states that may form as a consequence of the Kondo coupling between spinons and conduction electrons. For certain carrier concentrations the uniform Fermi liquid becomes unstable with respect to formation of a new kind of anharmonic "Kondo stripe" state with inhomogeneous Kondo screening strength and the charge density modulation. These feature are experimentally measurable, and thus may help to establish the relevance of the spin-liquid correlations to heavy fermion materials.

cond-mat.str-el↗

arXiv2008

On the Emergence of Unstable Modes in an Expanding Domain for Energy-Conserving Wave Equations

Motivated by recent work on instabilities in expanding domains in reaction-diffusion settings, we propose an analog of such mechanisms in energy-conserving wave equations. In particular, we consider a nonlinear Schr{ö}dinger equation in a finite domain and show how the expansion or contraction of the domain, under appropriate conditions, can destabilize its originally stable solutions through the modulational instability mechanism. Using both real and Fourier spacediagnostics, we monitor and control the crossing of the instability threshold and, hence, the activation of the instability. We also consider how the manifestation of this mechanism is modified in a spatially inhomogeneous setting, namely in the presence of an external parabolic potential, which is relevant to trapped Bose-Einstein condensates.

nlin.PS↗

arXiv2008

Localized polarons and doorway vibrons in finite quantum structures

We consider transport through finite quantum systems such as quantum barriers, wells, dots or junctions, coupled to local vibrational modes in the quantal regime. As a generic model we study the Holstein-Hubbard Hamiltonian with site-dependent potentials and interactions. Depending on the barrier height to electron-phonon coupling strength ratio and the phonon frequency we find distinct opposed behaviors: Vibration-mediated tunneling or intrinsic localization of (bi)polarons. These regimes are strongly manifested in the density correlations, mobility, and optical response calculated by exact numerical techniques.

cond-mat.str-el↗

arXiv2007

Commensurate-incommensurate transition and associated collective modes in the stripe state of cuprates near 1/8 hole-doping

We analyze the anomalous behavior in hole-doped cuprates near 1/8 doping in terms of the commensurate-incommensurate transition of a stripe phase. Based on an effective Ginzburg-Landau theory appropriate for weak pinning, we calculate the commensurate-incommensurate transition point and the energies of the phason and amplitudon collective modes. Using experimentally available parameters, we estimate the phason gap (pinning frequency), the conductivity and the contribution of the phason mode to the dielectric function.

cond-mat.str-el↗

arXiv2007

Polarized States and Domain Walls in Spinor Bose-Einstein Condensates

We study spin-polarized states and their stability in anti-ferromagnetic states of spinor (F=1) quasi-one-dimensional Bose-Einstein condensates. Using analytical approximations and numerical methods, we find various types of polarized states, including: patterns of the Thomas-Fermi type; structures with a pulse-shape in one component inducing a hole in the other components; states with holes in all three components; and domain walls. A Bogoliubov-de Gennes analysis reveals that families of these states contain intervals of a weak oscillatory instability, except for the domain walls, which are always stable. The development of the instabilities is examined by means of direct numerical simulations.

cond-mat.other↗

arXiv2007

Structure and Fragmentation in Colloidal Artificial Molecules and Nuclei

Motivated by recent experiments on colloidal systems with competing attractive and repulsive interactions, we simulate a two-dimensional system of colloids with competing interactions that can undergo fragmentation. In the absence of any other confining potential, the colloids can form stable clusters depending on the strength of the short range attractive term. By suddenly changing the strength of one of the interaction terms we find a rich variety of fragmentation behavior which is affected by the existence of "magic" cluster numbers. Such soft matter systems can be used to construct artificial nuclei.

cond-mat.soft↗

arXiv2007

Cerenkov-like radiation in a binary Schr{ö}dinger flow past an obstacle

We consider the dynamics of two coupled miscible Bose-Einstein condensates, when an obstacle is dragged through them. The existence of two different speeds of sound provides the possibility for three dynamical regimes: when both components are subcritical, we do not observe nucleation of coherent structures; when both components are supercritical they both form dark solitons in one dimension (1D) and vortices or rotating vortex dipoles in two dimensions (2D); in the intermediate regime, we observe the nucleation of a structure in the form of a dark-antidark soliton in 1D; subcritical component; the 2D analog of such a structure, a vortex-lump, is also observed.

cond-mat.soft↗

arXiv2006

Slow-light solitons: influence of relaxation

We have applied the transformation of the slow light equations to Liouville theory that we developed in our previous work, to study the influence of relaxation on the soliton dynamics. We solved the problem of the soliton dynamics in the presence of relaxation and found that the spontaneous emission from the upper atomic level is strongly suppressed. Our solution proves that the spatial shape of the soliton is well preserved even if the relaxation time is much shorter than the soliton time length. This fact is of great importance for applications of the slow-light soliton concept in optical information processing. We also demonstrate that the relaxation plays a role of resistance to the soliton motion and slows the soliton down even if the controlling field is constant.

quant-ph↗

arXiv2006

Comment on: Role of inelastic tunneling through the insulating barrier in scanning-tunneling-microscope experiments on cuprate superconductors

In a recent letter [1] Pilgram, Rice and Sigrist (PRS) propose to perform oxygen isotope dependent conductivity measurements along the c-axis of the cuprate superconductor BSSCO. In Raman isotope data for vibrations along the c-axis from 1988 [2], and in site selective susceptibility experiments determining Tc, no isotope effects were observed for oxygen ions in the insulating layer [3]. Based on these earlier not by PRS quoted experiments, we argue that the suggestion made in Ref. 1 is not worth to be undertaken, and if it is carried through, no effect will be seen. From the meanwhile 12 years old site selective data [3] the observed isotope effects stem to nearly 100% from oxygen ions in the CuO2-planes. These results evidence polaronic behavior in these planes [4].

cond-mat.supr-con↗

arXiv2006

Classical Propagation of Light in Spatio-Temporal Periodic Media

We analyze the propagation of electromagnetic waves in media where the dielectric constants undergo rapid temporal periodic modulation. Both spatially homogeneous and periodic media are studied. Fast periodic temporal modulation of the dielectric constant of a homogeneous medium leads to existence of photonic band-gap like phenomena. In the presence of both spatial and tem- poral periodicity the electromagnetic spectrum is described in a four-dimensional cube, defining an effective Brillouin zone. In the case of incommensurability between space and time periodicities, completely dispersed point spectra exist.

physics.optics↗

arXiv2006

Coexistence of polar order and local domain dynamics in ferroelectric SrTi18O3

Perovskite oxide ferroelectrics show classical soft mode behaviour typical for the onset of a homogeneous long-range polar state and a displacive phase transition. Besides these long wave length properties, local effects are observed by different probes which reveal that dynamical symmetry breaking already takes place already far above the actual instability. It is shown here that displacive mean-field type dynamics can indeed coexist with local dynamical symmetry breaking.

cond-mat.other↗

arXiv2006

Real and marginal isotope effects in cuprate superconductors

We critically review recent and earlier results on isotope effects in cuprate superconductors and emphasize that the sample preparation and the isotope exchange and back exchange are crucial in understanding and interpreting the data. Only extremely careful preparation techniques yield reliable results and permit differentiation between real isotope effects and marginal ones. The former are substantial and highlight the lattice vibrational importance in cuprate superconductors.

cond-mat.supr-con↗

arXiv2006

Optimization of soliton ratchets in inhomogeneous sine-Gordon systems

Unidirectional motion of solitons can take place, although the applied force has zero average in time, when the spatial symmetry is broken by introducing a potential $V(x)$, which consists of periodically repeated cells with each cell containing an asymmetric array of strongly localized inhomogeneities at positions $x_{i}$. A collective coordinate approach shows that the positions, heights and widths of the inhomogeneities (in that order) are the crucial parameters so as to obtain an optimal effective potential $U_{opt}$ that yields a maximal average soliton velocity. $U_{opt}$ essentially exhibits two features: double peaks consisting of a positive and a negative peak, and long flat regions between the double peaks. Such a potential can be obtained by choosing inhomogeneities with opposite signs (e.g., microresistors and microshorts in the case of long Josephson junctions) that are positioned close to each other, while the distance between each peak pair is rather large. These results of the collective variables theory are confirmed by full simulations for the inhomogeneous sine-Gordon system.

cond-mat.mes-hall↗