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A. R. Bishop

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

At least 181 records · Page 10Linked to original sources
arXiv1999

Universal Scaling of Wave Propagation Failure in Arrays of Coupled Nonlinear Cells

We study the onset of the propagation failure of wave fronts in systems of coupled cells. We introduce a new method to analyze the scaling of the critical external field at which fronts cease to propagate, as a function of intercellular coupling. We find the universal scaling of the field throughout the range of couplings, and show that the field becomes exponentially small for large couplings. Our method is generic and applicable to a wide class of cellular dynamics in chemical, biological, and engineering systems. We confirm our results by direct numerical simulations.

cond-mat.soft↗
arXiv1999

Discrete Nonlinear Schr{ö}dinger Breathers in a Phonon Bath

We study the dynamics of the discrete nonlinear Schr{ö}dinger lattice initialized such that a very long transitory period of time in which standard Boltzmann statistics is insufficient is reached. Our study of the nonlinear system locked in this {\em non-Gibbsian} state focuses on the dynamics of discrete breathers (also called intrinsic localized modes). It is found that part of the energy spontaneously condenses into several discrete breathers. Although these discrete breathers are extremely long lived, their total number is found to decrease as the evolution progresses. Even though the total number of discrete breathers decreases we report the surprising observation that the energy content in the discrete breather population increases. We interpret these observations in the perspective of discrete breather creation and annihilation and find that the death of a discrete breather cause effective energy transfer to a spatially nearby discrete breather. It is found that the concepts of a multi-frequency discrete breather and of internal modes is crucial for this process. Finally, we find that the existence of a discrete breather tends to soften the lattice in its immediate neighborhood, resulting in high amplitude thermal fluctuation close to an existing discrete breather. This in turn nucleates discrete breather creation close to a already existing discrete breather.

patt-sol↗
arXiv1999

Influence of Non-Resonant Effects on the Dynamics of Quantum Logic Gates at Room Temperature

We study numerically the influence of non-resonant effects on the dynamics of a single $π$-pulse quantum CONTROL-NOT (CN) gate in a macroscopic ensemble of fo ur-spin molecules at room temperature. The four nuclear spins in each molecule r epresent a four-qubit register. The qubits are ``labeled'' by the characteristic frequencies, $ω_k$, ($k=0$ to 3) due to the Zeeman interaction of the nuclear spins with the magnetic field. The qubits interact with each other through an Ising interaction of strength $J$. T he paper examines the feasibility of implementing a single-pulse quantum CN gate in an ensemble of quantum molecules at room temperature. We determine a paramet er region, $ω_k$ and $J$, in which a single-pulse quantum CN gate can be i mplemented at room temperature. We also show that there exist characteristic cri tical values of parameters, $Δω_{cr}\equiv|ω_{k^\prime}-ω_k|_{cr}$ and $J_{cr}$, such that for $J<J_{cr}$ and $Δω_k\equiv|ω_{k^\prime}-ω_k|<Δω_{cr}$, non-resonant effects are sufficient to d estroy the dynamics required for quantum logic operations.

quant-ph↗
arXiv1999

Dynamics of Vortices in Two-Dimensional Magnets

Theories, simulations and experiments on vortex dynamics in quasi-two-dimensional magnetic materials are reviewed. These materials can be modelled by the classical two-dimensional anisotropic Heisenberg model with XY (easy-plane) symmetry. There are two types of vortices, characterized by their polarization (a second topological charge in addition to the vorticity): Planar vortices have Newtonian dynamics (even-order equations of motion) and exhibit strong discreteness effects, while non-planar vortices have non-Newtonian dynamics (odd-order equations of motion) and smooth trajectories. The influence of thermal fluctuations on single vortices is investigated. Different types of noise and damping are discussed and implemented into the microscopic equations which yields stochastic equations of motion for the vortices. The solutions of the these equations are compared with Langevin dynamics simulations. Moreover, noise-induced transitions between opposite polarizations of a vortex are investigated. For temperatures above the Kosterlitz-Thouless vortex-antivortex unbinding transition, a phenomenological theory, namely the vortex gas approach, yields central peaks in the dynamic form factors for the spin correlations. Such peaks are observed both in combined Monte Carlo- and Spin Dynamics-Simulations and in inelastic neutron scattering experiments. However, the assumption of ballistic vortex motion appears questionable.

cond-mat↗
arXiv1999

Hierarchy of equations of motion for nonlinear coherent excitations applied to magnetic vortices

Starting from a travelling wave ansatz we show successively that the shape of a nonlinear excitation generally depends also on the 1st, 2nd, ... time derivative of the position X of the excitation. From the Hamilton equations we derive a hierarchy of equations of motion for X. The type of the excitation determines on which levels the hierarchy can be truncated consistently: "Gyrotropic" excitations are governed by odd-order equations, non-gyrotropic ones by even-order equations. Examples for the latter case are kinks in 1-dimensional models and planar vortices of the 2D anisotropic (easy-plane) Heisenberg model. The non-planar vortices of this model are the simplest gyrotropic example. For this case we solve the Hamilton equations for a finite system with one vortex and free boundary conditions and calculate the parameters of the 3rd-order equation of motion. This equation yields trajectories which are a superposition of two cycloids with different frequencies, which is in full agreement with computer simulations of the full many-spin model. Finally we demonstrate that the additional effects from the 5th-order equation are negligible.

cond-mat↗
arXiv1999

Stochastic vortex dynamics in two-dimensional easy-plane ferromagnets: Multiplicative versus additive noise

We study how thermal fluctuations affect the dynamics of vortices in the two-dimensional classical, ferromagnetic, anisotropic Heisenberg model depending on their additive or multiplicative character. Using a collective coordinate theory, we analytically show that multiplicative noise, arising from fluctuations in the local field term of the Landau-Lifshitz equations, and Langevin-like additive noise both have the same effect on vortex dynamics (within a very plausible assumption consistent with the collective coordinate approach). This is a non-trivial result, as multiplicative and additive noises usually modify the dynamics quite differently. We also carry out numerical simulations of both versions of the model finding that they indeed give rise to very similar vortex dynamics.

cond-mat↗
arXiv1999

Noise-induced switching between vortex states with different polarization in classical two-dimensional easy-plane magnets

In the 2-dimensional anisotropic Heisenberg model with XY-symmetry there are non-planar vortices which exhibit a localized structure of the z-components of the spins around the vortex center. We study how thermal noise induces a transition of this structure from one polarization to the opposite one. We describe the vortex core by a discrete Hamiltonian and consider a stationary solution of the Fokker-Planck equation. We find a bimodal distribution function and calculate the transition rate using Langer's instanton theory (1969). The result is compared with Langevin dynamics simulations for the full many-spin model.

cond-mat↗
arXiv1999

Quantum versus Semiclassical Description of Selftrapping: Anharmonic Effects

Selftrapping has been traditionally studied on the assumption that quasiparticles interact with harmonic phonons and that this interaction is linear in the displacement of the phonon. To complement recent semiclassical studies of anharmonicity and nonlinearity in this context, we present below a fully quantum mechanical analysis of a two-site system, where the oscillator is described by a tunably anharmonic potential, with a square well with infinite walls and the harmonic potential as its extreme limits, and wherein the interaction is nonlinear in the oscillator displacement. We find that even highly anharmonic polarons behave similar to their harmonic counterparts in that selftrapping is preserved for long times in the limit of strong coupling, and that the polaronic tunneling time scale depends exponentially on the polaron binding energy. Further, in agreement, with earlier results related to harmonic polarons, the semiclassical approximation agrees with the full quantum result in the massive oscillator limit of small oscillator frequency and strong quasiparticle-oscillator coupling.

cond-mat↗
arXiv1998

Localized Structures in Nonlinear Lattices with Diffusive Coupling and External Driving

We study the stabilization of localized structures by discreteness in one-dimensional lattices of diffusively coupled nonlinear sites. We find that in an external driving field these structures may lose their stability by either relaxing to a homogeneous state or nucleating a pair of oppositely moving fronts. The corresponding bifurcation diagram demonstrates a cusp singularity. The obtained analytic results are in good quantitative agreement with numerical simulations.

patt-sol↗
arXiv1998

Finite temperature dynamics of vortices in the two dimensional anisotropic Heisenberg model

We study the effects of finite temperature on the dynamics of non-planar vortices in the classical, two-dimensional anisotropic Heisenberg model with XY- or easy-plane symmetry. To this end, we analyze a generalized Landau-Lifshitz equation including additive white noise and Gilbert damping. Using a collective variable theory with no adjustable parameters we derive an equation of motion for the vortices with stochastic forces which are shown to represent white noise with an effective diffusion constant linearly dependent on temperature. We solve these stochastic equations of motion by means of a Green's function formalism and obtain the mean vortex trajectory and its variance. We find a non-standard time dependence for the variance of the components perpendicular to the driving force. We compare the analytical results with Langevin dynamics simulations and find a good agreement up to temperatures of the order of 25% of the Kosterlitz-Thouless transition temperature. Finally, we discuss the reasons why our approach is not appropriate for higher temperatures as well as the discreteness effects observed in the numerical simulations.

cond-mat.stat-mech↗
arXiv1998

Soliton motion in a parametrically ac-driven damped Toda lattice

We demonstrate that a staggered parametric ac driving term can support stable progressive motion of a soliton in a Toda lattice with friction, while an unstaggered drivng force cannot. A physical context of the model is that of a chain of anharmonically coupled particles adsorbed on a solid surface of a finite size. The ac driving force models a standing acoustic wave excited on the surface. Simulations demonstrate that the state left behind the moving soliton, with the particles shifted from their equilibrium positions, gradually relaxes back to the equilibrium state that existed before the passage of the soliton. Perturbation theory predicts that the ac-driven soliton exists if the amplitude of the drive exceeds a certain threshold. The analytical prediction for the threshold is in reasonable agreement with that found numerically. Collisions between two counter propagating solitons were also simulated, demonstrating that the collisions are, essentially fully elastic.

patt-sol↗
arXiv1998

Charge ordering and long-range interactions in layered transition metal oxides

We study the competition between long-range and short-range interactions among holes within the spin density wave picture of layered transition metal oxides. We focus on the problem of charge ordering and the charge phase diagram. We show that the main interactions are the long-range Coulomb interaction and a dipolar short-range interaction generated by the short-range antiferromagnetic fluctuations. We find four different phases depending on the strength of the dipolar interaction and the density of holes: Wigner crystal, diagonal stripes, horizontal-vertical stripes (loops) and a glassy-clumped phase. We discuss the effect of temperature, disorder and lattice effects on these phases.

cond-mat↗
arXiv1998

Aharonov-Anandan Effect Induced by Spin-Orbit Interaction and Charge-Density-Waves in Mesoscopic Rings

We study the spin-dependent geometric phase effect in mesoscopic rings of charge-density-wave(CDW) materials. When electron spin is explicitly taken into account, we show that the spin-dependent Aharonov-Casher phase can have a pronounced frustration effects on such CDW materials with appropriate electron filling. We show that this frustration has observable consequences for transport experiment. We identify a phase transition from a Peierls insulator to metal, which is induced by spin-dependent phase interference effects. Mesoscopic CDW materials and spin-dependent geometric phase effects, and their interplay, are becoming attractive opportunities for exploitation with the rapid development of modern fabrication technology.

cond-mat.mes-hall↗
arXiv1998

Signatures of Stripe Phases in Hole Doped $La_2NiO_4$

We study nickelate-centered and oxygen-centered stripe phases in doped La$_{2}$NiO$_{4}$ materials. We use an inhomogeneous Hartree-Fock and random-phase approximation approach including both electron-electron and electron-lattice(e-l) coupling for a layer of La$_{2}$NiO$_{4}$. We find that whether the ground state after commensurate hole doping comprises Ni-centered or O-centered charge-localized stripes depends sensitively on the e-l interaction. With increasing e-l interaction strength, a continuous transition from an O-centered stripe phase to a Ni-centered one is found. Various low- and high-energy signatures of these two kinds of stripe phases are predicted, which can clearly distinguish them. These signatures reflect the strongly correlated spin-charge-lattice features in the vicinity of Ni-centered or O-centered stripe domains. The importance of e-l interaction for recent experiments on stripe phases is discussed.

cond-mat.supr-con↗
arXiv1997

The dynamics of vortex lines in the three-dimensional complex Ginzburg-Landau equation: instability, stretching, entanglement, and helices

The dynamics of curved vortex filaments is studied analytically and numerically in the framework of a three-dimensional complex Ginzburg-Landau equation (CGLE). It is shown that a straight vortex line is unstable with respect to spontaneous stretching and bending in a substantial range of parameters of the CGLE, resulting in formation of persistent entangled vortex configurations. The boundary of the three-dimensional instability in parameter space is determined. Near the stability boundary, the supercritical saturation of the instability is found, resulting in the formation of stable helicoidal vortices.

patt-sol↗
arXiv1997

Quantum Breathers in Electron-phonon Systems

Quantum breathers are studied numerically in several electron-phonon coupled finite chain systems, in which the coupling results in intrinsic nonlinearity but with varying degrees of nonadiabaticity. As for quantum nonlinear lattice systems, we find that quantum breathers can exist as eigenstates of the system Hamiltonians. Optical responses are calculated as signatures of these coherent nonlinear excitations. We propose a new type of quantum nonlinear excitation, breather-excitons, which are bound states of breathers and excitons, whose properties are clarified with a minimal exciton-phonon model.

cond-mat.soft↗
arXiv1997

Mean Field Theory of Polynuclear Surface Growth

We study statistical properties of a continuum model of polynuclear surface growth on an infinite substrate. We develop a self-consistent mean-field theory which is solved to deduce the growth velocity and the extremal behavior of the coverage. Numerical simulations show that this theory gives an improved approximation for the coverage compare to the previous linear recursion relations approach. Furthermore, these two approximations provide useful upper and lower bounds for a number of characteristics including the coverage, growth velocity, and the roughness exponent.

cond-mat.stat-mech↗