Search Results (22 total)

Geometrical constraints imposed on higher-dimensional harmonic lattices generally lead to nonlinear dynamical lattice models. Helical lattices obtained by such a procedure are shown to be described by sine- plus linear-lattice equations. The interplay between sinusoidal and quadratic potential terms in such models is shown to yield localized nonlinear modes identified as intrinsic resonant modes.

We present an experimentally realizable, simple mechanical system with linear interactions whose geometric nature leads to nontrivial, nonlinear dynamical equations. The equations of motion are derived and their ground state structures are analyzed. Selective “static” features of the model are examined in the context of nonlinear waves including rotobreathers and kinklike solitary waves. We also explore “dynamic” features of the model concerning the resonant transfer of energy and the role of moving intrinsic localized modes in the process.

A method of quantizing weakly nonlinear lattices is proposed. It is based on introducing “pseudofield” operators. In this formalism quantum envelope solitons together with phonons are regarded as elementary quasiparticles making up a boson gas. In the classical limit the excitations corresponding to frequencies above a linear cutoff frequency are reduced to conventional envelope solitons. The approach allows one to identify a quantum soliton that is localized in space and to understand the existence of a narrow soliton frequency band.

A theory of localized modes in two-dimensional square anisotropic ferromagnets with a hole is extended to the antiferromagnetic case. Here a path-integral method based on the SU(2) coherent state representation is employed. Detailed numerical calculations are made for s-like modes, and their eigenfrequency is determined as a function of nonlinearity parameter and various anisotropic exchange interactions and uniaxial anisotropies. Particular attention is paid to interplaying between the intrinsic nonlinearity and extrinsic hole doping. It turns out that the former stabilizes the magnetic localized mode generated by the latter (or vice versa), and it takes a vortex shape in the neighborhood of a doped hole. In contrast to the ferromagnetic case, the mobile nonlinear self-localized mode is unlikely to exist.

By using the path-integral method with a SU(2) coherent-state basis, two-dimensional anisotropic Heisenberg ferromagnets bearing a fixed magnetic hole are investigated with particular attention paid to interplaying between the intrinsic nonlinearity and the extrinsic structural disorder due to hole doping. Detailed numerical calculations are made for s-like localized modes to determine their eigenfrequencies and profiles as a function of a nonlinearity parameter and various anisotropic exchange parameters. A localized magnetic vortex is found in the neighborhood of a hole. Analytical and numerical analyses on their time evolution show two kinds of localized modes separately; one is mobile under certain conditions and intrinsic due to the nonlinearity, and the other is immobile and extrinsic due to the fixed magnetic hole.

Various kinds of stationary dark localized modes in discrete nonlinear Schrödinger equations are considered. A criterion for the existence of such excitations is introduced and an estimation of a localization region is provided. The results are illustrated in examples of the deformable discrete nonlinear Schrödinger equation, of the model of Frenkel excitons in a chain of two-level atoms, and of the model of a one-dimensional Heisenberg ferromagnetic in the stationary phase approximation. The three models display essentially different properties. It is shown that at an arbitrary amplitude of the background it is impossible to reach strong localization of dark modes. In the meantime, in the model of Frenkel excitons, exact dark compacton solutions are found.

Vortices of trajectories of atoms on the surface of a crystal are found as a transient pattern in the numerical experiment to study martensitic transformation in an ideal crystal which has its surface as a sole lattice defect, but no other internal lattice defect. An empirical instability condition for the appearance of the vortex is interpreted in terms of the dependence of the excitation energy of a vortex on its size.

We use a classical approximation to investigate the existence of shock waves in one dimensional ferromagnets. As a result we find two types of shock waves, bright and dark, which can be interpreted as classical analogs of moving magnetic domains.

We calculate breather solutions for a two-dimensional lattice with one acoustic phonon branch. We start from the case of a system with homogeneous interaction potentials. We then continue the zero-strain breather solution into the model sector with additional quadratic and cubic potential terms with the help of a generalized Newton method. The breather continues to exist but is dressed with a strain field. In contrast to the ac breather components, which decay exponentially in space, the strain field (which has dipole symmetry) should decay like 1/r^a, a  =  2. On our rather small lattice ( 70×70) we find an exponent a≈1.85.

We use a small-amplitude multiple scale expansion to investigate the existence of shock waves in a chain of two-level atoms with both exchange and dipole-dipole interactions. We show that the exchange interaction allows the formation of the system of both bright and dark shock waves. Conversely, the dipole-dipole interaction results in the instability of the background and, as a consequence, in the prevention of the formation of shock waves. The analytical results are found to be in good qualitative agreement with a direct numerical integration of the system.

The need for a mechanism for energy transfer in proteins, such as the Davydov model, is emphasized. Here we concentrate on the finite-temperature properties of the Davydov model in three regimes: the quantum regime, in which both the excitation and the lattice are treated quantum mechanically; the mixed quantum-classical regime, in which the excitation is treated quantum mechanically but the lattice is considered classical; and the classical regime, in which both the excitation and the lattice are treated classically. The equilibrium behavior can be determined exactly in the three regimes and thus provides a way to evaluate the validity of the latter two regimes as well as a reference point for the nonequilibrium studies. Our results indicate that while at low temperature both the classical and the semiclassical regimes differ from the full quantum Davydov system, at biological temperatures the mixed quantum-classical regime leads to the same equilibrium behavior as the full quantum Davydov system. The nonequilibrium properties in the mixed quantum-classical regime are studied with a different set of equations of motion for finite temperature, which are derived in great detail in Sec. VI. At biological temperatures, these equations predict that the Davydov soliton is unstable. However, the states populated at biological temperatures preserve one of the features of the Davydov soliton, namely, the localization of the amide I excitation. The nonequilibrium equations in Sec. VI lead to a Brownian-like motion of the amide I excitation from the active site to other regions of the protein. This stochastic mechanism for energy transfer may constitute a first step in many biological processes.

Dark and bright soliton solutions (excitons) in one-dimensional chains of two-level atoms with exciton-exciton, dipole-dipole, and exchange interactions are obtained. It is shown that in some limiting cases evolution equations resulting from model Hamiltonians are reduced to the exactly integrable Ablowitz-Ladik model. Bloch oscillations of the excitons in inhomogeneous magnetic field and effects originated by the energy shift are discussed. An example of a multidimensional dark exciton is represented.

A path integral method based on the SU(2) coherent state representation is employed to investigate intrinsic stationary self-localized magnons in Heisenberg antiferromagnets. Lagrange equations derived from the stationary phase approximation yield lattice equations in which the intrinsic nonlinearity in the system are incorporated to all orders. The nonlinear eigenvalue problem is solved for a one-dimensional case to show the existence of two types of self-localized modes. Detailed numerical calculations are made to determine their eigenfrequencies and spin profiles as a function of a dimensionless nonlinearity parameter for various values of the anisotropy of exchange interactions and uniaxial anisotropies.

Lattice Green's functions are used to investigate localized rotating modes recently exhibited in some nonlinear lattices. For a one-dimensional lattice, analytical expressions of the solution are obtained, first in the rotating-wave approximation and then by including higher-order terms. Numerical simulations confirm the validity of these solutions. The method is not restricted to one-dimensional lattices.

It is shown that intrinsic localized modes in a nonlinear lattice with a hard quartic nonlinearity are governed by the discrete Hirota equation. The requirement for the solution to be real results in a very restricted class of admissible soliton solutions corresponding to the localized excitations. In particular, it is shown that a single-soliton solution exists only at definite values of the amplitude and velocity. Two-soliton and multisoliton localized-mode solutions are reperesented. A small parameter of the problem is discussed. © 1996 The American Physical Society.

Computer simulations show that in a one-dimensional lattice both even and odd anharmonic localized modes can move with constant velocity. For nearest-neighbor forces described by a harmonic plus hard quartic potential, the dispersion relation ω(k) has been calculated for both types of modes. Numerical experiments show that, in general, moving modes with a near-Gaussian excitation envelope occur in parts of ω(k) space, with this region becoming more restricted as the local-mode frequency increases.

The nonlinearity in magnon systems in one-dimensional Heisenberg antiferromagnets is shown to produce two types of intrinsic self-localized modes, symmetric and antisymmetric, below the magnon frequency band. In the case of extreme localization, the localized modes can be viewed as a two-spin bound state or a local spin-liquid state, where a pair of spins undergoes a large excursion as compared with the rest of the spins.

For disordered solids it is shown that anharmonic resonant modes can contribute both a linear and a cubic term to the temperature-dependent specific heat. The linear dependence is associated with resonant-mode diffusion while the excess cubic term comes from the stationary resonant-mode component. Both features are derived from the vibrational anharmonicity of the solid with the resonant mode frequency as the one important model parameter. When its value is fixed with the measured linear term then the enhanced resonant mode density of states has the correct order of magnitude and frequency position to account for the excess T³ specific heat observed in a number of glasses. The same mechanism also can account for both the presence and absence of the observed linear specific-heat contribution in solid ³He.

A new kind of localized mode is proposed to occur in a pure anharmonic lattice. Its localization properties are similar to those of a localized mode for a force-constant defect in a harmonic lattice. These modes, which are thermally generated like vacancies but with much smaller activation energies, may appear at cryogenic temperatures in strongly anharmonic solids such as quantum crystals as well as in conventional solids.

We have developed a temperature-dependent anharmonic theory for impurity-doped alkali halide crystals to accouant for the intensity of the infrared absorption by the zero-phonon resonant mode of the impurities. The theory has been compared with experiment and suggests a saturation of the absorption intensity at sufficiently low temperatures. Further, the relation of the root-mean-square impurity displacement to the mass and effective force constants is put on a more firm theoretical basis, and first-order corrections to the usual simple theory are presented. It is shown that the root-mean-square displacement of the lithium impurity as well as that of hydrogen are unusually large (of the order of 10% of the lattice distance).

A sharp and very low-frequency lattice absorption due to a lithium resonant mode has been found in KBr:LiBr. A large frequency shift with lithium isotopes has been observed. The experimental results can be understood with a simplified lattice model in which both nearest-neighbor force constants and the mass of the impurity are varied. It is concluded that the resonant mode comes from a remarkable softening of the forces between the impurity and the surrounding lattice.