Effect of lattice discreteness on the statistical mechanics of a dilute gas of kinks

Willis, C. R.; Boesch, R.

doi:10.1103/physrevb.41.4570

Cited by 29 publications

(11 citation statements)

References 12 publications

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“…Thus a Klein-Gordon kink when boosted can only radiate some energy away and finally stop to become a static kink solution! In order to account for these effects a collective coordinate approach was developed [195], [165], [28], [194], [29], [193], [57], [30]. Within this approach one performs a canonical transformation to new coordinates some of whom are collective (nonlocal in the old coordinates).…”

Section: Movabilitymentioning

confidence: 99%

Discrete breathers

1998

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Nonlinear classical Hamiltonian lattices exhibit generic solutions in the form of discrete breathers. These solutions are time-periodic and (typically exponentially) localized in space. The lattices exhibit discrete translational symmetry. Discrete breathers are not confined to certain lattice dimensions. Necessary ingredients for their occurence are the existence of upper bounds on the phonon spectrum (of small fluctuations around the groundstate) of the system as well as the nonlinearity in the differential equations. We will present existence proofs, formulate necessary existence conditions, and discuss structural stability of discrete breathers. The following results will be also discussed: the creation of breathers through tangent bifurcation of band edge plane waves; dynamical stability; details of the spatial decay; numerical methods of obtaining breathers; interaction of breathers with phonons and electrons; movability; influence of the lattice dimension on discrete breather properties; quantum lattices -quantum breathers.Finally we will formulate a new conceptual aproach capable of predicting whether discrete breather exist for a given system or not, without actually solving for the breather. We discuss potential applications in lattice dynamics of solids (especially molecular crystals), selective bond excitations in large molecules, dynamical properties of coupled arrays of Josephson junctions, and localization of electromagnetic waves in photonic crystals with nonlinear response.

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Section: Movabilitymentioning

confidence: 99%

Discrete breathers

1998

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“…From fundamental physical interest, the idea of a discrete nature has considerably improved our understanding of the effect of discreteness on topological solitons [4][5][6][7][8] and nontopological solitons [9], classical thermodynamic properties [10][11][12][13], modulational instabilities [14][15][16], wave-collapse phenomena [17,18], intrinsic localized vibrational states [19][20][21], diffusion in discrete nonlinear dynamical systems [22], self-induced gap solitons [23,24].…”

Section: Introductionmentioning

confidence: 99%

Dipolar effects on soliton dynamics on a discrete ferromagnetic chain

2002

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The contributions of dipole-dipole interactions to the dynamics of solitons on a one-dimensional discrete easy-plane Heisenberg ferromagnet, in which the biquadratic exchange interactions are taken into account in addition to the Zeeman energy, the uniaxial anisotropy, and the exchange energy, are studied numerically. The results of a numerical simulation of the dynamics of a single soliton, as well as collision between a soliton-antisoliton pair, indicated that the energy-velocity curves for the solitons in the ferromagnetic chain present the signature of five different branches corresponding to different types of nonlinear elementary excitations in the chain.

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“…The rank of the gyrocoupling matrix G is used to classify the excitations: In the case of vanishing G the excitations have an effective mass and exhibit Newtonian dynamics; in the case of regular G, the excitations behave like charged, massless particles in an external magnetic field, similar to the gyrotropic excitations defined in section 2.3. The above theory is a generalization of earlier work of Tomboulis [42], Boesch et al [43], and Willis et al [44], which applies only to "standard" Hamiltonians (i. e., consisting of the sum of kinetic and potential energy terms). This generalization is necessary, e. g., in the case of magnetic systems which cannot be modelled by standard Hamiltonians.…”

Section: An Alternative Approach: Coupling To Magnonsmentioning

confidence: 85%

Dynamics of Vortices in Two-Dimensional Magnets

Mertens¹,

Bishop²

Nonlinear Science at the Dawn of the 21st Century

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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 (evenorder equations of motion) and exhibit strong discreteness effects, while non-planar vortices have non-Newtonian dynamics (odd-order equations of motion) and smooth trajectories. These results are obtained by a collective variable theory based on a generalized travelling wave ansatz which allows a dependence of the vortex shape on velocity, acceleration etc.. An alternative approach is also reviewed and compared, namely the coupling of the vortex motion to certain quasi-local spinwave modes. 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 stochastic forces can be explicitly calculated and a vortex diffusion constant is defined. The solutions of the stochastic 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.

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Effect of lattice discreteness on the statistical mechanics of a dilute gas of kinks

Cited by 29 publications

References 12 publications

Discrete breathers

Discrete breathers

Dipolar effects on soliton dynamics on a discrete ferromagnetic chain

Dynamics of Vortices in Two-Dimensional Magnets

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