The lattice quantum Sine-Gordon model

The integrable statistical physics model on the rectangular two-dimensional lattice which we call the L-model is constructed. This model generates the integrable quantum sine-Gordon model on the one-dimensional lattice in the same way as the ice model generates the XXZ model.     

Quantum-thermal crossover in the dissipative dynamics of the Sine-Gordon model

The quantum-thermal crossover in the decay rate of metastable states of the quantum sine-Gordon model in dc field is discussed at low temperatures including dissipation in arbitrary dimension. In the low field limit, the thermal effect is always dominant, whereas in the higher field the quantum effect becomes important. The crossover field becomes larger by the dissipative effect. The crossover is sharp except the one dimensional underdamped case at low temperatures.     

Cylindrical magnetization model for glass-coated microwires with circular anisotropy: Statics

The static magnetization profile of glass-coated microwires with effective circular anisotropy is investigated using micromagnetics. In this family of microwires, the ferromagnetic nucleus with an amorphous character presents a magnetic structure composed of an inner region with axial domains and an outer region with circular domains, due to magnetoelastic anisotropy. A one-dimensional micromagnetic model is developed, taking into account both the exchange and magnetoelastic anisotropy energies, and solved quasi analytically. The total energy, magnetization profiles and magnetization curves are investigated as a function of radius and anisotropy constant of the nucleus. This work represents a fundamental study of the magnetization process in these amorphous microwires and provides guidelines for the production of microwires with tailored magnetic properties. En passant, the nucleation problem in an infinite cylinder, introduced by W.F. Brown, is revisited.     

Electrorheology: Statics and dynamics

The interaction between nanoparticles and an electric field is explored from the electrorheological (ER) point of view, using variational formulations for both the static and dynamic characteristics. In the first part the static characteristics of the ER fluid, consisting of a dispersion of solid particles in a liquid, is detailed by using the spectral representation approach for the effective dielectric constant. Predictions concerning the ground state structure, yield stress, upper bounds on the ER effect are presented together with comparisons to experimental results. The giant ER effect, involving a different paradigm of permanent electric dipoles, is described phenomenologically. In the second part the ER fluid dynamics is formulated via the variational principle of Onsager. Predictions of the model are compared with experiments. It is shown that the phenomenon of the diminishing ER effect at high shear rates may be mitigated by the planar interdigital electrode configuration.     

Sine-Gordon equation in curved space-time

We study the static solution of the sine-Gordon wave equation in a background geometry determined by a point mass in 1+1 dimension.     

Ring wave solutions of a n+1-dimensional Sine-Gordon model

The dynamical properties of the ring wave solutions of the model psi(tt)- nabla (n) (2)psi+sin psi+ varepsilon sin (psi/2)+alphapsi(t)=0 (00, alpha=0 (or alpha>0) the return effect of the ring wave does not occur only for well defined values of varepsilon. It will be shown numerically that the dissipative perturbation alphapsi(t) (alpha>0) stabilizes both the velocity and the wave profile of the ring wave when the return effect does not occur. (c) 1997 American Institute of Physics.     

Chaotic solitons in Sine-Gordon system

We extend the constant-variation method to the case of partial differential equations. Applying the method to periodically perturbed Sine-Gordon system, we find some novel solitons, which are embedded in a chaotic attractor and possess controllable velocity of motion. Taking periodically driven long Josephson junction as an example the corresponding chaotic region in parameter space and chaotic orbit are obtained analytically and numerically. Received 25 December 2000     

Renormalization group flow of a hierarchical Sine-Gordon model by partial differential equations

We use a renormalization group differential equation to rigorously control the renormalization group flow in a hierarchical lattice Sine-Gordon field theory in the Kosterlitz-Thouless phase.Supported in part by the Department of Energy under Grant DE-FG02-88ER25065     

Breather Dynamics of the Sine-Gordon Equation

This paper studies the adiabatic dynamics of the breather soliton of the sine-Gordon equation. The integrals of motion are found and then used in soliton perturbation theory to derive the differential equation governing the soliton velocity. Time-dependent functions arise and their properties are studied. These functions are found to be bounded and periodic and affect the soliton velocity. The soliton velocity is numerically plotted against time for different combinations of initial velocities and perturbation terms.     

The (N=1) Supersymmetric Sine-Gordon model in two dimensions. I

In this paper and its companion (II) we prove that the SupersymmetricN=1 massless Sine-Gordon field theory, at finite (space) volume, exists and is analytic in the coupling constant . Moreover at finite (space) volume is Witten index is=1.     

Dynamic damping in magnetic Sine-Gordon systems

We study the influence of the elastic degrees of freedom of a one-dimensional spin-chain with ferromagnetic Heisenberg coupling in situations, where the magnetic dynamics can be described by a Sine-Gordon model. Compatibility of the Sine-Gordon approach with spin-lattice coupling is shown, and CsNiF₃ and domain wall motion are discussed as concrete physical realizations. As a consequence of the spin-lattice interaction a soliton-phonon coupling arises, which destroys the formal Lorentz invariance of the Sine-Gordon system. The influence of this coupling on the soliton dynamics is investigated. It results in a dynamic damping of the soliton motion, which in general is not of viscous type. Moreover, the influences of the soliton-phonon coupling on the phonon dispersion are estimated and possible experimental consequences are discussed.Project of the Sonderforschungsbereich 65 Festkörperspektroskopie Darmstadt-Frankfurt financed by special funds of the Deutsche Forschungsgemeinschaft     

The (N=1) Supersymmetric Sine-Gordon model in two dimensions. II

In this second paper the technical part of the results about the SupersymmetricN=1 massless Sine-Gordon field theory, at finite (space) volume, is given. The proof that the theory exists and is analytic in the coupling constant and that, at finite (space) volume, its Witten index is 1, is, therefore, completed.     

Sine-Gordon form factors in finite volume

We compare form factors in sine-Gordon theory, obtained via the bootstrap, to finite volume matrix elements computed using the truncated conformal space approach. For breather form factors, this is essentially a straightforward application of a previously developed formalism that describes the volume dependence of operator matrix elements up to corrections exponentially decaying with the volume. In the case of solitons, it is necessary to generalize the formalism to include effects of non-diagonal scattering. In some cases it is also necessary to take into account some of the exponential corrections (so-called μ-terms) to get agreement with the numerical data. For almost all matrix elements the comparison is a success, with the puzzling exception of some breather matrix elements that contain disconnected pieces. We also give a short discussion of the implications of the observed behavior of μ-terms on the determination of operator matrix elements from finite volume data, as occurs e.g. in the context of lattice field theory.     

Sine-Gordon Model: Renormalization Group Solution and Applications

The sine-Gordon model is discussed and analyzed within the framework of the renormalization group theory. A perturbative renormalization group procedure is described, in which the sine-Gordon field is decomposed into slow and fast modes. An effective theory for the slow modes is derived and rescaled to yield the flow equations for the model. The resulting Kosterlitz–Thouless phase diagram is obtained and discussed in detail. The gap in this theory is estimated in terms of the sine-Gordon model parameters. The mapping between the sine-Gordon model and one-dimensional interacting-electron models, such as the g-ology and Hubbard models, is discussed. On the basis of the results borrowed from previous renormalization-group results for the sine-Gordon model, different aspects of Luttinger liquid systems are described, such as the nature of the excitations and phase transitions. The calculations are thoroughly and pedagogically described, to even reach the reader with no previous experience with the sine-Gordon model or the renormalization group approach.     

Defects in the discrete non-linear Schrödinger model

The discrete non-linear Schrödinger (NLS) model in the presence of an integrable defect is examined. The problem is viewed from a purely algebraic point of view, starting from the fundamental algebraic relations that rule the model. The first charges in involution are explicitly constructed, as well as the corresponding Lax pairs. These lead to sets of difference equations, which include particular terms corresponding to the impurity point. A first glimpse regarding the corresponding continuum limit is also provided.