Domain Wall Solitons Research Articles

D-branes in field theory

Certain gauge theories in four dimensions are known to admit semi-classical D-brane solitons. These are domain walls on which vortex flux tubes may end. The purpose of this paper is to develop an open-string description of these D-branes. The dynamics of the domain walls is shown to be governed by a Chern-Simons-Higgs theory which, at the quantum level, captures the classical "closed string" scattering of domain wall solitons.

Structural phase transition and soliton in an organic ferromagnetic polymer: Theoretical prediction

By a theoretical model consisting of Su-Schrieffer-Heeger Hamiltonian and a Hubbard term, the ground-state and soliton excitation of an organic ferromagnetic polymer $m$-polydiphenylcarbene are investigated. As the electron-phonon coupling $\ensuremath{\lambda}$ increases, there is a structure phase transition from a nondegenerate symmetric phase to a twofold degenerate symmetry-breaking phase. Both of the ground-state phases are ferrimagnetic and exhibit antiferromagnetic correlation between nearest-neighboring sites. There are domain-wall solitons describing the lattice deformation and spin envelopes describing spin localization if $\ensuremath{\lambda}$ is greater than a critical value, which depends on the electron-electron $U$.

Nonlinear Excitation in a Ferrimagnetic Zigzag Chain

We study the nonlinear excitation (solitons) in a ferrimagnetic polymerchain by using a total Hamiltonian consisting of Su–Schrieffer–HeegerHamiltonian and a Hubbard term. At half-filling, the distortion oflattices forms domain wall solitons, while the spin configuration formsenvelope solitons. The soliton pair is obtained in a range of theelectron–electron (e-e) interaction U, which depends on theelectron–phonon (e-ph) interaction. The spin solitons corresponding tothe left domain wall and the right domain wall of the displacement arequite different.

Intersoliton forces in the Wess–Zumino model

The spectrum of supersymmetric domain wall solitons of the Wess–Zumino model is known to be discontinuous across a curve (of marginal stability) in the moduli space of quartic superpotentials. Here we show how this phenomenon can be understood from the behaviour of the long-range inter-soliton force, which we compute by a method due to Manton.

Helium in one-dimensional nanopores: free dispersion, localization, and commensurate/incommensurate transitions with nonrigid orbitals.

The single-particle states of helium within a bundle of carbon nanotubes can range from nearly free-particle dispersion to localization, even within a single bundle. At intermediate effective masses, the corrugation in the external potential can be comparable to the intrasite He-He hard-core interaction. This results in a commensurate/incommensurate transition, where the mobility of the doubly occupied domain-wall solitons at high density greatly exceeds the corresponding hole mobility below the transition.

Nonlinear polarization dynamics of counterpropagating waves in an isotropic optical fiber: theory and experiments

The nonlinear interaction between two intense counterpropagating laser beams in an isotropic optical fiber may lead to spatiotemporal polarization instabilities of both waves. Experiments with various mutual polarization arrangements and different powers of the two counterpropagating input beams showed that nonlinear birefringence may lead to significant polarization cross switching of both beams. In the case of two counterrotating circular input waves, the cross-polarization interaction of the beams led to the generation of a polarization kink or domain wall soliton. This soliton is formed by a superposition of counterpropagating waves that represent switching of the state of polarization of light between two domains where both waves are circularly polarized and corotating. The experimental observations are found to be in good agreement with the theoretical predictions.

Complete characterization of terahertz pulse trains generated from nonlinear processes in optical fibers

The measurement technique of frequency-resolved optical gating (FROG) is used to characterize the intensity and phase of terahertz pulse trains generated from nonlinear and dispersive interactions in optical fibers. We show that existing FROG retrieval algorithms are easily adapted to allow the retrieval of periodic pulse characteristics and, using synthetic pulse trains generated from numerical simulations, we demonstrate how FROG can differentiate between periodic pulse trains with fundamentally different intensity and phase characteristics, yet qualitatively similar autocorrelation functions and spectra. Experimental results are presented for the FROG characterization of a 0.3-THz sinusoidal beat signal from a dual wavelength laser source, a 2.5-THz train of dark solitons generated in a high-birefringence fiber, and a 0.6-THz bright polarization domain wall soliton train generated in an ultra-low birefringence fiber. These results are shown to be in good agreement with nonlinear Schrodinger equation simulations.

Quantum dynamics of charged and neutral magnetic solitons: Spin-charge separation in the one-dimensional Hubbard model

We demonstrate that the Configuration Interaction (CI) Approximation recaptures essential features of the exact (Bethe Ansatz) solution to the 1D Hubbard model. As such, it provides valuable route for describing effects which go beyond mean-field theory for strongly correlated electron systems in higher dimensions. The CI method systematically describes fluctuation and quantum tunneling corrections to the Hartree-Fock Approximation (HFA). HFA predicts that doping a half-filled Hubbard chain leads to the appearance of charged spin-polarons or charged domain-wall solitons in the antiferromagnetic (AFM) background. The CI method, on the other hand, describes the quantum dynamics of these charged magnetic solitons and quantum tunneling effects between various mean-field configurations. In this paper, we test the accuracy of the CI method against the exact solution of the one-dimensional Hubbard model. We find remarkable agreement between the energy of the mobile charged bosonic domain-wall (as given by the CI method) and the exact energy of the doping hole (as given by the Bethe Ansatz) for the entire $U/t$ range. The CI method also leads to a clear demonstration of the spin-charge separation in 1D. Addition of one doping hole to the half-filled antiferromagnetic chain results in the appearance of two different carriers: a charged bosonic domain-wall (which carries the charge but no spin) and a neutral spin-1/2 domain wall (which carries the spin but no charge).

Boundary conditions, solitons, and spin configuration in interchain coupled organic ferromagnetic polymers

With an extended Su–Schrieffer–Heeger Hamiltonian including Hubbard energy and intersite Coulomb repulsion, we study the effects of two kinds of boundary conditions on the spin configuration and lattice distortion in organic ferromagnetic polymers with interchain coupling. It is shown that if the length L of the lattice is even, there is dimerization along the main chain and uniform spin density along side radicals. If L is odd, there exist domain wall solitons describing the displacement of the lattice along the main chain, and spin soliton with envelope shape describing the localization of spin at side radicals. Under the condition of strong interchain coupling, a great fluctuation of spin and distortion appear along the main chain and side radicals, and the system transfers to two-dimensional one. The e–e correlation reduces the amplitude of spin soliton and domain wall while electron–phonon coupling has the reverse effect.

Generation of optical domain-wall structures from modulational instability in a bimodal fiber.

We study experimentally modulational instability in a normally dispersive bimodal fiber under modal group-velocity-matching conditions. In the strong pump depletion regime, higher order sideband harmonics detected in the output spectra as well as autocorrelation measurements reveal the formation of subpicosecond domain-wall structures. Across these temporal structures the electromagnetic field distribution switches abruptly between the two transverse modes of the fiber. These structures are reminiscent of the so-called domain-wall soliton. Our results constitute therefore an experimental indication of the existence of this fundamental soliton.

Polarization Domain Wall Solitons with Counterpropagating Laser Beams

We report the experimental observation of a polarization kink or domain wall soliton by mixing two intense counterpropagating laser beams in a nonlinear isotropic dielectric. This soliton represents the switching of the state of polarization of light between two domains where both waves are circularly polarized and corotating. Good agreement is obtained with the theoretical description of the effect.

Solitons in quasi-one-dimensional π-conjugated organic ferromagnets

Abstract Quasi-one-dimensional π-conjugated organic polymer ferromagnets are studied self-consistently. It is shown that due to the electron-phonon interaction and the Hubbard energy, there exist domain wall solitons describing the displacement of lattices along the main chain, and spin solitons describing the localization of spin at side radicals. The spin soliton corresponds to the highly degenerate band in the middle of the energy spectra, which gives the main contribution in the high-spin state of the system.

Charged bosons in a doped Mott insulator: Electronic properties of domain-wall solitons and meron vortices

We demonstrate from first principles that when a charge carrier is added to a $\mathrm{spin}\ensuremath{-}1/2$ antiferromagnetic Mott insulator in either a one- or two-dimensional lattice, the self-consistent, Hartree-Fock ground state consists of a magnetic soliton texture with a doubly degenerate electronic level at the center of the Mott-Hubbard charge gap. This model is appropriate to systems with weak interchain or interlayer magnetic couplings in which long-range antiferromagnetic order is observed in the absence of charge carriers (doping). These magnetic solitons mediate the destruction of the magnetic order as the charge carrier concentration is increased. In a one-dimensional lattice with nearest-neighbor hopping $t$, on-site Coulomb repulsion $U,$ and self-consistent, antiferromagnetic moment amplitude $S$, we find that a charged, fermionic, magnetic domain wall soliton with a weakly ferromagnetic core, centered between two sites, has lower Hartree-Fock energy than a corresponding charged quasiparticle in one of the Mott-Hubbard bands. However, for $US/tg2$, this soliton is unstable to the formation of a lower energy charged, bosonic domain wall soliton, centered on a single site. For $US/tl2$, both of the above solitons are charged bosons. The self-consistent structure of these solitons exhibits no rotation of the local magnetic moments, but only a local suppression of the local moment amplitude in the vicinity of the hole. In the absence of doping, charge neutral domain wall solitons exhibit spin rotation within their core region. The equilibrium core size $\ensuremath{\rho}$ is determined by the degree of magnetic anisotropy. The ferromagnetic core soliton exhibits a pair of nondegenerate near-midgap electronic states. The antiferromagnetic core soliton exhibits a pair of nondegenerate electronic states that are symmetric about the midgap energy and that merge into the continuum as the anisotropy effects are made small and the soliton core radius $\ensuremath{\rho}$ becomes very large. The two-dimensional antiferromagnetic Mott insulator exhibits analogous behavior to the one-dimensional model. This analogy is precise for a 2D antiferromagnet exhibiting spin flux. For the undoped Mott insulator, the ferromagnetic core meron vortex (``lotus flower'' configuration of local magnetic moments) exhibits a doubly degenerate electronic midgap state in the continuum model and is the analog of the 1D neutral domain wall soliton. We demonstrate that a hole added to the 2D system can form a charged bosonic collective excitation, in which the spin background around the hole forms a planar vortex with local antiferromagnetic correlations at infinity and vanishing local-moment amplitude at the core of the soliton.

Self-dual Maxwell Chern-Simons solitons in 1+1 dimensions

We study the domain wall soliton solutions in the relativistic self-dual Maxwell Chern-Simons model in 1+1 dimensions obtained by the dimensional reduction of the 2+1 model. Both topological and nontopological self-dual solutions are found in this case. A la BPS dyons here the Bogomol'ny bound on the energy is expressed in terms of two conserved quantities. We discuss the underlying supersymmetry. Nonrelativistic limit of this model is also considered and static, nonrelativistic self-dual soliton solutions are obtained.

Ferromagnetic domain wall and a primordial magnetic field

We show that coherent magnetic field is generated spontaneously when a large domain wall is created in the early universe. It is caused by two dimensional massless fermions bounded to the domain wall soliton. We point out that the magnetic field is a candidate of primordial magnetic field.

BPS domain wall solutions in self-dual Chern-Simons-Higgs systems

We study domain wall solitons in the relativistic self-dual Chern-Simons Higgs systems by the dimensional reduction method to two dimensional spacetime. The Bogomolny bound on the energy is given by two conserved quantities in a similar way that the energy bound for BPS dyons is set in some Yang-Mills-Higgs systems in four dimensions. We find the explicit soliton configurations which saturate the energy bound and their nonrelativistic counter parts. We also discuss the underlying N=2 supersymmetry.

OPTICAL DOMAIN WALLS IN ATOMIC VAPORS

We present a theoretical analysis of the recently discovered optical domain-wall solitons. We discuss the fundamental link which exists between diffractive spatial domain-wall solitons and the instability responsible for the self-filamentation of polarized laser beams in self-defocusing Kerr media. We show that the vector properties of the third-order nonlinear response of atomic vapors satisfy the conditions of occurrence of this instability and are therefore suited to the experimental observation of the spatial polarization domain-wall solitons.

Spatiotemporal dynamics of domain-wall solitons in the fully frustrated Josephson-junction ladder arrays.

We studied the spatiotemporal dynamics of the magnetic vortex patterns in the fully frustrated overdamped Josephson-junction ladder arrays and found a type of solitonic motion of the domain walls between two ground-state vortex patterns, which is clearly manifested in the $I\ensuremath{-}V$ characteristics by the bump in the voltage drop inside the integer and half-integer steps. These patterns of propagating solitons persist in the presence of small bond disorders, displaying interesting phenomena of soliton reflection, refraction, and confinement, and are also found for other values of the filling factor $f$ and in multiladder arrays. We also found rich space-time vortex patterns, including the soliton turbulence which is responsible for the major voltage onset at the end of the voltage steps. Our finding is discussed in connection with spatiotemporal patterns of soliton turbulence found in the coupled circle map lattices.

Dynamical confinement of twisted soliton pairs in biaxial ferromagnets.

The dynamics of a classical continuum model of a ferromagnet with exchange and anisotropy energies of hard- and easy-axis type is considered. Exact solutions of soliton pairs with vanishing center of mass velocity are presented. They reveal the counterintuitive existence of a family of bound states of a repulsive, twisted domain wall (soliton) pair. These breather states have energies which lie above the continuum of the corresponding scattering states of two solitons

μSR study of hexagonal ABX 3

To elucidate the magnetic ordering process in quasi one-dimensional antiferromagnets, hexagonal ABX 3 compounds which have spin frustration among the magnetic chains on the triangular lattice, μ +SR experiments were performed on a typical Ising spin system CsCoCl 3. Below T N2 = 9 K, precession component was observed with the precession frequency extrapolated to 4.2 MHz at 0 K. In the partially disordered phase below T N1 = 21 K, a relaxation component of muon polarization is superimposed on the precession spectra due to static magnetic dipolar field indicating remarkable spin fluctuations despite of long range ordering. In the paramagnetic phase, only the relaxation component was observed. The results are interpreted in terms of domain wall solitons which propagate along the magnetic chains. The missing signal and its temperature dependence are future problems.