Quantum soliton in 1D Heisenberg spin chains with Dzyaloshinsky-Moriya and next-nearest-neighbor interactions.

We report in this work, an analytical study of quantum soliton in 1D Heisenberg spin chains with Dzyaloshinsky-Moriya Interaction (DMI) and Next-Nearest-Neighbor Interactions (NNNI). By means of the time-dependent Hartree approximation and the semi-discrete multiple-scale method, the equation of motion for the single-boson wave function is reduced to the nonlinear Schrödinger equation. It comes from this present study that the spectrum of the frequencies increases, its periodicity changes, in the presence of NNNI.

Instabilities and relaxation to equilibrium in long-range oscillator chains.

We study instabilities and relaxation to equilibrium in a long-range extension of the Fermi-Pasta-Ulam-Tsingou (FPU) oscillator chain by exciting initially the lowest Fourier mode. Localization in mode space is stronger for the long-range FPU model. This allows us to uncover the sporadic nature of instabilities, i.

Quantum signatures of breathers in a finite Heisenberg spin chain.

A map of a quantum Heisenberg spin chain into an extended Bose-Hubbard-like Hamiltonian is set up. Within this framework, the spectrum of the corresponding Bose-Hubbard chain, on a periodic one-dimensional lattice containing two, four, and six bosons shows interesting detailed band structures. These fine structures are studied using numerical diagonalization, and nondegenerate and degenerate perturbation theory.

Dipolar effects on soliton dynamics on a discrete ferromagnetic chain.

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.