Topological Textures Research Articles

Kinetics of phase ordering with topological textures.

We study the role played by topological textures and antitextures during the phase ordering of a two-dimensional system described by the discretised nonlinear O(3) sigma model with purely dissipative dynamics. We identify and characterise two distinct mechanisms for the decay of the order parameter variations --- single texture unwinding, and topological charge annihilation. Our results show that while at early times after the quench, the annihilation process dominates, the unwinding processes become of comparable importance at later times. We calculate the correlations in the order parameter and in the topological charge density, and show that dynamical scaling is strongly violated due to the occurence of multiple length scales growing differently in time.

Energy-scaling approach to phase-ordering growth laws.

We present a simple, unified approach to determining the growth law for the characteristic length scale, $L(t)$, in the phase ordering kinetics of a system quenched from a disordered phase to within an ordered phase. This approach, based on a scaling assumption for pair correlations, determines $L(t)$ self-consistently for purely dissipative dynamics by computing the time-dependence of the energy in two ways. We derive growth laws for conserved and non-conserved $O(n)$ models, including two-dimensional XY models and systems with textures. We demonstrate that the growth laws for other systems, such as liquid-crystals and Potts models, are determined by the type of topological defect in the order parameter field that dominates the energy. We also obtain generalized Porod laws for systems with topological textures.

Unwinding scaling violations in phase ordering.

The one-dimensional $\mathrm{O}(2)$ model is the simplest example of a system with topological textures. The model exhibits anomalous ordering dynamics due to the appearance of two characteristic length scales: the phase coherence length $L\ensuremath{\sim}{t}^{1/z}$ and the phase winding length ${L}_{w}\ensuremath{\sim}{L}^{\ensuremath{\chi}}$. We derive the scaling law $z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2+\ensuremath{\mu}\ensuremath{\chi}$, where $\ensuremath{\mu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ ( $\ensuremath{\mu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$) for nonconserved (conserved) dynamics and $\ensuremath{\chi}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2$ for uncorrelated initial orientations. From hard-spin equations of motion, we consider the evolution of the topological defect density and recover a simple scaling description.

Scaling violations with textures in two-dimensional phase ordering.

Scaling violations are found in the phase-ordering two-dimensional Heisenberg [O(3)] model, which has nonsingular topological textures, under dissipative nonconserved dynamics. Three separate length scales are found: ${\mathit{L}}_{\mathit{T}}$ characterizes the scale of individual textures, ${\mathit{L}}_{\mathit{N}}$ characterizes the separation between textures, and ${\mathit{L}}_{\mathit{C}}$ characterizes the distance between oppositely charged textures.

Methods of topological obstruction theory in condensed matter physics

The notion of relative topological textures — nonuniform states of the general type in condensed (ordered) media — is introduced. For the classification of such states, an effective method is proposed which is based on the topological obstruction theory. The examples of relative topological textures are examined within the framework of the approach studied here.

Planar and linear solitons in superfluidHe3

A means of classifying the planar and linear topological textures in superfluid phases of $^{3}\mathrm{He}$ by taking into account the effects of both magnetic field and boundary conditions is described. The method of the conventional homotopic groups is applied. The structure and stability of various solitons is considered in detail. This method may be applied to the description of topologically stable solitons in other ordered systems.