A unified field theory of topological defects and non-linear local excitations

Abstract

Topological defects and smooth excitations determine the properties of systems showing collective order. We introduce a generic non-singular field theory that comprehensively describes defects and excitations in systems with $O(n)$ broken rotational symmetry. Within this formalism, we explore fast events, such as defect nucleation/annihilation and dynamical phase transitions where the interplay between topological defects and non-linear excitations is particularly important. To highlight its versatility, we apply this formalism in the context of Bose-Einstein condensates, active nematics, and crystal lattices.

References in corpus (33)

• Topological Photonics
• Modeling Elasticity in Crystal Growth
• Modeling Elastic and Plastic Deformations in Non-Equilibrium Processing Using Phase Field Crystals
• Grain-Boundary Kinetics: A Unified Approach
• Observation of vortex dipoles in an oblate Bose-Einstein condensate
• Active Turbulence
• Motion of a heavy impurity through a Bose-Einstein condensate
• Characteristics of Two-Dimensional Quantum Turbulence in a Compressible Superfluid
• Onset of meso-scale turbulence in living fluids
• Renormalization group approach to multiscale simulation of polycrystalline materials using the phase field crystal model
• Inverse Energy Cascade in Forced 2D Quantum Turbulence
• Vorticity, Defects and Correlations in Active Turbulence
• Renormalization group theory for the phase field crystal equation
• Avalanches and Plastic Flow in Crystal Plasticity: An Overview
• Critical Velocity for Vortex Shedding in a Bose-Einstein Condensate
• Dislocation dynamics and crystal plasticity in the phase field crystal model
• Quantum turbulence in quantum gases
• Mass-driven vortex collisions in flat superfluids
• A phase field crystal theory of the kinematics of dislocation lines
• Controlling the energy of defects and interfaces in the amplitude expansion of the phase-field crystal model
• The role of fluid flow in the dynamics of active nematic defects
• Vortex clustering and universal scaling laws in two-dimensional quantum turbulence
• Revisiting Phase Diagrams of Two-Mode Phase-Field Crystal Models
• Defects at grain boundaries: A coarse-grained, three-dimensional description by the amplitude expansion of the phase-field crystal model
• Phase-field simulations of viscous fingering in shear-thinning fluids
• Non-linear elastic effects in phase field crystal and amplitude equations: Comparison to ab initio simulations of bcc metals and graphene
• An efficient numerical framework for the amplitude expansion of the phase-field crystal model
• Stress in ordered systems: Ginzburg-Landau type density field theory
• Metastability, excitations, fluctuations, and multiple-swallowtail structures of a superfluid in a Bose-Einstein condensate in the presence of a uniformly moving defect
• Dislocation nucleation in the phase field crystal model
• Hydrodynamic phase field crystal approach to interfaces, dislocations, and multi-grain networks
• Flow around topological defects in active nematic films
• Classical analogies for the force acting on an impurity in a Bose-Einstein condensate

Cited by in corpus (7)

• Chirality, anisotropic viscosity and elastic anisotropy in three-dimensional active nematic turbulence
• Gradient elasticity in Swift-Hohenberg and phase-field crystal models
• Mesoscale Field Theory for Quasicrystals
• Electrodynamics of Vortices in Quasi-2D Scalar Bose-Einstein Condensates
• Mesoscale modeling of deformations and defects in thin crystalline sheets
• Topological defects in polar active matter
• Modeling dislocations in quasicrystals through amplitude equations