Energy bounds of linked vortex states

Energy bounds of knotted and linked vortex states in a charged two-component system are considered. It is shown that a set of local minima of free energy contains new classes of universality. When the mutual linking number of vector order parameter of vortex lines is less than the Hopf invariant, these states have lower lying energies.     

Dynamics of fields in the gauged nonlinear (2+1)D Schrödinger equation model

We study the solutions of the equations of motion in the gauged (2+1)-dimensional nonlinear Schrödinger equation. The contribution of the Chern-Simons gauge fields leads to a significant decrease of the critical power of self-focusing. We also show that for appropriate boundary conditions in the model considered there exists a regime of turbulent motion of a hydrodynamic type.     

Strong correlations in a model of a gauged (2+1)-dimensional nonlinear Schrödinger equation

Phenomena caused by strong correlations between nonlinear modes in planar systems are briefly reviewed. The analysis is restricted to the model of a nonlinear Schrödinger equation. Stationary field distributions are found. The number of particles is obtained as a function of a parameter characterizing the degree of linking of the world lines of excitations. It is shown that, for small values of this parameter, a two-dimensional lattice is characterized by universal attraction, which can be a dynamical cause for the transition to the coherent state. The relation between the chiral nonlinear edge modes and breaking of the Galilei invariance in the system under consideration is discussed.     

Inhomogeneous Current States in a Gauged Two-Component Ginzburg-Landau Model

We consider the energy bounds of inhomogeneous current states in doped antiferromagnetic insulators in the framework of the two-component Ginzburg-Landau model. Using the formulation of this model in terms of the gauge-invariant order parameters (the unit vector n, spin stiffness field ρ², and particle momentum c), we show that this strongly correlated electron system involves a geometric small parameter that determines the degree of packing in the knots of filament manifolds of the order parameter distributions for the spin and charge degrees of freedom. We find that as the doping degree decreases, the filament density increases, resulting in a transition to an inhomogeneous current state with a free energy gain.__________Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 144, No. 1, pp. 182–189, July, 2005.     

Yang-Mills potentials and the van der Waals force between hadrons

The colour-induced magnetic dipole interaction between hadrons is discussed. Fermion motion in a gauge field obtained by solving the classical Yang-Mills equations is considered. It is shown that the spectrum of stationary fermion states is discrete and bound states are colourless. The long range asymptotic behaviour of the gauge potential results in the van der Waals interaction of hadrons.     

New topological surface state in layered topological insulators: Unoccupied dirac cone

The unoccupied states in topological insulators Bi₂Se₃, PbSb₂Te₄, and Pb₂Bi₂Te₂S₃ are studied by the density functional theory methods. It is shown that a surface state with linear dispersion emerges in the inverted conduction band energy gap at the center of the surface Brillouin zone on the (0001) surface of these insulators. The alternative expression of ?₂ invariant allowed us to show that a necessary condition for the existence of the second $\bar \Gamma $ Dirac cone is the presence of local gaps at the time reversal invariant momentum points of the bulk spectrum and change of parity in one of these points.     

Electronic states with nontrivial topology in Dirac materials

The theoretical studies of phase states with a linear dispersion of the spectrum of low-energy electron excitations have been reviewed. Some main properties and methods of experimental study of these states in socalled Dirac materials have been discussed in detail. The results of modern studies of symmetry-protected electronic states with nontrivial topology have been reported. Combination of approaches based on geometry with homotopic topology methods and results of condensed matter physics makes it possible to clarify new features of topological insulators, as well as Dirac and Weyl semimetals.     

Structure of zero modes in a model of the discrete (2+1)-dimensional nonlinear Schrödinger equation

The structure of the zero modes in a discrete (2+1)-dimensional model of the gauge-invariant nonlinear Schrödinger equation is studied. Including the compactification of the Chern-Simons gauge fields eliminates the difficulties with the continuous model [L. A. Abramyan and A. P. Protogenov, JETP Lett. 64, 859 (1996); L. A. Abramyan, V. I. Berezhiani, and A. P. Protogenov, Phys. Rev. E 56, 6026 (1997)] and leads to a prediction of the existence of a transition region characterized by a hierarchical sequence of collapses which are enumerated by the Chern-Simons coefficient. Using the zero modes in calculating the dependence of the critical power N on the Chern-Simons coefficient, we have found that the transition region lies in the interval 11.703≤N≤12.01.