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.     

Control of the tunnel current flowing though nonuniform heterogeneous barriers with spherically symmetric inclusions

The effect of spherical quantum objects (scatterers) embedded into semiconductor barriers on the tunnel current flowing through them has been studied. For this purpose, the problem of the scattering of incident and reflected wave functions (damping if their energy is less than the barrier potential) of the electron by the stepwise spherically symmetric scattering potential has been solved.     

Terahertz negative conductivity of heterostructure barriers during ballistic transport of hot electrons

A mechanism for achieving the terahertz negative conductivity on transmit time effects during ballistic transport of hot carriers in nanoscale semiconductor heterostructures was theoretically considered. It was shown that selection of the heterostructure potential profile can significantly increase high-frequency negative conductivity.     

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.     

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.     

Transit-time frequency quantum beats and THz negative conductance in nanoscale semiconductor heterostructures

A quantum-mechanical calculation of the THz negative conductance of hot ballistic electrons in nanoscale semiconductor heterostructures has been performed. It is shown that quantum beats of the ballistic electron wave function induce an ac current in the structure, which can do negative work on the ac field.     

Equations of motion and conserved quantities in non-Abelian discrete integrable models

Conserved quantities for the Hirota bilinear difference equation, which is satisfied by eigenvalues of the transfer matrix, are studied. The transfer-matrix eigenvalue combinations that are integrals of motion for discrete integrable models, which correspond to A_k−1 algebras and satisfy zero or quasi-periodic boundary conditions, are found. Discrete equations of motion for a non-Abelian generalization of the Liouville model and the discrete analogue of the Tsitseiko equation are obtained. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 119, No. 1, pp. 34–46, April. 1999.     

Bloch Hamiltonians and topologically ordered states

We consider a universal representation for the Hamiltonian of systems in topologically ordered phase states. We show that for strongly correlated electronic systems, the Hamiltonian expressed in terms of projectors of the Temperley-Lieb algebra on the spin singlet state has the form of a two-dimensional Bloch matrix in the case of doubly linked excitation world lines; in this case, different topological orderings are separated by a quantum critical point where the matrix elements of the Hamiltonian vanish. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 160, No. 1, pp. 220–228, July, 2009.     

Chern-Simons correlations on (2+1)D lattice

The contribution of zero modes to the value of the number of particles in a discrete model of the (2+1)-dimensional nonlinear Schrödinger equation is computed. It is shown for the first time that in the region of small values of the Chern-Simons coefficient k there exists a universal attraction between field configurations. For k=2 this phenomenon may be a dynamic origin of the semion pairing in the high-temperature superconducting state of planar systems. The preliminary results of this paper were presented in the proceedings of the XI International Conference on Problems of Quantum Field Theory (Dubna, 13–17 July 1998).