Dynamics of Fluxon Lattice in Two Coupled Josephson Junctions

We study theoretically the dynamics of a fluxon Lattice (FL) in two coupled Josephson junctions. We show that when the velocity of the moving FL exceeds certain values $(V_{a,b})$, sharp resonances arise in the system which are related to the excitation of the optical and acoustic collective modes. In the interval $(V_a, V_b)$ a reconstruction of the FL occurs. We also establish that one can excite localized nonlinear distortions (dislocations) which may propagate through the FL and carry an arbitrary magnetic flux.Comment: 4 pages, 3 figures, corected typo

Quantum lattice KdV equation

A quantum theory is developed for a difference-difference system which can serve as a toy-model of the quantum Korteveg-de-Vries equation.Comment: 12 pages, LaTe

The Tomonaga-Luttinger Model and the Chern-Simons Theory for the Edges of Multi-layer Fractional Quantum Hall Systems

Wen's chiral Tomonaga-Luttinger model for the edge of an m-layer quantum Hall system of total filling factor nu=m/(pm +- 1) with even p, is derived as a random-phase approximation of the Chern-Simons theory for these states. The theory allows for a description of edges both in and out of equilibrium, including their collective excitation spectrum and the tunneling exponent into the edge. While the tunneling exponent is insensitive to the details of a nu=m/(pm + 1) edge, it tends to decrease when a nu=m/(pm - 1) edge is taken out of equilibrium. The applicability of the theory to fractional quantum Hall states in a single layer is discussed.Comment: 15 page

Ternary numbers and algebras. Reflexive numbers and Berger graphs

The Calabi-Yau spaces with SU(m) holonomy can be studied by the algebraic way through the integer lattice where one can construct the Newton reflexive polyhedra or the Berger graphs. Our conjecture is that the Berger graphs can be directly related with the $n$-ary algebras. To find such algebras we study the n-ary generalization of the well-known binary norm division algebras, ${\mathbb R}$, ${\mathbb C}$, ${\mathbb H}$, ${\mathbb O}$, which helped to discover the most important "minimal" binary simple Lie groups, U(1), SU(2) and G(2). As the most important example, we consider the case $n=3$, which gives the ternary generalization of quaternions and octonions, $3^p$, $p=2,3$, respectively. The ternary generalization of quaternions is directly related to the new ternary algebra and group which are related to the natural extensions of the binary $su(3)$ algebra and SU(3) group. Using this ternary algebra we found the solution for the Berger graph: a tetrahedron.Comment: Revised version with minor correction

Pion Polarizability in the NJL model and Possibilities of its Experimental Studies in Coulomb Nuclear Scattering

The charge pion polarizability is calculated in the Nambu-Jona-Lasinio model, where the quark loops (in the mean field approximation) and the meson loops (in the $1/N_c$ approximation) are taken into account. We show that quark loop contribution dominates, because the meson loops strongly conceal each other. The sigma-pole contribution $(m^2_\sigma-t)^{-1}$ plays the main role and contains strong t-dependence of the effective pion polarizability at the region $|t|\geq 4M_\pi^2$. Possibilities of experimental test of this sigma-pole effect in the reaction of Coulomb Nuclear Scattering are estimated for the COMPASS experiment.Comment: 11 pages, 8 figure

Transition between ordinary and topological insulator regimes in two-dimensional resonant magnetotransport

In the two-dimensional case the transition between ordinary and topological insulator states can be described by a massive Dirac model with the mass term changing its sign at the transition point. We theoretically investigate how such a transition manifests itself in resonant transport via localized helical edge states. The resonance occurs in the middle of the band gap due to a zero edge-state mode which is protected by the time-reversal symmetry, also when coupled to the conducting leads. We obtain the explicit dependence of the resonant conductance on the mass parameter and an external magnetic field. The proposal may be of practical use, allowing one to determine the orbital g-factor of helical edge states in two-dimensional topological insulators.Comment: 7 pages, 3 eps figures, Phys. Rev. B (in press