Persistent Currents in Helical Structures

Recent discovery of mesoscopic electronic structures, in particular the carbon nanotubes, made necessary an investigation of what effect may helical symmetry of the conductor (metal or semiconductor) have on the persistent current oscillations. We investigate persistent currents in helical structures which are non-decaying in time, not requiring a voltage bias, dissipationless stationary flow of electrons in a normal-metallic or semiconducting cylinder or circular wire of mesoscopic dimension. In the presence of magnetic flux along the toroidal structure, helical symmetry couples circular and longitudinal currents to each other. Our calculations suggest that circular persistent currents in these structures have two components with periods $\Phi_0$ and $\Phi_0/s$ ($s$ is an integer specific to any geometry). However, resultant circular persistent current oscillations have $\Phi_0$ period. \pacs{PACS:}PACS:73.23.-bComment: 4 pages, 2 figures. Submitted to PR

Theory of Submanifolds, Associativity Equations in 2D Topological Quantum Field Theories, and Frobenius Manifolds

We prove that the associativity equations of two-dimensional topological quantum field theories are very natural reductions of the fundamental nonlinear equations of the theory of submanifolds in pseudo-Euclidean spaces and give a natural class of potential flat torsionless submanifolds. We show that all potential flat torsionless submanifolds in pseudo-Euclidean spaces bear natural structures of Frobenius algebras on their tangent spaces. These Frobenius structures are generated by the corresponding flat first fundamental form and the set of the second fundamental forms of the submanifolds (in fact, the structural constants are given by the set of the Weingarten operators of the submanifolds). We prove in this paper that each N-dimensional Frobenius manifold can locally be represented as a potential flat torsionless submanifold in a 2N-dimensional pseudo-Euclidean space. By our construction this submanifold is uniquely determined up to motions. Moreover, in this paper we consider a nonlinear system, which is a natural generalization of the associativity equations, namely, the system describing all flat torsionless submanifolds in pseudo-Euclidean spaces, and prove that this system is integrable by the inverse scattering method.Comment: 10 pages, Proceedings of the Workshop "Nonlinear Physics. Theory and Experiment. IV. Gallipoli (Lecce), Italy, June 22 - July 1, 200

Stability of dynamic coherent states in intrinsic Josephson-junction stacks near internal cavity resonance

Stacks of intrinsic Josephson junctions in the resistive state can by efficiently synchronized by the internal cavity mode resonantly excited by the Josephson oscillations. We study the stability of dynamic coherent states near the resonance with respect to small perturbations. Three states are considered: the homogeneous and alternating-kink states in zero magnetic field and the homogeneous state in the magnetic field near the value corresponding to half flux quantum per junction. We found two possible instabilities related to the short-scale and long-scale perturbations. The homogeneous state in modulated junction is typically unstable with respect to the short-scale alternating phase deformations unless the Josephson current is completely suppressed in one half of the stack. The kink state is stable with respect to such deformations and homogeneous state in the magnetic field is only stable within a certain range of frequencies and fields. Stability with respect to the long-range deformations is controlled by resonance excitations of fast modes at finite wave vectors and typically leads to unstable range of the wave-vectors. This range shrinks with approaching the resonance and increasing the in-plane dissipation. As a consequence, in finite-height stacks the stability frequency range near the resonance increases with decreasing the height.Comment: 15 pages, 8 figures, to appear in Phys. Rev.