295 research outputs found

    Non-additive properties of finite 1D Ising chains with long-range interactions

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    We study the statistical properties of Ising spin chains with finite (although arbitrary large) range of interaction between the elements. We examine mesoscopic subsystems (fragments of an Ising chain) with the lengths comparable with the interaction range. The equivalence of the Ising chains and the multi-step Markov sequences is used for calculating different non-additive statistical quantities of a chain and its fragments. In particular, we study the variance of fluctuating magnetization of fragments, magnetization of the chain in the external magnetic field, etc. Asymptotical expressions for the non-additive energy and entropy of the mesoscopic fragments are derived in the limiting cases of weak and strong interactions.Comment: 20 pages, 4 figure

    Special K\"ahler-Ricci potentials on compact K\"ahler manifolds

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    A special K\"ahler-Ricci potential on a K\"ahler manifold is any nonconstant C∞C^\infty function τ\tau such that J(∇τ)J(\nabla\tau) is a Killing vector field and, at every point with dτ≠0d\tau\ne 0, all nonzero tangent vectors orthogonal to ∇τ\nabla\tau and J(∇τ)J(\nabla\tau) are eigenvectors of both ∇dτ\nabla d\tau and the Ricci tensor. For instance, this is always the case if τ\tau is a nonconstant C∞C^\infty function on a K\"ahler manifold (M,g)(M,g) of complex dimension m>2m>2 and the metric g~=g/τ2\tilde g=g/\tau^2, defined wherever τ≠0\tau\ne 0, is Einstein. (When such τ\tau exists, (M,g)(M,g) may be called {\it almost-everywhere conformally Einstein}.) We provide a complete classification of compact K\"ahler manifolds with special K\"ahler-Ricci potentials and use it to prove a structure theorem for compact K\"ahler manifolds of any complex dimension m>2m>2 which are almost-everywhere conformally Einstein.Comment: 45 pages, AMSTeX, submitted to Journal f\"ur die reine und angewandte Mathemati

    Self-induced tunable transparency in layered superconductors

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    We predict a novel nonlinear electromagnetic phenomenon in layered superconducting slabs irradiated from one side by an electromagnetic plane wave. We show that the reflectance and transmittance of the slab can vary over a wide range, from nearly zero to one, when changing the incident wave amplitude. Thus changing the amplitude of the incident wave can induce either the total transmission or reflection of the incident wave. In addition, the dependence of the superconductor transmittance on the incident wave amplitude has an unusual hysteretic behavior with jumps. This remarkable nonlinear effect (self-induced transparency) can be observed even at small amplitudes, when the wave frequency ω\omega is close to the Josephson plasma frequency ωJ\omega_J.Comment: 9 pages, 7 figure
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