295 research outputs found
Non-additive properties of finite 1D Ising chains with long-range interactions
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
A special K\"ahler-Ricci potential on a K\"ahler manifold is any nonconstant
function such that is a Killing vector field
and, at every point with , all nonzero tangent vectors orthogonal
to and are eigenvectors of both and
the Ricci tensor. For instance, this is always the case if is a
nonconstant function on a K\"ahler manifold of complex
dimension and the metric , defined wherever , is Einstein. (When such exists, 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 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
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 is close to the Josephson plasma frequency .Comment: 9 pages, 7 figure
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