The trace formulas for a half-line Schrodinger operator with long-range potentials

Thesis (M.S.) University of Alaska Fairbanks, 2002The present work deals with trace formulas for a half-line Schrödinger operator with long-range potentials. These formulas relate the potential with some scattering data. We generalize some relevant results by Buslaev; Faddeev; Gesztesy, Holden, Simon, and others to the case of square integrable potentials. The relation between the number of the trace formulas and the number of integrable derivatives of the potential is also given.Preface -- 1. Introduction -- 2. Notation -- 3. The WKB asymptotics -- 4. Some key asymptotics -- 5. The spectral shift function -- 6. Trace formulas -- References

Magnification of Subwavelength Field Distributions at Microwave Frequencies Using a Wire Medium Slab Operating in the Canalization Regime

Magnification of subwavelength field distributions using a wire medium slab operating in the canalization regime is demonstrated using numerical simulations. The magnifying slab is implemented by radially enlarging the distance between adjacent wires, and the operational frequency is tuned to coincide with the Fabry-Perot resonance condition. The near-field distribution of a complex-shaped source is canalized over an electrical distance corresponding roughly to $3\lambda$, and the distribution details are magnified by a factor of three. The operation of the slab is studied at several frequencies deviating from the Fabry-Perot resonance.Comment: 7 pages, 2 figure

Mesoscopic effective material parameters for thin layers modeled as single and double grids of interacting loaded wires

As an example of thin composite layers we consider single and double grids of periodically arranged interacting wires loaded with a certain distributed reactive impedance. Currents induced to the wires by a normally incident plane wave are rigorously calculated and the corresponding dipole moment densities are determined. Using this data and the averaged fields we assign mesoscopic material parameters for the proposed grid structures. These parameters depend on the number of grids, and measure the averaged induced polarizations. It is demonstrated that properly loaded double grids possess polarization response that over some frequency range can be described by assigning negative values for the mesoscopic parameters. Discussion is conducted on the physical meaningfulness to assign such material parameters for thin composite slabs. The results predicted by the proposed method for the double-grid structures are compared with the results obtained using the commonly adopted S-parameter retrieval procedure.Comment: 36 pages, 23 figure

Retrieval of Effective Parameters of Subwavelength Periodic Photonic Structures

We revisit the standard Nicolson–Ross–Weir method of effective permittivity and permeability restoration of photonic structures for the case of subwavelength metal-dielectric multilayers. We show that the direct application of the standard method yields a false zero-epsilon point and an associated spurious permeability resonance. We show how this artifact can be worked around by the use of the cycle shift operator to the periodic multilayer in question

Deformations of Lie Algebras using σ\sigma-derivations

In this article we develop an approach to deformations of the Witt and Virasoro algebras based on $\sigma$-derivations. We show that $\sigma$-twisted Jacobi type identity holds for generators of such deformations. For the $\sigma$-twisted generalization of Lie algebras modeled by this construction, we develop a theory of central extensions. We show that our approach can be used to construct new deformations of Lie algebras and their central extensions, which in particular include naturally the $q$-deformations of the Witt and Virasoro algebras associated to $q$-difference operators, providing also corresponding q-deformed Jacobi identities.Comment: 52 page