Zygmunt Jacek Zawistowski

Affine symmetry in mechanics of collective and internal modes. Part II. Quantum models

Abstract Discussed is the quantized version of the classical description of collective and internal affine modes as developed in Part I. We perform the Schrodinger quantization and reduce effectively the quantized problem from n 2 to n degrees of freedom. Some possible applications in nuclear physics and other quantum many-body problems are suggested. Discussed is also the possibility of half-integer angular momentum in composed systems of spinless particles.

Affine symmetry in mechanics of collective and internal modes. Part I. Classical models

Discussed is a model of collective and internal degrees of freedom with kinematics based on affine group and its subgroups. The main novelty in comparison with the previous attempts of this kind is that it is not only kinematics but also dynamics that is affinely-invariant. The relationship with the dynamics of integrable one-dimensional lattices is discussed. It is shown that affinely-invariant geodetic models may encode the dynamics of something like elastic vibrations.

Symmetries of Integro-Differential Equations

Abstract A new general method is presented for the determination of Lie symmetry groups of integro-differential equations. The suggested method is a natural extension of the Ovsiannikov method developed for differential equations. The method leads to important applications for instance to the Vlasov—Maxwell equations.

General criterion of invariance forintegro-differential equations*

Abstract General criterion of invariance of integro-differential equations under Lie symmetry groupof point transformations is derived. It is a generalization of the previous form of the criterion to the case of a moving range of integration. This is the situation when a region of integration depends on external, with respect to integration, variables which leads to its explicit dependence on a group parameter.

Symmetries of equations with functional arguments

Abstract The method of determining of the Lie symmetry groups of integro-differential equations is generalized to the case of equations with functional arguments. It leads to significant applications, for instance to the nonlocal nonlinear Schrodinger equation.

Widely tunable directional coupler filters with 1D photonic crystal

We present two concept examples for adding a wide range tunability to Si/SiO/sub 2/ devices involving a photonic crystal element. They are based on a directional coupler filter of two different geometries, where one of the arms is a Bragg reflection waveguide (BRW) used for the bandwidth improvement. The tuning relies on changing the properties of the BRW core. As an illustration we consider the smectic A* liquid crystal as the core material and show that ca 100 nm tuning range is achievable by the core index variations of 0.006 under applying electric field of 5 V//spl mu/m.

Electrically tunable filter based on directional coupler with 1D photonic crystal arm infiltrated with smectic liquid crystal

We propose a concept for an electrically tunable optical filter based on a directional coupler consisting of a conventional silica glass waveguide and a 1D photonic-crystal waveguide formed as a stack of alternating Si and SiO/sub 2/ layers with an electroclinic smectic A* liquid crystal as a defect layer (core). We show theoretically that with a commercially available liquid crystal, BDH764E, tuning ranges as large as 80 nm in the 1.55 /spl mu/m WDM band are possible under an applied electric field of less than 5 V//spl mu/m.

Applications of wavelength dispersion in 1D and 2D photonic crystals

One of the most distinctive features of photonic crystals (PhCs) is their unique wavelength dispersion allowing novel device concepts for enhancement of photonic functionality and performance. Here, we present examples of our design and demonstrations utilizing dispersion properties of 1D and 2D photonic crystals. This includes the demonstration of negative refraction in 2D PhC at optical wavelengths, filters based on 1D and 2D PhC waveguides, and the design of a widely tunable filter involving 1D PhC.