Strict Deformation Quantization via Geometric Quantization in the Bieliavsky Plane

Using standard techniques from geometric quantization, we rederive the integral product of functions on ℝ2 (non-Euclidian) which was introduced by Pierre Bieliavsky as a contribution to the area of strict quantization. More specifically, by pairing the nontransverse real polarization on the pair groupoid ℝ2×ℝ¯2, we obtain the well-defined integral transform. Together with a convolution of functions, which is a natural deformation of the usual convolution of functions on the pair groupoid, this readily defines the Bieliavsky product on a subset of L2ℝ2.

Models of inhomogeneous polarization of ferroelectrics and their practical application

A three-dimensional mathematical model is proposed that describes the ferroelectric response of polycrystalline ferroelectrics to an electric field in the absence of mechanical stresses. It is based on the separation of the switching process into two related parts: the rotation of the spontaneous polarization vectors and the destruction of the domain wall fixing mechanisms. For each of the parts, the energy costs are calculated, which are the components of the energy balance in the real polarization process. The constitutive relations for the induced and residual components of the polarization vector of the representative volume are obtained. A number of numerical experiments were performed, which showed good agreement with the experimental data.

Investigation of real polarization resistance for electrode performance in proton-conducting electrolysis cells

An equivalent circuit has firstly been proposed to evaluate proton-conducting electrolysis cells for their intrinsic electrode performance concealed by electronic conduction in electrolyte.

KLAUDER’S QUANTIZATION IN THE ALMOST-KAEHLER CASE

We prove that a regularized projection operator on the physical subspace ℋ phys ⊂ℒ2(Ω) can be defined for a symplectic manifold Ω=T*M equipped with an “Almost-Kaehler” structure, provided that a suitable counterterm is added to Klauder’s definition. The present result extends Klauder’s quantization to the case in which geometric quantization requires a real polarization.