Conformally equivariant quantization: Existence and uniqueness

We prove the existence and the uniqueness of a conformally equivariant symbol calculus and quantization on any conformally flat pseudo-Riemannian manifold (M,\rg). In other words, we establish a canonical isomorphism between the spaces of polynomials on $T^*M$ and of differential operators on tensor densities over $M$, both viewed as modules over the Lie algebra \so(p+1,q+1) where $p+q=\dim(M)$. This quantization exists for generic values of the weights of the tensor densities and compute the critical values of the weights yielding obstructions to the existence of such an isomorphism. In the particular case of half-densities, we obtain a conformally invariant star-product.Comment: LaTeX document, 32 pages; improved versio

Direct solar-pumped iodine laser amplifier

A XeCl laser which was developed earlier for an iodine laser oscillator was modified in order to increase the output pulse energy of XeCl laser so that the iodine laser output energy could be increased. The electrical circuit of the XeCl laser was changed from a simple capacitor discharge circuit of the XeCl laser to a Marx system. Because of this improvement the output energy from the XeCl laser was increased from 60 mj to 80 mj. Subsequently, iodine laser output energy was increased from 100 mj to 3 mj. On the other hand, the energy storage capability and amplification characteristics of the Vortek solar simulator-pumped amplifier was calculated expecting the calculated amplification factor is about 2 and the energy extraction efficiency is 26 percent due to the very low input energy density to the amplifier. As a result of an improved kinetic modeling for the iodine solar simulator pumped power amplifier, it is found that the I-2 along the axis of the tube affects seriously the gain profile. For the gas i-C3F7I at the higher pressures, the gain will decrease due to the I-2 as the pumping intensity increases, and at these higher pressures an increase in flow velocity will increase the gain

The two dimensional Hubbard model:a theoretical tool for molecular electronics

When speaking about molecular electronics, the obvious question which occurs is how does one study it theoretically. The simplest theoretical model suitable for application in molecular electronics is the two dimensional Hubbard model. The aim of the present paper is to introduce this model, and give some examples of the systems which it can describe. After a short mathematically oriented discussion, it will be shown how to calculate the electrical conductivity of a particular planar system: a rectangular lattice with mutually independent conductivities along the two axes,but without using the 2D Hamiltonian. This system could find applications in high Tc studies. It will finally be shown that the electrical conductivity of graphene can be determined not by using the full formalism of the $2D$ Hubbard model, but by a slight reformulation of the Hamiltonian of the 1D Hubbard modelComment: Lecture given at the 16 Int.School of Cond.Matt.Physics,August 29.,-September 3 2010.,Varna (Bulgaria

Andreev scattering in nanoscopic junctions at high magnetic fields

We report on the measurement of multiple Andreev resonances at atomic size point contacts between two superconducting nanostructures of Pb under magnetic fields higher than the bulk critical field, where superconductivity is restricted to a mesoscopic region near the contact. The small number of conduction channels in this type of contacts permits a quantitative comparison with theory through the whole field range. We discuss in detail the physical properties of our structure, in which the normal bulk electrodes induce a proximity effect into the mesoscopic superconducting part.Comment: 4 page

Action functionals of single scalar fields and arbitrary--weight gravitational constraints that generate a genuine Lie algebra

We discuss the issue initiated by Kucha\v{r} {\it et al}, of replacing the usual Hamiltonian constraint by alternative combinations of the gravitational constraints (scalar densities of arbitrary weight), whose Poisson brackets strongly vanish and cast the standard constraint-system for vacuum gravity into a form that generates a true Lie algebra. It is shown that any such combination---that satisfies certain reality conditions---may be derived from an action principle involving a single scalar field and a single Lagrange multiplier with a non--derivative coupling to gravity.Comment: 26 pages, plain TE

Microscopy study of ripples created on steel surface by use of ultra short laser pulses

This paper concentrates on ripples on the surface of steel that arise from lasermaterial interaction. In particular we have observed two different sets of ripples on steel samples that were machined by 210 fs laser pulses with 800 nm wavelength at normal incidence. Small ripples were found with spacing of about 250 nm lying longitudinal to the vector of laser beam polarization. Big ripples exhibited at a much larger distance of about 500 nm and they are perpendicular to the polarization vector. The laser treated surfaces were investigated with\ud Scanning Electron, Confocal and Atomic Force Microscopy. The laser-material interaction could be divided into three subsequent steps: absorption of laser light via electron gas excitations, transfer of heat into the lattice followed by a thermal expansion of material. From our microscopic observations it is concluded that the small ripples are formed by solidification of liquid material present as a thin layer near the interface of solid bulk material

Relational Orientation versus Firm Orientation: Want versus Should

This paper provides insights into employee decision making when there is a conflict between doing what is best for the firm (firm orientation) and doing what is best for one s interpersonal relationship with an external stakeholder representative (relational orientation). We apply construal level theory (Liberman and Trope, 1998; Trope and Liberman, 2003) to propose a framework that explains the effects of psychological distance dimensions on an employee's choice to act either in the best interests of their interpersonal relationships (what they want to do), or their firm (what they should do)