Spinors and multivectors as a unified tool for spacetime geometry and for elementary particle physics

From the definition of spinors as the minimal left (right) modules of multivectors (that is, of vectors and their outer products), we can construct a unified mathematical approach for the study of matter and its interaction fields, which are either defined as fields in the geometrical spacetime or considered as generators of the physical spacetime. It is also shown how matter and interaction fields can be represented either by spinor fields or by multivector fields, both types of fields carrying the same information as the traditional corresponding spinors, vectors, or tensors. Geometry is more transparent in one representation (multivector form), and physics is more obvious in the spinor representation. Our theory provides a unified and totally self-consistent representation of quarks (barions), leptons, and all their known interactions.     

Continuous-wave mode-locked solid-state lasers with enhanced spatial hole burning

In Part I of this paper [1] experimental results were presented and discussed. In this part, we investigate theoretically the dynamics of end-pumped solid-state lasers due to enhanced spatial hole burning. This becomes possible by a fast numerical implementation of the saturated gain in the presence of strong spatial hole burning that allows to treat the multimode case for an arbitrary pumping level. We find for a wide range of laser parameters that the mode spacing of the cw running modes is essentially determined by the length of the gain medium and only weakly depends on the absorption depth of the pump transition. It is shown that spatial hole burning can lead to a completely flat saturated gain profile over half of the gain bandwidth. In mode-locked lasers, the flat gain due to spatial hole burning results in shorter pulses. But the pulses are neither Gaussian-nor sech-shaped as they are in actively or passively mode-locked lasers without spatial hole burning. Further, we show that soliton-like pulse shaping can be used to restore a transform-limited sech-shaped pulse in an end-pumped solid-state laser while exploiting the full gain bandwidth of the laser material.     

High-energy picosecond Nd:YVO4 slab amplifier for OPCPA pumping

We demonstrate 12-ps pulses with up to 0.6-mJ pulse energy at repetition rates of 50 kHz and 100 kHz from a Nd:YVO₄ slab amplifier built in a simple four-pass configuration. Excellent noise performance with pulse energy fluctuations below 0.8% rms has been achieved by using 10-μJ seed pulses from a highly stable industrial laser system and moderate gain (30–46) in the slab amplifier.     

Zur Theorie der Chiralitätsfunktionen

The Algebraic Theory of Chirality Functions is derived by means of exclusively qualitative considerations. Hence, the significance of quantitative results is questionable. Moreover the construction of “Näherungsansätze” (”Approximation-Ansatz”), which may be interpreted as semiempirical methods, is achieved on the basis of plausibility and mathematical simplicity. Since physical arguments are not included, the consistency or inconsistency of “Näherungsansätze” with experimental results do not justify direct physical conclusions.     

Absolutely indecomposable symmetric matrices

Let A be a symmetric matrix of size n×n with entries in some (commutative) field K. We study the possibility of decomposing A into two blocks by conjugation by an orthogonal matrix T∈Mat_n(K). We say that A is absolutely indecomposable if it is indecomposable over every extension of the base field. If K is formally real then every symmetric matrix A diagonalizes orthogonally over the real closure of K. Assume that K is a not formally real and of level s. We prove that in Mat_n(K) there exist symmetric, absolutely indecomposable matrices iff n is congruent to 0, 1 or −1 modulo 2s.     

Variational Solution of Stochastic Schrödinger Equations With Power-Type Nonlinearity

We investigate a Schrödinger problem with multiplicative Gaussian noise term and power-type nonlinearity on a bounded one-dimensional domain. In order to prove the existence and uniqueness of the variational solution, a further process will be introduced which allows to transform the stochastic nonlinear Schrödinger problem into a pathwise one. Galerkin approximations and compact embedding results are used.     

Passively mode-locked high-power Nd:YAG lasers. with multiple laser heads

We discuss power scaling of passively mode-locked lasers using multiple laser heads in the resonator. We experimentally compared two different approaches for the cavity design, both using three side-pumped Nd:YAG laser heads. We obtained a record-high average output power of up to 27 W with close to diffraction-limited beam quality, a pulse duration of 19 ps, a pulse energy of 0.5 7J, and 23 kW peak power. Single-pass second-harmonic generation in a 10-mm-long LBO crystal yields 16.2 W of 532-nm radiation.     

Formation of a crosslinked POSS network by an unusual hydrosilylation: Thermo‐oxidative stabilization of the α‐cristobalite phase in its amorphous regions

A semicrystalline inorganic–organic hybrid crosslinked network containing polyhedral oligomeric silsesquioxane (POSS) cores was constructed by the unusual hydrosilylation of the terminal vinyl groups of an internal acetylene‐containing silane linker by a POSS monomer. Products from the thermal treatments of this network in either argon or air at 250, 550, and 1000 °C, respectively, were characterized by Fourier transform infrared, Solid‐state ¹³C and ²⁹Si magic angle spinning NMR, X‐ray diffraction and XPS analyses. The highly symmetrically functionalized POSS silica clusters, in the fluorite silica phase, in the network were found to remain unchanged on thermal treatment possibly due to the shielding of the silica core by the functionalities and a cancellation of thermal stresses on the silica core. Stabilization of the metastable α‐cristobalite phase, which is typically formed on cooling by a β‐ to α‐transition of the β‐cristobalite phase formed above 1400 °C, was observed in the amorphous regions in the network sample treated only to 1000 °C in air. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012