Optische Absorptionsspektren und Kristallfeldaufspaltungen des Er3+-Ions in YPO4 und YVO4

The optical absorption spectra of trivalent erbium in isostructural single crystals of YPO₄ and YVO₄ have been obtained between 14000 and 29000 cm^?1. The observed crystal field splittings are interpreted in terms of crystal potentials of symmetryD _2d. From the positions of 33 Stark components the five crystal field parametersB ₀ ² , B ₀ ⁴ , B ₀ ⁶ , B ₄ ⁴ andB ₄ ⁶ have been determined. The values of the parameters for Er³⁺:YPO₄ are significantly different from those of Er³⁺:YVO₄.     

Erhaltungssätze und Topologie

Conservation Laws and Topology It is shown, that for every conserved matter tensor T^ν_μ there exists a frame of reference h^a_μ, orthonormalized in a given gravitational field, such that the components h^a_νT^ν_μ are four conserved currents. The definition of global energy-momentum connected with these currents contains as special causes the definition of inertial frames in Minkowski space as well as the definition of energy in a comoving system in presence of Killing vectors in general relativity. Given on the other hand four closed 3-forms in a space-time with non-trivial topology, one can introduce an orthonormal frame of reference h^a_μ in such a way, that the space-time- components of the 1-forms, dual to the given 3-forms, define a symmetric matter tensor, which generates according to Einstein's equations the gravitional field. This means a partly topological definition of matter, since the non-trivially closed part of the 3-forms is determined by the topology of the manifold.     

Hermitizität und Eichinvarianz

Hermiticity and Gauge Invariance In the Theory of Hermitian Relativity (HRT) the postulates of hermiticity and gauge invariance are formulated in different ways, due to a different understanding of the idea of hermiticity. However all hermitian systems of equations have to satisfy Einstein's weak system of equations being equivalent to Einstein-Schrödinger equations.     

Anfachung und Dämpfung magneto-akustischer Wellen in MHD-Kanälen und ihr Einfluß auf die mittlere Stromdichte und die mittlere Hall-Feldstärke

Magneto-acoustic waves generated by fluctuations in the Hall parameter, the electric conductivity and the stream velocity are theoretically investigated in a weakly ionized plasma streaming across a strong external magnetic field and bearing a current flowing perpendicular to both magnetic field and stream velocity. The investigations hold for seeded rare gas plasmas at any degree of seed ionization but are resticted to waves propagating in parallel or antiparallel direction to the current density vector and in parallel or antiparallel direction to the stream velocity vector and to wave lengths which are small in comparsion to the interaction length which occurs as a characteristic wave length. The influence of these waves on the mean current density and the mean Hall field intensity is calculated in case of small amplitudes and low degree of seed ionization up to second order terms. Omitting Ohmic heating the dispersion equation can be solved exactly. A phase shift exists between the fluctuations in gas density and gas velocity. The phase velocity and the amplification rate depend on the wave length. Typical results are represented in a diagram. For both types of waves the phase velocity slightly rises with increasing wave length, while the amplification rate decreases. Waves propagating in opposite direction to the current density vector are amplified, if the electron velocity exceeds a critical value. They reduce the mean current density and the mean Hall field intensity. Waves propagating in opposite direction to the stream velocity vector are also amplified except for very high degrees of seed ionization. The threshold current density is greater than that for the waves of the first type approximately by the Hall parameter as factor. At extremely high degree of seed ionization the phase velocity is directed opposite to the direction occuring at weakly ionized seed. Waves of the second type decrease the mean current density, but increase the mean Hall field intensity.     

Gedämpfter Laserverstärker und Phasenunschärfe

Damped Laser Amplifier and Phase Uncertainty In extension of a paper about the possibility to measure the phase of a microscopic field by linear amplification the damping is introduced in the linear amplifier. For this end the Fokker-Planck equation is solved and a quasiprobability distribution is obtained for an arbitrary initial state. With the help of this distribution the phase uncertainty for the largely amplified field is calculated. It is shown that appreciable damping destroys the result which was obtained for a lossless laser amplifier.     

Paramagnetische Resonanz des dreiwertigen Gadoliniums in YPO4, YVO4 und YAsO4

The EPR spectra of Gd³⁺-doped isostructural single crystals of YPO₄, YVO₄, and YAsO₄ have been measured in X-band at room temperature and at nitrogen and helium temperatures. The zero-field splitting can be described by the five crystal-field parametersb ₂ ⁰ ,b ₄ ⁰ ,b _6/0,b ₄ ⁴ , and b ₆ ⁴ fitted to a tetragonal spin-Hamiltonian corresponding to the point symmetry D_2d of the Gd³⁺ site. The values ofg and b ₂ ⁰ vary significantly with host lattice and with temperature.     

Integrabilität,Irreversibilität und Kosmogonie

Integrability, Irreversibility, and Cosmogony Leading the famous discussion with Boltzmann on the foundation of statistical thermodynamics Zermelo was backed by Planck himself. Zermelo's objections to Boltzmann's atomism and Boltzmann's answers are again vital today. After all Boltzmann founded statistical thermodynamics cosmogonically.     

Phänomenologie und Energiebilanz von Lichtbogenkatoden bei niedrigen Drücken und hohen Stromstärken

The behaviour of an arc cathode in a coaxial gas stream is investigated experimentally in a pressure and current range of 15 to 120 mms Hg and 400 to 1000 A, respectively. Argon and hydrogen are used as ambient test gases. Particular phenomena occurring during the short instationary ignition period are described. Stationary operation characterized by a diffused cathode attachment covering a relatively large area is more closely studied. Measurements of the extension of the arc attachment and the distribution of the cathode temperature are made and evaluated quantitatively. Average current densities in the attachment are presented, as functions of pressure and current, by empirical expressions. Using a quasi-onedimensional approach, an interior energy balance of the cathode is set up and heat entering the cathode in the attachment region is calculated. Finally, under further simplifying assumptions, the cathode drop voltage and the fraction of current carried by ions are estimated and the so-called Richardson constant is determined assuming electron emission according to the Richardson-Schottky-equation. All data discussed depends — in general, strongly — on ambient pressure and current, and the type of gas has a substantial qualitative and quantitative influence.