A study of local and non-local spatial densities in quantum field theory

We use a one-dimensional model system to compare the predictions of two different 'yardsticks' to compute the position of a particle from its quantum field theoretical state. Based on the first yardstick (defined by the Newton-Wigner position operator), the spatial density can be arbitrarily narrow and its time-evolution is superluminal for short time intervals. Furthermore, two spatially distant particles might be able to interact with each other outside the light cone, which is manifested by an asymmetric spreading of the spatial density. The second yardstick (defined by the quantum field operator) does not permit localized states and the time evolution is subluminal.Comment: 29 pages, 3 figure

Structural, electronic, vibrational and dielectric properties of LaBGeO5_5 from first principles

Structural, electronic, vibrational and dielectric properties of LaBGeO$_5$ with the stillwellite structure are determined based on \textit{ab initio} density functional theory. The theoretically relaxed structure is found to agree well with the existing experimental data with a deviation of less than $0.2\%$. Both the density of states and the electronic band structure are calculated, showing five distinct groups of valence bands. Furthermore, the Born effective charge, the dielectric permittivity tensors, and the vibrational frequencies at the center of the Brillouin zone are all obtained. Compared to existing model calculations, the vibrational frequencies are found in much better agreement with the published experimental infrared and Raman data, with absolute and relative rms values of 6.04 cm$^{-1}$, and $1.81\%$, respectively. Consequently, numerical values for both the parallel and perpendicular components of the permittivity tensor are established as 3.55 and 3.71 (10.34 and 12.28), respectively, for the high-(low-)frequency limit

Moving system with speeded-up evolution

In the classical (non-quantum) relativity theory the course of the moving clock is dilated as compared to the course of the clock at rest (the Einstein dilation). Any unstable system may be regarded as a clock. The time evolution (e.g., the decay) of a uniformly moving physical system is considered using the relativistic quantum theory. The example of a moving system is given whose evolution turns out to be speeded-up instead of being dilated. A discussion of this paradoxical result is presented.Comment: 10 pages, LaTe

Time dilation in relativistic two-particle interactions

We study the orbits of two interacting particles described by a fully relativistic classical mechanical Hamiltonian. We use two sets of initial conditions. In the first set (dynamics 1) the system\u27s center of mass is at rest. In the second set (dynamics 2) the center of mass evolves with velocity V. If dynamics 1 is observed from a reference frame moving with velocity-V, the principle of relativity requires that all observables must be identical to those of dynamics 2 seen from the laboratory frame. Our numerical simulations demonstrate that kinematic Lorentz space-time transformations fail to transform particle observables between the two frames. This is explained as a result of the inevitable interaction dependence of the boost generator in the instant form of relativistic dynamics. Despite general inaccuracies of the Lorentz formulas, the orbital periods are correctly predicted by the Einstein\u27s time dilation factor for all interaction strengths

Semiempirical Hartree-Fock calculations for KNbO3

In applying the semiempirical intermediate neglect of differential overlap (INDO) method based on the Hartree-Fock formalism to a cubic perovskite-based ferroelectric material KNbO3, it was demonstrated that the accuracy of the method is sufficient for adequately describing the small energy differences related to the ferroelectric instability. The choice of INDO parameters has been done for a system containing Nb. Based on the parametrization proposed, the electronic structure, equilibrium ground state structure of the orthorhombic and rhombohedral phases, and Gamma-TO phonon frequencies in cubic and rhombohedral phases of KNbO3 were calculated and found to be in good agreement with the experimental data and with the first-principles calculations available.Comment: 7 pages, 2 Postscript figures, uses psfig.tex. To be published in Phys.Rev.B 54, No.4 (1996