Grand Unification, Axion, and Inflation in Intermediate Scale Supersymmetry

A class of supersymmetric grand unified theories is introduced that has a single scale below the cutoff, that of the supersymmetry breaking masses $\tilde{m}$. For a wide range of the dimensionless parameters, agreement with the observed mass of the Higgs boson determines $\tilde{m} \sim 10^9-10^{13} {\rm GeV}$, yielding Intermediate Scale Supersymmetry. We show that within this framework it is possible for seesaw neutrino masses, axions, and inflation to be described by the scale $\tilde{m}$, offering the possibility of a unified origin of disparate phenomena. Neutrino masses allowing for thermal leptogenesis can be obtained, and the axion decay constant lies naturally in the range $f_a \sim 10^9-10^{11} {\rm GeV}$, consistent with a recent observational suggestion of high scale inflation. A minimal $SU(5)$ model is presented that illustrates these features. In this model, the only states at the grand unified scale are those of the heavy gauge supermultiplet. The grand unified partners of the Higgs doublets have a mass of order $\tilde{m}$, leading to the dominant proton decay mode $p \rightarrow \bar{\nu} K^+$, which may be probed in upcoming experiments. Dark matter may be winos, with mass environmentally selected to the TeV scale, and/or axions. Gauge coupling unification is found to be successful, especially if the wino is at the TeV scale.Comment: 27 pages, 7 figures; minor corrections, references and discussion adde

Empiric Models of the Earth's Free Core Nutation

Free core nutation (FCN) is the main factor that limits the accuracy of the modeling of the motion of Earth's rotational axis in the celestial coordinate system. Several FCN models have been proposed. A comparative analysis is made of the known models including the model proposed by the author. The use of the FCN model is shown to substantially increase the accuracy of the modeling of Earth's rotation. Furthermore, the FCN component extracted from the observed motion of Earth's rotational axis is an important source for the study of the shape and rotation of the Earth's core. A comparison of different FCN models has shown that the proposed model is better than other models if used to extract the geophysical signal (the amplitude and phase of FCN) from observational data.Comment: 8 pages, 3 figures; minor update of the journal published versio

MnAs dots grown on GaN(0001)-(1x1) surface

MnAs has been grown by means of MBE on the GaN(0001)-(1x1) surface. Two options of initiating the crystal growth were applied: (a) a regular MBE procedure (manganese and arsenic were delivered simultaneously) and (b) subsequent deposition of manganese and arsenic layers. It was shown that spontaneous formation of MnAs dots with the surface density of 1$\cdot 10^{11}$ cm$^{-2}$ and $2.5\cdot 10^{11}$ cm$^{-2}$, respectively (as observed by AFM), occurred for the layer thickness higher than 5 ML. Electronic structure of the MnAs/GaN systems was studied by resonant photoemission spectroscopy. That led to determination of the Mn 3d - related contribution to the total density of states (DOS) distribution of MnAs. It has been proven that the electronic structures of the MnAs dots grown by the two procedures differ markedly. One corresponds to metallic, ferromagnetic NiAs-type MnAs, the other is similar to that reported for half-metallic zinc-blende MnAs. Both system behave superparamagnetically (as revealed by magnetization measurements), but with both the blocking temperatures and the intra-dot Curie temperatures substantially different. The intra-dot Curie temperature is about 260 K for the former system while markedly higher than room temperature for the latter one. Relations between growth process, electronic structure and other properties of the studied systems are discussed. Possible mechanisms of half-metallic MnAs formation on GaN are considered.Comment: 20+ pages, 8 figure

Conditional Intensity and Gibbsianness of Determinantal Point Processes

The Papangelou intensities of determinantal (or fermion) point processes are investigated. These exhibit a monotonicity property expressing the repulsive nature of the interaction, and satisfy a bound implying stochastic domination by a Poisson point process. We also show that determinantal point processes satisfy the so-called condition $(\Sigma_{\lambda})$ which is a general form of Gibbsianness. Under a continuity assumption, the Gibbsian conditional probabilities can be identified explicitly.Comment: revised and extende

Eigenfunctions decay for magnetic pseudodifferential operators

We prove rapid decay (even exponential decay under some stronger assumptions) of the eigenfunctions associated to discrete eigenvalues, for a class of self-adjoint operators in $L^2(\mathbb{R}^d)$ defined by ``magnetic'' pseudodifferential operators (studied in \cite{IMP1}). This class contains the relativistic Schr\"{o}dinger operator with magnetic field

Detection of Phase Jumps of Free Core Nutation of the Earth and their Concurrence with Geomagnetic Jerks

We detected phase jumps of the Free Core Nutation (FCN) of the Earth directly from the analysis of the Very Long Baseline Interferometer (VLBI) observation of the Earth rotation for the period 1984-2003 by applying the Weighted Wavelet Z-Transform (WWZ) method and the Short-time Periodogram with the Gabor function (SPG) method. During the period, the FCN had two significant phase jumps in 1992 and 1998. These epochs coincide with the reported occurrence of geomagnetic jerks.Comment: 8 pages, 4 figure