Orbital moment in CoO and in NiO

The total, orbital and spin moment of the Co2+ ion in CoO has been calculated within the quasi-atomic approach with taking into account strong correlations, crystal-field interactions and the intra-atomic spin-orbit coupling. The orbital moment of 1.39 \mu B amounts at 0 K, in the magnetically-ordered state, to more than 34% of the total moment (4.01 \mu B). The same calculations yield for NiO the orbital and total moment of 0.46 \mu B and 2.45 \mu B, respectively. PACS No: 71.70.E; 75.10.D Keywords: 3d magnetism, crystal field, spin-orbit coupling, orbital moment, CoO, NiOComment: 6 pages in tex+3 figs, submitted for PNSXM-03, Venic

Orbital and Spin Excitations in Cobalt Oxide

By means of neutron scattering we have determined new branches of magnetic excitations in orbitally active CoO (TN=290 K) up to 15 THz and for temperatures from 6 K to 450 K. Data were taken in the (111) direction in six single-crystal zones. From the dependence on temperature and Q we have identified several branches of magnetic excitation. We describe a model for the coupled orbital and spin states of Co2+ subject to a crystal field and tetragonal distortion.Comment: To be published in Physica B (Proceedings of SCES07 conference in Houston

Quantum Mechanical Properties of Bessel Beams

Bessel beams are studied within the general framework of quantum optics. The two modes of the electromagnetic field are quantized and the basic dynamical operators are identified. The algebra of these operators is analyzed in detail; it is shown that the operators that are usually associated to linear momentum, orbital angular momentum and spin do not satisfy the algebra of the translation and rotation group. In particular, what seems to be the spin is more similar to the helicity. Some physical consequences of these results are examined.Comment: 17 pages, no figures. New versio

Levinson's theorem for the Schr\"{o}dinger equation in two dimensions

Levinson's theorem for the Schr\"{o}dinger equation with a cylindrically symmetric potential in two dimensions is re-established by the Sturm-Liouville theorem. The critical case, where the Schr\"{o}dinger equation has a finite zero-energy solution, is analyzed in detail. It is shown that, in comparison with Levinson's theorem in non-critical case, the half bound state for $P$ wave, in which the wave function for the zero-energy solution does not decay fast enough at infinity to be square integrable, will cause the phase shift of $P$ wave at zero energy to increase an additional $\pi$.Comment: Latex 11 pages, no figure and accepted by P.R.A (in August); Email: [email protected], [email protected]

The Relativistic Levinson Theorem in Two Dimensions

In the light of the generalized Sturm-Liouville theorem, the Levinson theorem for the Dirac equation in two dimensions is established as a relation between the total number $n_{j}$ of the bound states and the sum of the phase shifts $\eta_{j}(\pm M)$ of the scattering states with the angular momentum $j$: $$\eta_{j}(M)+\eta_{j}(-M)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$$ $$~~~=\left\{\begin{array}{ll} (n_{j}+1)\pi &{\rm when~a~half~bound~state~occurs~at}~E=M ~~{\rm and}~~ j=3/2~{\rm or}~-1/2\\ (n_{j}+1)\pi &{\rm when~a~half~bound~state~occurs~at}~E=-M~~{\rm and}~~ j=1/2~{\rm or}~-3/2\\ n_{j}\pi~&{\rm the~rest~cases} . \end{array} \right.$$ \noindent The critical case, where the Dirac equation has a finite zero-momentum solution, is analyzed in detail. A zero-momentum solution is called a half bound state if its wave function is finite but does not decay fast enough at infinity to be square integrable.Comment: Latex 14 pages, no figure, submitted to Phys.Rev.A; Email: [email protected], [email protected]

The origin of human chromosome 2 analyzed by comparative chromosome mapping with a DNA microlibrary

Fluorescencein situ hybridization (FISH) of microlibraries established from distinct chromosome subregions can test the evolutionary conservation of chromosome bands as well as chromosomal rearrangements that occurred during primate evolution and will help to clarify phylogenetic relationships. We used a DNA library established by microdissection and microcloning from the entire long arm of human chromosome 2 for fluorescencein situ hybridization and comparative mapping of the chromosomes of human, great apes (Pan troglodytes, Pan paniscus, Gorilla gorilla, Pongo pygmaeus) and Old World monkeys (Macaca fuscata andCercopithecus aethiops). Inversions were found in the pericentric region of the primate chromosome 2p homologs in great apes, and the hybridization pattern demonstrates the known phylogenetically derived telomere fusion in the line that leads to human chromosome 2. The hybridization of the 2q microlibrary to chromosomes of Old World monkeys gave a different pattern from that in the gorilla and the orang-utan, but a pattern similar to that of chimpanzees. This suggests convergence of chromosomal rearrangements in different phylogenetic lines

Levinson's Theorem for the Klein-Gordon Equation in Two Dimensions

The two-dimensional Levinson theorem for the Klein-Gordon equation with a cylindrically symmetric potential $V(r)$ is established. It is shown that $N_{m}\pi=\pi (n_{m}^{+}-n_{m}^{-})= [\delta_{m}(M)+\beta_{1}]-[\delta_{m}(-M)+\beta_{2}]$, where $N_{m}$ denotes the difference between the number of bound states of the particle $n_{m}^{+}$ and the ones of antiparticle $n_{m}^{-}$ with a fixed angular momentum $m$, and the $\delta_{m}$ is named phase shifts. The constants $\beta_{1}$ and $\beta_{2}$ are introduced to symbol the critical cases where the half bound states occur at $E=\pm M$.Comment: Revtex file 14 pages, submitted to Phys. Rev.

A pulsed source of continuous variable polarization entanglement

We have experimentally demonstrated polarization entanglement using continuous variables in an ultra-short pulsed laser system at telecommunication wavelengths. Exploiting the Kerr-nonlinearity of a glass fibre we generated a polarization squeezed pulse with S2 the only non-zero Stokes parameter thus S1 and S3 being the conjugate pair. Polarization entanglement was generated by interference of the polarization squeezed field with a vacuum on a 50:50 beam splitter. The two resultant beams exhibit strong quantum noise correlations in S1 and S3. The sum noise signal of S3 was at the respective shot noise level and the difference noise signal of S1 fell 2.9dB below this value

Levinson's Theorem for Non-local Interactions in Two Dimensions

In the light of the Sturm-Liouville theorem, the Levinson theorem for the Schr\"{o}dinger equation with both local and non-local cylindrically symmetric potentials is studied. It is proved that the two-dimensional Levinson theorem holds for the case with both local and non-local cylindrically symmetric cutoff potentials, which is not necessarily separable. In addition, the problems related to the positive-energy bound states and the physically redundant state are also discussed in this paper.Comment: Latex 11 pages, no figure, submitted to J. Phys. A Email: [email protected], [email protected]

Heating of gas inside radio sources to mildly relativistic temperatures via induced Compton scattering

Measured values of the brightness temperature of low-frequency synchrotron radiation emitted by powerful extragalactic sources reach 10^11--10^12 K. If some amount of nonrelativistic ionized gas is present within such sources, it should be heated as a result of induced Compton scattering of the radiation. If this heating is counteracted by cooling due to inverse Compton scattering of the same radio radiation, then the plasma can be heated up to mildly relativistic temperatures kT~10--100 keV. The stationary electron velocity distribution can be either relativistic Maxwellian or quasi-Maxwellian (with the high-velocity tail suppressed), depending on the efficiency of Coulomb collisions and other relaxation processes. We derive several easy-to-use approximate expressions for the induced Compton heating rate of mildly relativistic electrons in an isotropic radiation field, as well as for the stationary distribution function and temperature of electrons. We also give analytic expressions for the kernel of the integral kinetic equation (one as a function of the scattering angle and another for the case of an isotropic radiation field), which describes the redistribution of photons in frequency caused by induced Compton scattering in thermal plasma. These expressions can be used in the parameter range hnu<< kT<~ 0.1mc^2 (the formulae earlier published in Sazonov, Sunyaev, 2000 are less accurate).Comment: 22 pages, 7 figures, submitted to Astronomy Letter