Coherent state quantization of paragrassmann algebras

By using a coherent state quantization of paragrassmann variables, operators are constructed in finite Hilbert spaces. We thus obtain in a straightforward way a matrix representation of the paragrassmann algebra. This algebra of finite matrices realizes a deformed Weyl-Heisenberg algebra. The study of mean values in coherent states of some of these operators lead to interesting conclusions.Comment: We provide an erratum where we improve upon our previous definition of odd paragrassmann algebra

On causality, apparent 'superluminality' and reshaping in barrier penetration

We consider tunnelling of a non-relativistic particle across a potential barrier. It is shown that the barrier acts as an effective beam splitter which builds up the transmitted pulse from the copies of the initial envelope shifted in the coordinate space backwards relative to the free propagation. Although along each pathway causality is explicitly obeyed, in special cases reshaping can result an overall reduction of the initial envelope, accompanied by an arbitrary coordinate shift. In the case of a high barrier the delay amplitude distribution (DAD) mimics a Dirac $\delta$-function, the transmission amplitude is superoscillatory for finite momenta and tunnelling leads to an accurate advancement of the (reduced) initial envelope by the barrier width. In the case of a wide barrier, initial envelope is accurately translated into the complex coordinate plane. The complex shift, given by the first moment of the DAD, accounts for both the displacement of the maximum of the transmitted probability density and the increase in its velocity. It is argued that analysing apparent 'superluminality' in terms of spacial displacements helps avoid contradiction associated with time parameters such as the phase time

Linewidths in bound state resonances for helium scattering from Si(111)-(1x1)H

Helium-3 spin-echo measurements of resonant scattering from the Si(111)–(1 × 1)H surface, in the energy range 4–14 meV, are presented. The measurements have high energy resolution yet they reveal bound state resonance features with uniformly broad linewidths. We show that exact quantum mechanical calculations of the elastic scattering, using the existing potential for the helium/Si(111)–(1 × 1)H interaction, cannot reproduce the linewidths seen in the experiment. Further calculations rule out inelastic and other mechanisms that might give rise to losses from the elastic scattering channels. We show that corrugation in the attractive part of the atom–surface potential is the most likely origin of the experimental lineshapes

Compact and Loosely Bound Structures in Light Nuclei

A role of different components in the wave function of the weakly bound light nuclei states was studied within the framework of the cluster model, taking into account of orbitals "polarization". It was shown that a limited number of structures associated with the different modes of nucleon motion can be of great importance for such systems. Examples of simple and quite flexible trial wave functions are given for the nuclei $^8$Be, $^6$He. Expressions for the microscopic wave functions of these nuclei were found and used for the calculation of basic nuclear characteristics, using well known central-exchange nucleon-nucleon potentials.Comment: 19 pages, 3 ps figure

Two-photon correlations as a sign of sharp transition in quark-gluon plasma

The photon production arising due to time variation of the medium has been considered. The Hamilton formalism for photons in time-variable medium (plasma) has been developed with application to inclusive photon production. The results have been used for calculation of the photon production in the course of transition from quark-gluon phase to hadronic phase in relativistic heavy ion collisions. The relative strength of the effect as well as specific two- photon correlations have been evaluated. It has been demonstrated that the opposite side two-photon correlations are indicative of the sharp transition from the quark-gluon phase to hadrons.Comment: 23 pages, 2 figure

Radioactive decays at limits of nuclear stability

The last decades brought an impressive progress in synthesizing and studying properties of nuclides located very far from the beta stability line. Among the most fundamental properties of such exotic nuclides, usually established first, is the half-life, possible radioactive decay modes, and their relative probabilities. When approaching limits of nuclear stability, new decay modes set in. First, beta decays become accompanied by emission of nucleons from highly excited states of daughter nuclei. Second, when the nucleon separation energy becomes negative, nucleons start to be emitted from the ground state. Here, we present a review of the decay modes occurring close to the limits of stability. The experimental methods used to produce, identify and detect new species and their radiation are discussed. The current theoretical understanding of these decay processes is overviewed. The theoretical description of the most recently discovered and most complex radioactive process - the two-proton radioactivity - is discussed in more detail.Comment: Review, 68 pages, 39 figure

Effective Non-Hermitian Hamiltonians for Studying Resonance Statistics in Open Disordered Systems

We briefly discuss construction of energy-dependent effective non-hermitian hamiltonians for studying resonances in open disordered systemsComment: Latex, 20 pages, 1 fig. Expanded version of a talk at the Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics IX, June 21-24 2010, Zhejiang University, Hangzhou, China. Accepted for publication in the Internationa Journal of Theoretical Physics (Springer Verlag

New q-deformed coherent states with an explicitly known resolution of unity

We construct a new family of q-deformed coherent states $|z>_q$, where $0 < q < 1$. These states are normalizable on the whole complex plane and continuous in their label $z$. They allow the resolution of unity in the form of an ordinary integral with a positive weight function obtained through the analytic solution of the associated Stieltjes power-moment problem and expressed in terms of one of the two Jacksons's $q$-exponentials. They also permit exact evaluation of matrix elements of physically-relevant operators. We use this to show that the photon number statistics for the states is sub-Poissonian and that they exhibit quadrature squeezing as well as an enhanced signal-to-quantum noise ratio over the conventional coherent state value. Finally, we establish that they are the eigenstates of some deformed boson annihilation operator and study some of their characteristics in deformed quantum optics.Comment: LaTeX, 26 pages, contains 9 eps figure

Local Density Approximation for proton-neutron pairing correlations. I. Formalism

In the present study we generalize the self-consistent Hartree-Fock-Bogoliubov (HFB) theory formulated in the coordinate space to the case which incorporates an arbitrary mixing between protons and neutrons in the particle-hole (p-h) and particle-particle (p-p or pairing) channels. We define the HFB density matrices, discuss their spin-isospin structure, and construct the most general energy density functional that is quadratic in local densities. The consequences of the local gauge invariance are discussed and the particular case of the Skyrme energy density functional is studied. By varying the total energy with respect to the density matrices the self-consistent one-body HFB Hamiltonian is obtained and the structure of the resulting mean fields is shown. The consequences of the time-reversal symmetry, charge invariance, and proton-neutron symmetry are summarized. The complete list of expressions required to calculate total energy is presented.Comment: 22 RevTeX page