Barut-Girardello coherent states for u(p,q) and sp(N,R) and their macroscopic superpositions

The Barut-Girardello coherent states (BG CS) representation is extended to the noncompact algebras u(p,q) and sp(N,R) in (reducible) quadratic boson realizations. The sp(N,R) BG CS take the form of multimode ordinary Schr\"odinger cat states. Macroscopic superpositions of 2^{n-1} sp(N,R) CS (2^n canonical CS, n=1,2,...) are pointed out which are overcomplete in the N-mode Hilbert space and the relation between the canonical CS and the u(p,q) BG-type CS representations is established. The sets of u(p,q) and sp(N,R) BG CS and their discrete superpositions contain many states studied in quantum optics (even and odd N-mode CS, pair CS) and provide an approach to quadrature squeezing, alternative to that of intelligent states. New subsets of weakly and strongly nonclassical states are pointed out and their statistical properties (first- and second-order squeezing, photon number distributions) are discussed. For specific values of the angle parameters and small amplitude of the canonical CS components these states approaches multimode Fock states with one, two or three bosons/photons. It is shown that eigenstates of a squared non-Hermitian operator A^2 (generalized cat states) can exhibit squeezing of the quadratures of A.Comment: 29 pages, LaTex, 5 figures. Improvements in text, corrections in some formulas. To appear in J. Phys. A, v. 3

Nucleosome DNA sequence structure of isochores

<p>Abstract</p> <p>Background</p> <p>Significant differences in G+C content between different isochore types suggest that the nucleosome positioning patterns in DNA of the isochores should be different as well.</p> <p>Results</p> <p>Extraction of the patterns from the isochore DNA sequences by Shannon N-gram extension reveals that while the general motif YRRRRRYYYYYR is characteristic for all isochore types, the dominant positioning patterns of the isochores vary between TAAAAATTTTTA and CGGGGGCCCCCG due to the large differences in G+C composition. This is observed in human, mouse and chicken isochores, demonstrating that the variations of the positioning patterns are largely G+C dependent rather than species-specific. The species-specificity of nucleosome positioning patterns is revealed by dinucleotide periodicity analyses in isochore sequences. While human sequences are showing CG periodicity, chicken isochores display AG (CT) periodicity. Mouse isochores show very weak CG periodicity only.</p> <p>Conclusions</p> <p>Nucleosome positioning pattern as revealed by Shannon N-gram extension is strongly dependent on G+C content and different in different isochores. Species-specificity of the pattern is subtle. It is reflected in the choice of preferentially periodical dinucleotides.</p

Calculation of parameters of particles in a plasma jet and modeling of kinematic modes of spraying of wear resistant material

© 2018 Institute of Physics Publishing. All rights reserved. In this article the calculations on the strength of the coupling halves of the CV joint by the finite element method in the system of APM FEM. This calculation method is a method of creating a mathematical model and method of investigation. The assigned technological parameters of plasma spraying, namely, the estimated capacity of the plasma generator is 50 kW, and reach air temperature at the output of 3000 K, and the corresponding enthalpy of 3.8•106 j/kgK. Based on the analysis of the wear of the contact surfaces of the coupling halves, and also carried out strength calculations, was chosen as the material for plasma spraying - tungsten carbide. Developed mathematical model to determine the temperature of the powder particles and their velocities in a plasma jet. Based on the earlier dependence of the kinematic regimes of plasma spraying, the resulting system of equations for the kinematic modes that enable you to organize control of the kinematics of the deposition process details with the internal spherical surface

Uncertainty Relations in Deformation Quantization

Robertson and Hadamard-Robertson theorems on non-negative definite hermitian forms are generalized to an arbitrary ordered field. These results are then applied to the case of formal power series fields, and the Heisenberg-Robertson, Robertson-Schr\"odinger and trace uncertainty relations in deformation quantization are found. Some conditions under which the uncertainty relations are minimized are also given.Comment: 28+1 pages, harvmac file, no figures, typos correcte

Robertson Intelligent States

Diagonalization of uncertainty matrix and minimization of Robertson inequality for n observables are considered. It is proved that for even n this relation is minimized in states which are eigenstates of n/2 independent complex linear combinations of the observables. In case of canonical observables this eigenvalue condition is also necessary. Such minimizing states are called Robertson intelligent states (RIS). The group related coherent states (CS) with maximal symmetry (for semisimple Lie groups) are particular case of RIS for the quadratures of Weyl generators. Explicit constructions of RIS are considered for operators of su(1,1), su(2), h_N and sp(N,R) algebras. Unlike the group related CS, RIS can exhibit strong squeezing of group generators. Multimode squared amplitude squeezed states are naturally introduced as sp(N,R) RIS. It is shown that the uncertainty matrices for quadratures of q-deformed boson operators a_{q,j} (q > 0) and of any k power of a_j = a_{1,j} are positive definite and can be diagonalized by symplectic linear transformations. PACS numbers: 03.65.Fd, 42.50.DvComment: 23 pages, LaTex. Minor changes in text and references. Accepted in J. Phys.

Characterizing heralded single-photon sources with imperfect measurement devices

Any characterization of a single-photon source is not complete without specifying its second-order degree of coherence, i.e., its $g^{(2)}$ function. An accurate measurement of such coherence functions commonly requires high-precision single-photon detectors, in whose absence, only time-averaged measurements are possible. It is not clear, however, how the resulting time-averaged quantities can be used to properly characterize the source. In this paper, we investigate this issue for a heralded source of single photons that relies on continuous-wave parametric down-conversion. By accounting for major shortcomings of the source and the detectors--i.e., the multiple-photon emissions of the source, the time resolution of photodetectors, and our chosen width of coincidence window--our theory enables us to infer the true source properties from imperfect measurements. Our theoretical results are corroborated by an experimental demonstration using a PPKTP crystal pumped by a blue laser, that results in a single-photon generation rate about 1.2 millions per second per milliwatt of pump power. This work takes an important step toward the standardization of such heralded single-photon sources.Comment: 18 pages, 9 figures; corrected Eq. (11) and the description follows Eq. (22