An effective method of investigation of positive maps on the set of positive definite operators

Let $\text{A}$₁ be the algebra of linear operators on the n-dimensional Hilbert space $\text{H}$₁, and let $\text{A}$₂ be the algebra of linear operators of the m-dimensional Hilbert space $\text{H}$₂. Let $\text{L}$($\text{A}$₁, $\text{A}$₂) denote the complex space of linear maps from $\text{A}$₁ to $\text{A}$₂. By a positive map we mean an element of the space $\text{L}$($\text{A}$₁, $\text{A}$₂) (superoperator with respect to $\text{H}$₁) which maps positive definite operators in $\text{A}$₁ into positive definite operators in $\text{A}$₂. The aim of this paper is to present an effective method which allows to verify whether a given superoperator Λ∈$\text{L}$($\text{A}$₁, $\text{A}$₂) is a positive map. Besides that necessary and sufficient conditions for the positive definiteness of even-degree forms in many variables are given.     

Elastic constants of single crystals of the three phases of In---Pb alloys

In a study of the elastic behaviour of the InPb alloys, the elastic stiffness tensor components of crystals of each of the three phases (fct, $\text{c}\text{a}\text{> 1}$; fct, $\text{c}\text{a}\text{> 1}$; fcc) have been obtained as a function of temperature from pulse superposition measurements of ultrasonic wave velocities. Comparison of the elastic stiffness constants obtained for a fct ($\text{c}\text{a}\text{> 1}$) 5 atm.% Pb alloy with those of In itself and those of InTl and InCd alloys, establishes for this phase that alloying with Pb, as with TI and Cd, enhances the softening of the acoustic [110] phonon mode, polarization [1$\text{1}$0] near the Brillouin zone centre. The elastic properties of a 17 atm.% Pb crystal, which is in the fct ($\text{c}\text{a}\text{> 1}$) phase, are quite different from those shown by In alloys in the fct ($\text{c}\text{a}\text{> 1}$ phase; in particular the response to a shear stress is remarkably isotropie: there is no phonon mode softening in this alloy. Neither is there softening of this mode (which corresponds at the zone centre to the shear stiffness $\text{1}\text{2}$(C₁₁;C₁₂)) in crystals of the fee phase — in complete contrast to the dominating influence of the softening of $\text{1}\text{2}$(C₁₁;C₁₂) in the InTl and InCd fee alloys. In fact for a fcc In-75 atm.% Pb alloy the anistropy ratio for shear $\text{2C}{}_{44}\text{(C}{}_{11}\text{C}{}_{12}\text{)}$ is close to unity. The transitions between the three phases of the InPb alloys are markedly first order and acoustic mode softening has a much smaller influence on the elastic behaviour of the fct ($\text{c}\text{a}\text{< 1}$) and fcc InPb alloys than it has on the fct ($\text{c}\text{a}\text{< 1}$) InPb, InCd and InTl alloys.     

Comparison of pp and pp interactions at s = 53 GeV

Results are presented from the first p$\text{p}$ colliding beam runs at the CERN ISR, using the UA5 streamer chamber detector. p$\text{p}$ interactions at $\text{s}\text{= 53}\text{GeV}$ are compared with pp data taken in the same experiment. The results are in good agreement with extrapolations of low-energy p$\text{p}$ data.     

AES,photoemission and work function study of the deposition of Cs on (100) and (111)B GaAs epitaxial layers

Work function, photoemission and AES measurements have been made on (100) and (111)B epitaxial GaAs layers as a function of caesium coverage. It has been shown that the photoemission maximum and work function minimum occur at a coverage of $\text{2}\text{3}$ of a monolayer. The reduction of the work function takes place in distinct stages with changes in the rate of fall occurring at $\text{1}\text{8}$ and $\text{1}\text{2}$ of a monolayer for the (111)B face and $\text{1}\text{8}$, $\text{1}\text{4}$, $\text{1}\text{3}$ and $\text{1}\text{2}$ of a monolayer for the (100) face. This indicates the presence of specific adsorption sites which have not been observed in previous work on these faces.     

The energy spectra and electromagnetic transitions of odd-a titanium isotopes

The isotopes ^{55, 47, 49, 51}Ti are studied in the framework of the deformed configuration mixing shell model. The calculated spectra and electromagnetic properties agree well with the observed ones. The calculations suggest the existence of an excited $\text{K =}\text{1}\text{2}$ band of states in ^{45, 47, 49}Ti and a $\text{K =}\text{7}\text{2}$ band in ⁵¹Ti. In ⁴⁹Ti this excited $\text{K =}\text{1}\text{2}$ band is more deformed than the “ground state band”. On the basis of the overall agreement between the calculated and experimental spectra and decay properties we suggest the spin assignments $\text{J =}\text{5}\text{2}$, $\text{7}\text{2}$, $\text{9}\text{2}$, $\text{5}\text{2}$ and $\text{7}\text{2}$ to the states in ⁴⁷Ti observed at 2.168, 2.97, 2.408, 2.835 and 3.223 MeV, respectively.     

Analysis of derivative spectrum of indirect exciton absorption in silicon

It is shown that an analysis of the wavelength modulated absorption spectrum enables us to estimate the transition matrix elements in indirect absorption. The transition matrix elements in silicon are determined to be $\text{0.110}\text{h}\text{?}\text{A}\text{?}$ for indirect absorption with the TO phonon, $\text{0.0367}\text{h}\text{?}\text{A}\text{?}$ for the LO phonon and 0.0178 $\text{h}\text{?}\text{A}\text{?}$ for the TA phonon.     

Triality,exotics and the dynamical basis of the quark model

A non-relativistic three-triplet model with a simple two-body interaction is shown to bind only q$\text{q}$ and qqq states. Three triplets and unobserved charmed states are crucial in preventing binding of 4q$\text{q}$ and 2 q$\text{q}$ systems. They provide repulsive channels to make the q$\text{q}$ and 3q systems behave like “neutral atoms” with canceling attractive and repulsive forces between them and additional quarks. The ratio of q$\text{q}$ and qq interactions is just right to bind the q$\text{q}$ and 3q systems properly while leaving the qq system with the mass of a quark.     

The magnetic-non magnetic transition of cerium impurities in lanthanum-thorium based alloys

A simple theoretical model which assumes a linear increase with thorium concentration for the cerium 4? level with respect to the Fermi level can explain both the decrease $\text{ΔT}{}_{\mathrm{c}}\text{c}$ of the superconducting temperature and the logarithmic slope $\text{d}\text{ρ}\text{c}\text{dln}\text{T}$ of the Kondo resistivity in LaTh based alloys with cerium impurities. The model yields two different maxima for |$\text{d}\text{ρ}\text{c}\text{dln}\text{T}$| and $\text{ΔT}{}_{\mathrm{c}}\text{c}$, the second one of which occurs when the resistivity minimum disappears, in very good agreement with experimental data.     

Test of amplitude signs in pion photoproduction predicted by the transformation from current to constituent quarks

The transformation from current to constituent quark basis states is discussed as it applies to relating amplitudes for photon-nucleon decays of baryon resonances. The predictions for the relative signs of pion photoproduction amplitudes through baryon resonances in the $\text{70}\text{L = 1}$ and $\text{56}\text{L = 2}$ multiplets are presented and compared with experiment. Theory and experiment are found to be completely, with the pion-nucleom decay amplitudes of resonances in the $\text{70}\text{L = 1}$ having the signs characteristic of the $\text{3,}\text{3}\text{)?(}\text{3}\text{, 3)}$ rather than (8, 1)?(1, 8) term in the transformation axial-vector charge.     

Signatures of excited leptons in pp̄ collisions

We argue that the coupling strength of excited leptons to Z⁰ and W^± could be large. If excited leptons $\text{l}$¹ decay mainly radiatively they will produce a clean $\text{l}$⁺$\text{l}$^?γ signature in pp? → Z⁰ → $\text{l}$¹$\text{l}$ → $\text{l}$⁺$\text{l}$^?γ . For $\text{m}{}_{\mathrm{<mtext>l</mtext>}}{}^1\text{?40}$ GeV the photon always follows the less energetic lepton and this system has a fairly small invariant mass. The ratio of $\text{l}$⁺$\text{l}$^?γ final states to $\text{l}$⁺$\text{l}$^? final states, with the photon-lepton angle less than 90°, could be as high as 25%, an order of magnitude larger than expected from bremsstrahlung.     

Mössbauer effect studies of excited states of 155Gd

Mössbauer effect studies of the 60.0, 86.5 and 105.3 keV transitions of ¹⁵⁵Gd, yield the following nuclear parameters: $\text{τ}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(60}\text{keV level}\text{) = 194 ± 15}\text{ps}$, $\text{g(87)}\text{g(0)}\text{= 1.235 ± 0.008}$, $\text{g(105)}\text{g(0)}\text{= 2.01 ± 0.05 or ?0.55 ± 0.05}$; $\text{Q(87)}\text{Q(0)}\text{= +0.087 ± 0.006}$ and $\text{Q(105)}\text{Q(0)}\text{= 1.00 ± 0.03}$ or $\text{Q(87)}\text{Q(0)}\text{= ?0.083 ± 0.008}$ and $\text{Q(105)}\text{Q(0)}\text{= = 1.16 ± 0.03}$. Theoretical considerations favour the first set of values of $\text{Q(87)}\text{Q(0)}$ and $\text{Q(105)}\text{Q(0)}$.     

Effect of Bragg-Williams disorder on reconstructed polar surfaces of tetrahedrally coordinated compound semiconductors by optically simulated leed patterns

Laser generated optical diffraction patterns obtained from two-dimensional model gratings have been used to simulate the surface reconstructions observed by LEED with the polar surfaces of tetrahedrally coordinated compound semiconductors. The 2 × 2 and $\text{4}\text{3}\text{× 4}\text{3}\text{?30°}$ reconstructions conform ideally with the $\text{1}\text{4}$-monolayer criterion dictated by bonding ionicity [Nosker, Mark and Levine, Surface Science 19 (1970) 291] while the 3 × 3, $\text{3}\text{×}\text{3}\text{?30°}$ and $\text{19}\text{×}\text{19}\text{?23.4°}$ reconstructions do not. It is shown that the introduction of Bragg-Williams disorder that preserves long-range order into the latter structures does permit the achievement of conformity with the $\text{1}\text{4}$-monolayer criterion without altering the symmetry of the diffraction pattern. Specifically the intensities of the fractional order beams are reduced relative to those of the integral order beams. Thus all the observed reconstruction LEED patterns can be consistent with the $\text{1}\text{4}$-monolayer criterion, provided account is taken of the insensitivity of LEED to surface defect structure.     

Lattice specific heat of copper based dilute alloys at low temperature

The low-temperature lattice specific heat of copper-based dilute alloys $\text{Cu}$ Sn, $\text{Cu}$ Ga, $\text{Cu}$ Ge, $\text{Cu}$ Zn and $\text{Cu}$ Ni has been studied theoretically on the basis of Green's function theory. A nearest-neighbour impurity model, with certral and non-central force constant changes has been employed. The effect of volume change is taken into account, and is seen to be important. The calculated results are in excellent agreement with experimental measurements, and the derived force constants are seen to be reasonable.     

Decays of 185m + gHg: Low-spin levels of 185Au as a test of nuclear models

The decay of ^{185m + g}Hg has been studied on-line with mass-separated sources from the ISOCELE facility. Precise conversion-electron measurements were performed with a 180° spectrograph. The $\text{13}\text{2}{}^{\mathrm{+}}$ isomeric state of ¹⁸⁵Hg ($\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 28 ± 5 s}$) was located with respect to the $\text{1}\text{2}$^? ground state ($\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 55 ± 10 s}$). A level scheme of ¹⁸⁵Au has been established. Two abnormally converted M1 transitions de-excite a state local at 330.2 keV. Excited states of ¹⁸⁵Au have been discussed in the framework of a “quasi-particle + axial rotor” approach, quasi-particle states being issued from Hartree-Fock plus BCS calculations using the SIII Skyrme force. Most of the low-spin negative-parity levels have been identified as h_{$\text{9}\text{2}$} + f _{$\text{5}\text{2}$} or p_{$\text{3}\text{2}$} + f_{$\text{7}\text{2}$} mixed states. The h_{$\text{11}\text{2}$} system has also been discussed using a model of asingle-j quasi-particle coupled to a triaxial rotor.     

Complete N=4 structure of low-energy effective action in N=4 super-Yang–Mills theories

Using the $\text{N}\text{=2}$ superfield approach, we construct full $\text{N}\text{=4}$ supersymmetric low-energy effective actions for $\text{N}\text{=4}$ SYM models, with both $\text{N}\text{=2}$ gauge superfield strengths and hypermultiplet superfields included. The basic idea is to complete the known non-holomorphic effective potentials which depend only on $\text{N}\text{=2}$ superfield strengths W and W̄ to the full on-shell $\text{N}\text{=4}$ invariants by adding the appropriate superfield hypermultiplet terms. We prove that the effective potentials of the form $\text{ln}\text{W}\text{ln}\text{W}\text{̄}$ can be $\text{N}\text{=4}$ completed in this way and present the precise structure of the corresponding completions. However, the effective potentials of the non-logarithmic form suggested in hep-th/9811017 and hep-th/9909020 do not admit the $\text{N}\text{=4}$ completion. Therefore, such potentials cannot come out as (perturbative or non-perturbative) quantum corrections in $\text{N}\text{=4}$ SYM models.     

Intrinsic and rotational excitations in 175Lu

The γ-ray cascades following the ¹⁷⁶Yb(p, 2n)¹⁷⁵Lu reaction are studied with Ge(Li) detectors and interpreted within the level scheme of ¹⁷⁵Lu. According to this interpretation the $\text{1}\text{2}$⁺[411], $\text{1}\text{2}$^?[541], $\text{5}\text{2}$⁺[402], $\text{7}\text{2}$⁺[404] and $\text{9}\text{2}$^?[514] rotat $\text{15}\text{2}$⁺, $\text{21}\text{2}$^?, $\text{13}\text{2}$⁺, $\text{19}\text{2}$⁺ and $\text{19}\text{2}$^? members, respectively. Fu band head is determined to be 626.6 keV. The data for the rotational bands are discussed within the particle-rotor model and compared with the available information on the corresponding bands in the adjacent Lu isotopes.     

Spins and lifetimes of levels in 55Mn

The study of excited ⁵⁵Mn levels with the ⁵²Cr(α, pγ) reaction was extended to levels up to 3161 keV. With a Ge(Li) detector, DSA measurements in gold-backed targets were made, as well as angular correlations; both of these experiments were done in coincidence with protons detected near 180°. A multiple-detector NaI(Tl) array was also used in the same reaction geometry for better γ-ray detection efficiency. Mean lifetimes of 12 levels from 2727 to 3161 keV are reported. Spins and sometimes parities of the following levels were deduced from the angular-correlation analyses and lifetime results: 1885 keV, $\text{7}\text{2}$^?; 2199 keV, $\text{7}\text{2}$(^?); 2311 keV, ($\text{13}\text{2}$); 2366keV, $\text{5}\text{2}$^?; 2727 keV, $\text{7}\text{2}$; 2823 keV, $\text{9}\text{2}$. Multipole mixing ratios and M1 and E2 transition rates of the radiations from these and from the 1292 keV level are presented. The similarity of the low-lying level structure and of interlevel transitions in ⁵⁵Mn to those in certain other f_{$\text{7}\text{2}$}³ nuclei is examined.     

On universality for area-preserving maps of the plane

We present detailed evidence that one-parameter families of area-preserving maps exhibit cascades of period doubling with universal geometric scaling in the parameter. We relate this behaviour to a fixed point equation of the form

$\text{Λ}{}^{\mathrm{?1}}\text{°Φ°Φ°Λ = Φ}$

and

$\text{det}\text{DΦ = 1}$

, Φ:$\text{R}$²→$\text{R}$². In particular we argue that the scaling transformation Λ:$\text{R}$²→$\text{R}$² is conjugate to the transformation Λ₀:(x, y)→(λx, μy), with λ² ≠ μ, and in fact λ² >μ. We present some numerical evidence that

$\text{δ = 8.721}$

…,

$\text{?}\text{1}\text{λ}\text{= 4.018}$

…,

$\text{1}\text{μ}\text{= 16.36}$

…, where δ is the asymptotic ratio of the differences of the parameter values corresponding to the successive periods 2^k described above.