Coherence parameter, defined

One extension in which there is now renewed interest was performed by the group at Stirling. This was to perform a full polarisation analysis of the coincident photons from which the Stokes parameters may be obtained. The state which was studied was the 3 P state of helium which decays to the 2 S state by emission of a visible photon (501.6nm) in addition to the decay to the ground state with a uv photon (53.7nm). The photons are viewed normal to the scattering plane and the Stokes parameters associated with the linear (ni and ria) circular polarisation (TI2) measurements were obtained. The coherence of a photon beam can be denoted by the coherence parameter defined as... 

Again, these solutions are identical to those derived by Miranowicz et al. [3] [compare Eq. (25) in Ref. 1]. Of course, we can write the equations for arbitrary value of the parameter N and hence, get the formulas for the probability amplitudes for the n-photon state expansion of the FD coherent state defined in the iV-dimensional Hilbert space. In general, for any dimension N and arbitrary real periodic function /(f) with the period T, we find that the system evolves at t = kT into the state [33]... 

Electron Nuclear Dynamics (48) departs from a variational form where the state vector is both explicitly and implicitly time-dependent. A coherent state formulation for electron and nuclear motion is given and the relevant parameters are determined as functions of time from the Euler equations that define the stationary point of the functional. Yngve and his group have currently implemented the method for a determinantal electronic wave function and products of wave packets for the nuclei in the limit of zero width, a "classical" limit. Results are coming forth protons on methane (49), diatoms in laser fields (50), protons on water (51), and charge transfer (52) between oxygen and protons. 

If the electrolysis parameters (precursor concentrations, pH, temperature, cur-rent/potential, substrate) be defined in a precise manner, a self-regulated growth of the compound can be established, and highly (111 )-oriented zinc blende (ZB) deposits up to several p,m thickness are obtained at potentials lying at the anodic limit of the diffusion range (Fig. 3.3) [60]. Currently, the typical method of cathodic electrodeposition has been developed to yield quite compact and coherent, polycrystalline, ZB n-CdSe films of well-defined stoichiometry. The intensity of the preferred ZB(f 11) orientation obtained with as-deposited CdSe/Ni samples has been quite high [61]. 

In the conventional vision, product quality is mainly based on external, nutritive and sensory properties and is strongly directed by traders and trends. Besides tastiness and ripeness, organic consumers expect products to have properties such as vitality and coherence , which are not easy to define and thus to explain and transfer. In the past, experimental parameters have been proposed to estimate vitality and coherence , but they were neither scientifically validated nor related to a validated quality concept with relation to human health. 

To determine the phase properties of the calcined bimetallic nanoparticles, a detailed x-ray diffraction (XRD) study was carried out. The XRD data of AuPt/C showed that the diffraction patterns for the carbon-supported nanoparticles show a series of broad Bragg peaks, a picture typical for materials of limited structural coherence. Nevertheless, the peaks are defined well enough to allow a definitive phase identification and structural characterization. The diffraction patterns of Au/C and Pt/C could be unambiguously indexed into an fcc-type cubic lattice occurring with bulk gold and platinum. We estimated the corresponding lattice parameters by carefully determining... 

As far as the controls are concerned, we here consider time-continuous modulation of the system Hamiltonian, which allows for vastly more freedom compared to control that is restricted to stroboscopic pulses as in DD [42, 55, 91]. We do not rely on rapidly changing control fields that are required to approximate stroboscopic a -pulses. These features allow efficient optimization under energy constraint. On the other hand, the generation of a sequence of well-defined pulses may be preferable experimentally. We may choose the pulse timings and/or areas as continuous control parameters and optimize them with respect to a given bath spectrum. Hence, our approach encompasses both pulsed and continuous modulation as special cases. The same approach can also be applied to map out the bath spectrum by measuring the coherence decay rate for a narrow-band modulation centered at different frequencies [117]. 

The next step is the scattering by an atom. This effect is basically the addition of the scattering of the electron cloud around the nucleus, since each electron in the atom scatters part of the incident radiation in a coherent form in agreement with the Thomson equation. Owing to the fact that the electrons in an atom are located at different points within the atom, and the fact that the x-ray wavelength is of the same order as the atomic dimensions, there will be path differences between waves scattered by different electrons if these path differences are less than one wavelength, then the interference will be partially destructive [20,22,26], To describe this effect, the parameter/is defined, also called the atomic scattering factor, which is the ratio of the amplitude scattered by an atom, Aa, to the amplitude scattered by an electron, Ae, that is [21]... 

The outstanding advantage of determining all four Stokes parameters is that they define the state of polarization completely. As a consequence, the spectrum of the degree of polarization P as commonly defined as well as the spectrum of a similar quantity Ppi, referring to the phase A can be derived. The latter is closely related to the degree of coherence as introduced by Bom and Wolf (1980). It is reduced when the detected radiation comprises components with different values of A, since due to averaging one has... 

In order to assess magnetization transfer in a multiple-spin system, it is necessary to define a measure that reflects the efficiency of the transfer between two spins i and j. This parameter should reflect the amplitude of the ideal polarization transfer as well as the duration of the mixing process, because, in practice, Hartmann-Hahn transfer competes with relaxation. Relaxation effects result in a damping of the ideal polarization-transfer functions 7j . The damping due to relaxation depends not only on the structure and dynamics of the molecule that hosts the spin system of interest, but also on the actual trajectories of polarizations and coherences under a specific multiple-pulse Hartmann-Hahn mixing sequence (see Section IV.D). For specific sample conditions and a specific experiment, the coherence-transfer efficiency can be defined as the maximum of the damped magnetization-transfer function. 

The thermal stability of phase-coherent protectorate of hole pairs, which are dynamically ordered on collectivized zigzag orbitals, is defined by the formula Tc Pip) = CpD r,ho o/ 2kB 2Tj +Tf)] [5,6]. Here, the parameter C <1 takes into account the compatibility of given BS with the potential extra-relief from dopant ions, ks is the Boltzmann constant, ficOo 2.06 eV is the binding energy of... 

A rigorous examination of the various MQ MAS sequences has been carried out with reference to sensitivity enhancement in the isotropic dimension and the lineshapes of the corresponding MAS peaks in the anisotropic dimension. An echo efficiency parameter has been defined as an indicator of the performance aspects of the various sequences. A consequence of the systematic analysis has been the combination of a spin-lock pulse for excitation of MQ coherences and an amplitude-modulated pulse for their conversion into observable single-quantum coherences. This approach has resulted in an improved performance over other sequences with respect to both the anisotropic lineshapes and the isotropic intensities. 

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