Coherent relation

If there is no epitaxial (coherent) relation between the substrate and the growing crystals, and the nuclei formed initially have completely random orientation, and the growth rate is more or less isotropic, geometrical selection operates in one direction only perpendicular to the substrate surface. When there is an epitaxial and coherent relation between the substrate and the crystals, and the growth rate... 

Particular problems are encountered where the detector / couples to more than one S spin since the assembly of S spins can act as a unit. The result is false coherences relating the / spin to the sums or differences of the frequencies of the S spins and intensity distortions. In the worst case this can result in an HMQC spectrum in which only coherences resulting from multiple S spin transitions are seen. None of these transitions occur at the chemical shift of the S spin (Figure 12). 

The x-ray standing-wave technique represents an extremely sensitive tool for determining the position of impurity atoms within a crystal or adsorbed onto crystal surfaces. This technique is based on the x-ray standing-wave fields that arise as a result of the interference between the coherently related incident and Bragg-diffracted beams from a perfect crystal, and is described by the theory of dynamical diffraction of x-rays. ... 

As mentioned above, the XSW field arises from the interference between the coherently related incident and Bragg-diffracted beams from the surface of a perfect crystal. In the vicinity of a Bragg reflection (Fig. 24A-B), an incident plane wave (with wave vector fco) and a reflected wave (with wave vector kfi) interfere to generate a standing wave with a periodicity equivalent to that of the (h, k, 1) diffracting planes. The ratio of the electric field amplitudes of the reflected and incident waves is given by... 

Abstract We review recent developments in coherence related phenomena involving metastable states embedded in (multiple) continua via the action of (strong) laser pulses. The role of Laser-Induced Continuum Structure (LICS)... 

Waveform composed of set of discrete, coherently related sinusodial components, i.e., wave-form is described by a conventional Fourier series. "Faradaic admittance analysis (or a.c. polarography) in the coherent wave frequency multiplex mode"... 

Complete coherence of emission requires spatial (transverse) coherence, related to source divergence, and temporal (longitudinal) coherence, related to source monochromaticity. The undulator has a high spatial coherence, of the order of For example for E= 500 MeV,... 

The zirconia/mullite interphase has been examined indicating a coherent relation between both types of crystals, as is shown in Fig. 8. Only the A labeled grain shows this coherency while the B grain oriented with respect to the other does not show this effect. Therefore, the HREM allows us to distinguish the critical orientations of crystals at interphases. Domains of closure interpenetrating into the zirconia are visible at the boundary [25]. 

In the case of a non-polarized medium, the momentum-energy tensor due to the field is nidi. It follows from this that the only compatibility (or coherence) relations are given by ... 

Finite values of the off-diagonal elements p would imply that the phases of the oscillating electric dipole moments induced in different atoms were coherently related to one another. Such a situation can only be achieved if the atoms are stationary and are interacting with a beam of radiation of high spatial and temporal coherence, as for instance obtained from a laser. 

As a final point, it should again be emphasized that many of the quantities that are measured experimentally, such as relaxation rates, coherences and time-dependent spectral features, are complementary to the thennal rate constant. Their infomiation content in temis of the underlying microscopic interactions may only be indirectly related to the value of the rate constant. A better theoretical link is clearly needed between experimentally measured properties and the connnon set of microscopic interactions, if any, that also affect the more traditional solution phase chemical kinetics. 

Since there is a definite phase relation between the fiindamental pump radiation and the nonlinear source tenn, coherent SH radiation is emitted in well-defined directions. From the quadratic variation of P(2cii) with (m), we expect that the SH intensity 12 will also vary quadratically with the pump intensity 1 ... 

As the spins precess in the equatorial plane, they also undergo random relaxation processes that disturb their movement and prevent them from coming together fiilly realigned. The longer the time i between the pulses the more spins lose coherence and consequently the weaker the echo. The decay rate of the two-pulse echo amplitude is described by the phase memory time, which is the time span during which a spin can remember its position in the dephased pattern after the first MW pulse. Tyy is related to the homogeneous linewidth of the individual spin packets and is usually only a few microseconds, even at low temperatures. 

Related results of promotion (catalysis) and inliibition of stereonuitation by vibrational excitation have also been obtained for the much larger molecule, aniline-NHD (CgH NHD), which shows short-time chirality and stereonuitation [104. 105]. This kind of study opens the way to a new look at kinetics, which shows coherent and mode-selective dynamics, even in the absence of coherent external fields. The possibility of enforcing coherent dynamics by fields ( coherent control ) is discussed in chapter A3.13. 

A term that is nearly synonymous with complex numbers or functions is their phase. The rising preoccupation with the wave function phase in the last few decades is beyond doubt, to the extent that the importance of phases has of late become comparable to that of the moduli. (We use Dirac s terminology [7], which writes a wave function by a set of coefficients, the amplitudes, each expressible in terms of its absolute value, its modulus, and its phase. ) There is a related growth of literatm e on interference effects, associated with Aharonov-Bohm and Berry phases [8-14], In parallel, one has witnessed in recent years a trend to construct selectively and to manipulate wave functions. The necessary techifiques to achieve these are also anchored in the phases of the wave function components. This bend is manifest in such diverse areas as coherent or squeezed states [15,16], elecbon bansport in mesoscopic systems [17], sculpting of Rydberg-atom wavepackets [18,19], repeated and nondemolition quantum measurements [20], wavepacket collapse [21], and quantum computations [22,23], Experimentally, the determination of phases frequently utilizes measurement of Ramsey fringes [24] or similar" methods [25]. 

Coherent states and diverse semiclassical approximations to molecular wavepackets are essentially dependent on the relative phases between the wave components. Due to the need to keep this chapter to a reasonable size, we can mention here only a sample of original works (e.g., [202-205]) and some summaries [206-208]. In these, the reader will come across the Maslov index [209], which we pause to mention here, since it links up in a natural way to the modulus-phase relations described in Section III and with the phase-fiacing method in Section IV. The Maslov index relates to the phase acquired when the semiclassical wave function haverses a zero (or a singularity, if there be one) and it (and, particularly, its sign) is the consequence of the analytic behavior of the wave function in the complex time plane. 

From these relations it follows that is related to the angular momentum modulus, and that the pairs of angle a, P and y, 8 are the azimuthal, and the polar angle of the (J ) and the (L ) vector, respectively. The angle is associated with the relative orientation of the body-fixed and space-fixed coordinate frames. The probability to find the particular rotational state IMK) in the coherent state is... 

The time period A/ia which the light wave undergoes random changes is called the coherence time. It is related to the Hnewidth Av of the laser by the equation... 

The system is coherent. There is no dupHcation of units for a quantity, and all derived units are obtained by a direct one-to-one relation of base units or derived units eg, one newton is the force required to accelerate one kilogram at the rate of one meter per second squared one joule is the energy... 

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