Interference term

Werbelow L G 1996 Relaxation processes cross correlation and interference terms Encyclopedia of Nuclear Magnetic Resonance ed D M Grant and R K Harris (Chichester Wiley) pp 4072-8... 

The first sum on the right is precisely the same as in Eq. (7-91) provided we let l l2 = pl. The remainder contains terms, sometimes called interference terms, that are not present in (7-91). 

Insufficient reason in risk analysis, 316 Integral curves, construction, 336 Interaction representation, 418 Interference terms in quantum mechanics, 425... 

In Eq. (12), l,m are the photoelectron partial wave angular momentum and its projection in the molecular frame and v is the projection of the photon angular momentum on the molecular frame. The presence of an alternative primed set l, m, v signifies interference terms between the primed and unprimed partial waves. The parameter ct is the Coulomb phase shift (see Appendix A). The fi are dipole transition amplitudes to the final-state partial wave I, m and contain dynamical information on the photoionization process. In contrast, the Clebsch-Gordan coefficients (CGC) provide geometric constraints that are consequent upon angular momentum considerations. 

In the more novel case of the P coefficient, only interference terms for which 7 = 1 1 arise, so now all summands contributing to contain phase shift information. This hints that the chiral parameters could be more sensitive to phase differences than traditional (3 parameters, and one would... 

It was shown in the preceding section that PECD can be anticipated to have an enhanced sensitivity (compared to the cross-section or p anisotropy parameter) to any small variations in the photoelectron scattering phase shifts. This is because the chiral parameter is structured from electric dipole operator interference terms between adjacent -waves, each of which depends on the sine of the associated channels relative phase shifts. In contrast, the cross-section has no phase dependence, and the p parameter has only a partial dependence on the cosine of the relative phase. The distinction between the sine... 

The interaction with the detector at slit A has changed the interference term from j7ab(x) to. (x). 

The former phase, external control tool that can be tuned to vary the interference term and hence the reaction outcome. The latter phase, 5(E), serves as an analytical tool that provides a route to the phases of the scattering wavefunctions. 

The third experimental knob is the relative amplitudes of the two laser fields. These are typically chosen to maximize the modulation depth without affecting the phase of the interference term. 

The interference term is thus of the form of Eq. (4), where in the present case 8s reflects the molecular as well as the environment properties. Within our occupation space formalism, it is given as a simple analytical function of system parameters, and its physical content is explicit. In the isolated molecule limit, where pure dephasing vanishes, Eq. (58) reduces to... 

Using a perturbative analysis of the time-dependent signal, and focusing on the interference term between the one- and two-photon processes in Fig. 14, we consider first the limit of ultrashort pulses (in practice, short with respect to all time scales of the system). Approximating the laser pulse as a delta function of time, we have... 

Interference term, two-pathway excitation, coherence spectroscopy, energy domain, 180—182... 

The indices k in the Ihs above denote a pair of basis operators, coupled by the element Rk. - The indices n and /i denote individual interactions (dipole-dipole, anisotropic shielding etc) the double sum over /x and /x indicates the possible occurrence of interference terms between different interactions [9]. The spectral density functions are in turn related to the time-correlation functions (TCFs), the fundamental quantities in non-equilibrium statistical mechanics. The time-correlation functions depend on the strength of the interactions involved and on their modulation by stochastic processes. The TCFs provide the fundamental link between the spin relaxation and molecular dynamics in condensed matter. In many common cases, the TCFs and the spectral density functions can, to a good approximation, be... 

That all scattering by phonons is inelastic has been disproved by Afonin and Schmidt (1986) see Chapter 10, where we maintain none the less that L-,=a in liquids, all collisions being inelastic, so the quantum-interference term is absent. 

We emphasize that the use of g in these equations may be justified only if /—a, because of the Edwards cancellation theorem (Section 6). We should expect a metal-insulator transition to occur for some value of in the neighbourhood of For several liquid systems there is experimental evidence that the interference term in (52) is absent. Thus for liquid TeTl alloys, with variation of composition and temperature, for a less than the Ioffe-Regel value e2/3hai the conductivity is proportional to the square of the Pauli paramagnetic susceptibility and then to 2. These results are due to Cutler (1977). Warren (1970a, b, 1972a, b) examined... 

Mott (1985,1989a) proposed that in liquids all collisions are inelastic, so that l—Li and the interference term in (52) vanishes. Thus, in a sense, amorphous solids, where strong phonon interaction leads over a certain temperature range to the relation Lx a. We find that, as the energy drops into a region of small density of states, increases and the normal localization condition again becomes valid. 

We note that the intermolecular force effect was once thought to lead in general to positive M 0, but Table 6.6 shows that at low temperatures the M are negative. The interference terms M Q, on the other hand, are generally negative (unless they are zero) and may actually be more significant than the force terms for the zeroth moments. 

The remarkable conclusion is that the microscopic quantum state, specified by the wave function ip, can be described on a macroscopic level by the probability distribution Pj. A single pure state corresponds to a macroscopic ensemble. The interference terms that are typical for quantum mechanics no longer appear. Incidentally, this resolves the paradox of Schrodinger s cat and, in general, the quantum mechanical measurement problem. )... 

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