Frequency-dependent phase, definition

These results are the same as those obtained by Freund, Herbst, Mariella and Klemperer [112] except for the. /-dependent phase factors in our matrices. These arise because of our specific definitions of the parity-conserved basis function and are necessary if the energies of the A-doublet components are to alternate with J. If we know the values of the five molecular constants appearing in these matrices, we can calculate the energies of the levels, of both parity types, for each value of J. In practice, of course, it was the task of the experimental spectroscopists to solve the reverse problem of determining the molecular parameters from the observed transition frequencies. 

A more direct definition of a dielectric is a material in which the capacitive (displacement) current is larger than the in-phase current, wC > G or f > gUtze. According to this definition, saline (a = 1 S/m, e = 80 x 8.85 x 10 F/m) is a conductor for f < 250 MHz, and a dielectric for f > 250 MHz. At sufficiently high frequencies, even a metal becomes a dielectric. The definition is frequency dependent, and this is not very practical for a general grouping of materials. In any case, a material is classified as a dielectric if it has an ability to store energy capacitively, not just dissipate it. 

Fig. 7.12 Frequency dependence of the real solid line) and imaginary dash curve) parts of the dielectric permittivity of an isotropic liquid (a) and the definition of the phase angle < ) (b)...

Propagation constant F and characteristic impedance Zq of a conductor are frequency dependent as they are functions of the impedance of the conductor, as explained in Section 1.2. It should be noted that a and p in Section 1.3.4.1 (see Figure 1.10) are not frequency dependent (in the sense discussed in this section). The frequency dependence of the attenuation constant a(co) and phase constant P(co) in Section 1.3.4.1 comes from the definition of impedance Z and admittance Fof a conductor ... 

Despite random orientation of the molecule with respect to the direction of the laser beam polarization, the intensity of a Raman line for substances in the gaseous and liquid phase depends on the polarization of the incident beam and the symmetry of the vibrational mode. For geometries of Raman experiments as illustrated in Figure 17, the ratio of the X-polarized (IJ to the Z-polarized (In) Raman intensity at any frequency is, by definition, the depolarization ratio p ... 

According to classical theory the vibrational motion of a polyatomic molecule can be represented as a superposition of 3N-6 harmonic modes in each of which the atoms move synchronously (i.e. in phase) with a definite frequency v. These normal modes are characterized by time-dependent normal coordinates which indicate, on a mass-weighted scale, the relative displacement of the atoms from their equilibrium positions (Wilson et al., 1955). Figure 2 shows the general shape of the normal coordinates for a non-linear symmetric molecule AB2. The... 

The detachment frequency (Udiss is characteristic for the particular site x. It depends on the structure of the site but not on the general structure of the surface. The detachment frequency is, obviously, a system property. Being generally different from the deposition frequency cudep,, it cannot be used for the definition of the equilibrium of the crystal with its ambient phase. The equality (eq. 2.16), however, involving and , can be used for the definition of the equilibrium coverages as a function of the potential. 

Within the density-matrix formalism (Vol. 1, Sect. 2.9) the coherent techniques measure the off-diagonal elements pab of the density matrix, called the coherences, while incoherent spectroscopy only yields information about the diagonal elements, representing the time-dependent population densities. The off-diagonal elements describe the atomic dipoles induced by the radiation field, which oscillate at the field frequency radiation sources with the field amplitude Ak(r, t). Under coherent excitation the dipoles oscillate with definite phase relations, and the phase-sensitive superposition of the radiation amplitudes Ak results in measurable interference phenomena (quantum beats, photon echoes, free induction decay, etc.). 

The type of neutron scattering depends on the incident wave frequency vq and the scattered wave frequency v. If vq is equai to v, we have coherentiy scattered radiation if not, we have incoherently scattered radiation. In coherently scattered radiation, phases of the electric and magnetic fields of incident radiation and those of scattered radiation are in a definite relation to each other. 

The semi-log plots in FIGURES 6 and 7 show the temperature dependence of the relaxation frequencies for the two compounds. The Debye behaviour of the isotropic phase with the expected Arrhenius temperature dependence is quite evident in the oriented phases instead the temperature dependence of the two relaxation times is clearly non-linear on a log scale, thus preventing the definition of an activation energy for the relaxation processes involved. In TABLE 1 we have... 

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