Bloch spectral function

FIGURE 34 Bloch spectral function of Gd in the hexagonal BZ, calculated at the Fermi energy. 

FIGURE 35 Bloch spectral function of Gd on the HLMK plane of the hexagonal BZ. Panels (A), (B), and (C) are for c/a ratios 1.54,1.57, and 1.66, respectively, with theoretical unit cell volumes used. The centre of the plane is the L point. Nesting vectors are indicated by arrows. The colour plot can be found in Hughes et al. (2007). 

Figure 4 Spin-resolved Bloch spectral functions on the Ga-sublattice for (a) (Gao.96Mno.o5)As and for (b) (Gao.94Mno.o5Aso.or)As (full lines). Bloch spectral functions of the reference GaAs host (dashed lines) are labeled by correspondirtg group notations. The Femti level coincides with the energy zero.

Within the Debye approximation the spectral functions oc F are proportional to (o in the energy range co kgGo (0 denotes the Debye temperature). This leads to a temperature dependence of the matrix elements Qoo from which the well known Bloch-Griineisen relation for pp follows (see Blatt 1968). For the low- and high-temperature regions the Bloch-Griineisen law reveals ... 

The resonances observed under MAS and strong proton decoupling were separated and analyzed as a function of the delay between scans to infer the relaxation times, T, and to extrapolate the corresponding intensities to infinite delay. No new spectral features were detected under a Bloch decay experiment, as compared to those under a CP/MAS experiment. The extrapolated Bloch decay intensities were then compared with that of a standard. The results of these measurements are presented in Table 1, The number of surface platinum atoms was also calculated on the basis of the Pt dispersion and Pt loading. Subsequently, the number of chemisorbed carbon atoms per surface platinum atom (Table 1, last column) was calculated. The results indicated that there were 4.0 0.6 chemisorbed carbon atoms per one surface Pt atom and 10.2 1.0 carbon atoms in the highly... 

Since Peng and Wagner (1992) formulated spectral density mapping techniques which can diredly determine the spectral density fimction at severd frequencies, the isotropic tumbling or the Lipari-Szabo (1982) models may be too simplistic. Finding an acceptable spectral density function then requires an adequate motional model. The recent version of the BLOCH program by Madrid and Jardetzky (unpublished) can take any spectral density function as input and optimize the structure ensemble relative to Ihe NOE pattern. However, the basic problem of defining the correct spectral density function for each case remains. 

In this context, it is worthwhile to recall the quantum jump approach developed in the quantum optics community. In this approach, an emission of a photon corresponds to a quantum jump from the excited to the ground state. For a molecule with two levels, this means that right after each emission event, = 0 (i.e., the system is in the ground state). Within the classical approach this type of wave function collapse never occurs. Instead, the emission event is described with the probability of emission per unit time being Fp (t), where Pee(0 is described by the stochastic Bloch equation. At least in principle, the quantum jump approach, also known as the Monte Carlo wave function approach [98-103], can be adapted to calculate the photon statistics of a SM in the presence of spectral diffusion. 

Like the exact QDT counterpart [cf. Eq. (4.6)], the POP-CS-QDT preserves both the reduced Gaussian dynamics and the effective local field pictinre for the DBO system. Its TZg [Eq. (4.11a)] has the same dissipation superoperator terms as those in ]Zf [Eq. (4.6b)]. The first and the last terms in the right-hand-side of Eq. (4.11a) for TZg or Eq. (4.6b) for are mainly responsible for the energy renormalization (or self-energy) contribution [38] and their dynamics implications are often neglected in phenomenological quantum master equations such as the optical Bloch-Redfield theory [36]. Note that the bath response function relates to the spectral density as [cf. Eq. (2.8)]... 

Krainik, Lisenko, Zhurakovsky and Ivashchenko (1989) also calculated the Fermi surface of MoC, for x = 1.0,0.7,0.5,0.75. As the Fermi surface analogue for nonstoichiometric compounds the authors took the spectral Bloch function characterising the probability of electron location at the state with the wave vector k and energy Epi... 

The interaction of the particle with its surroundings causes a random shift of the phase of the particle s wave function in each of its steady states, which is not necessarily accompanied by the decay of the particle to the lower level. The mean time of such a phase relaxation is denoted by T2, and the relaxation itself is frequently referred to as transverse relaxation (Bloch 1946). The phase relaxation has no effect on the relaxation of the population of levels, but it broadens the spectral line of the 1 —> 2 transition. The homogeneous half-width F of the Lorentzian in eqn (2.47) is related to the time T2 by a simple relation at Ti T2 ... 

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