Susceptibility density matrix approach

The nonlinear interaction of light with matter is useful both as an optical method for generating new radiation fields and as a spectroscopic means for probing the quantum-mechanical structure of molecules [1-5]. Light-matter interactions can be formally classified [5,6] as either active or passive processes and for electric field based interactions with ordinary molecules (electric dipole approximation), both may be described in terms of the familiar nonlinear electrical susceptibilities. The nonlinear electrical susceptibility represents the material response to incident CW radiation and its microscopic quantum-mechanical formalism can be found directly by diagrammatic techniques based on the perturbative density matrix approach including dephasing effects in their fast-modulation limit [7]. Since time-independent (DC) fields can only induce a... 

Using the same density matrix approach, we can obtain the imaginary part of the susceptibility, which accounts for absorption. 

Spectroscopic methods are very useful for determining molecular properties. Time-resolved spectroscopic methods are useful for monitoring the evolution of the molecular properties in real time. Moreover, time-resolved spectroscopic techniques have the best time resolution available among all kinds of time-resolved experimental techniques. Thus, very often time-resolved spectroscopic methods reveal the dynamics of a molecular system in the non-equilibrium regime. In this section, the density matrix method is applied to calculate the spectroscopic properties of molecular systems. These include the linear and non-linear optical processes, in equilibrium or non-equilibrium cases. The approach is based on the susceptibility theory. 

In the Atoms In Molecules approach (Section 9.3), the Laplacian (trace of the second derivative matrix with respect to the coordinates) of the electron density measures the local increase or decrease of electrons. Specifically, if is negative, it marks an area where the electron density is locally concentrated, and therefore susceptible to attack by an electrophile. Similarly, if is positive, it marks an area where the electron density is locally depleted, and therefore susceptible to attack by a... 

We applied the generating functional approach to the periodic Anderson model. Calculation of the electron GFs gdd, 9ds, 9sd and gss reduces to calculation of only the d-electron GF. For this, an exact matrix equation was derived with the variational derivatives. Iterations with respect to the effective matrix element Aij(to) allow to construct a perturbation theory near the atomic limit. Along with the self-energy, the terminal part of the GF Q is very important. The first order correction for it describes the interaction of d-electrons with spin fluctuations. In the paramagnetic phase this term contains a logarithmic singularity near the Fermi-level and thus produces a Kondo-like resonance peak in the d-electron density of states. The spin susceptibility of d-electrons... 

Ceramic composites, which consist of a ceramic fiber or whisker reinforcement embedded in a ceramic matrix, are less susceptible to the brittle failure which is characteristic of bulk ceramics because the reinforcement intercepts, deflects, and slows crack propagation (see Ch. 14, Secs. 6 and 7). At the same time, the load is transferred from the matrix to the fibers to be distributed uniformly. A common ceramic composite consists of a SiC-fiber array and SiC or Si3N4 matrices produced by chemical-vapor infiltration (CVI). Densities approaching 90% are achieved.0 10 ... 

---