Time domain, resonances states

Equation (A 1.6.94) is called the KHD expression for the polarizability, a. Inspection of the denominators indicates that the first temi is the resonant temi and the second temi is tire non-resonant temi. Note the product of Franck-Condon factors in the numerator one corresponding to the amplitude for excitation and the other to the amplitude for emission. The KHD fonnula is sometimes called the siim-over-states fonnula, since fonnally it requires a sum over all intennediate states j, each intennediate state participating according to how far it is from resonance and the size of the matrix elements that coimect it to the states i. and The KHD fonnula is fiilly equivalent to the time domain fonnula, equation (Al.6.92). and can be derived from the latter in a straightforward way. However, the time domain fonnula can be much more convenient, particularly as one detunes from resonance, since one can exploit the fact that the effective dynamic becomes shorter and shorter as the detuning is increased. 

D. Le Botlan, L. Ouguerram, L. Smarfi and L. Pugh, Characterization of a semisolid state in milk fat through T2 resolved T1 distributions by time domain nuclear magnetic resonance, J. Am. Oil Chem. Soc., 76(2), 255-261 (1999). 

The original linear prediction and state-space methods are known in the nuclear magnetic resonance literature as LPSVD and Hankel singular value decomposition (HSVD), respectively, and many variants of them exist. Not only do these methods model the data, but also the fitted model parameters relate directly to actual physical parameters, thus making modelling and quantification a one-step process. The analysis is carried out in the time domain, although it is usually more convenient to display the results in the frequency domain by Fourier transformation of the fitted function. 

CW experiments (sometimes called stationary or steady state ) are ones in which either no modulations are used, or they are so low in frequency that no spectral complications ensue. (This is only approximately the case if 100 kHz field modulation is employed. This frequency gives rise to modulation sidebands and, under saturating conditions, rapid passage effects.) Time-domain ESR involves monitoring the spin system response as a function of time. Pulse ESR can be divided into two broad categories the response of spin systems to sequences of microwave pulses (spin echo) and the response of spin systems to step changes in resonance conditions (saturation recovery). 

Figure 1. Current Nanoscale Optofluidic Sensor Arrays, (a) 3D rendering of the NOSA device, (b) 3D rendering after association of the corresponding antibody to the antigen immobilized resonator, (c) Experimental data illustrating the successful detection of 45 pg/ml of anti-streptavidin antibody. The blue trace shows the initial baseline spectrum corresponding to Fig. la where the first resonator is immobilized with streptavidin. The red trace shows the test spectra after the association of anti-streptavidin. (d) Finite difference time domain (FDTD) simulation of the steady state electric field distribution within the 1-D photonic crystal resonator at the resonant wavelength, (e) SEM image demonstrating the two-dimensional multiplexing capability of the NOSA architecture.

Rotational reorientation of frans-stilbene in alkane solution at room temperature occurs in the 10 to 30-ps time domain [347]. Rare-gas complexes with trons-stilbene were studied by purely rotational coherence spectroscopy [51,364]. Moreover, the decay kinetics of excited trans-stil-bene-cyclodextrin complexes were examined [366], It is worth mentioning that great progress has also been made in high-resolution spectroscopy [52, 369-372], Resonance coherent Raman spectroscopy showed a large enhancement of the electronic hyperpolarizability of t with respect to ground state trons-stilbene [374]. Vibrational motions were observed with ps transient Raman spectroscopy [375]. 

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