Quasi-energy spectrum

Samuelides, M., Fleckinger, R., Touziller, L. and Bellissard, J. (1986). Instabilities of the quantmn rotator and transition in the quasi-energy spectrum, Europhys. Lett. 1, 203-208. 

For the parameters 8 = 2Qq and <2max = O0, corresponding to the path (a) on the surfaces in Fig. 19, we show in Fig. 20 the solution of the semiclassical Schrodinger equation (321). It features a STIRAP-like process inducing a complete population transfer for this choice of the delays. Two zones of the quasi-energy spectrum associated with the surfaces of Fig. 19 are pictured as a function of time in Fig. 21b. We notice that the state 11 0,0) is... 

The energy spectrum of the resonance states will be quasi-discrete it consists of a series of broadened levels with Lorentzian lineshapes whose full-width at half-maximum T is related to the lifetime by F = Fn. The resonances are said to be isolated if the widths of their levels are small compared with the distances (spacings) between them, that is... 

The molecular time scale may be taken to start at 10 14 s following energy absorption (see Sect. 2.2.3). At this time, H atoms begin to vibrate and most OH in water radiolysis is formed through the ion-molecule reaction H20+ + H20 H30+ + OH. Dissociation of excited and superexcited states, including delayed ionization, also should occur in this time scale. The subexcitation electron has not yet thermalized, but it should have established a quasi-stationary spectrum its mean energy is expected to be around a few tenths of an eV. 

As pointed out by Edmonds and Starace,12,13 the atoms are excited near the origin and can only escape in the z directions. The motion in the x,y plane is bound and is most likely to be the source of the quasi Landau resonances. To find the locations of the resonances it is adequate to ignore the z motion entirely and simply compute the energy spectrum of the motion in x,y plane. Applying the Bohr-Sommerfeld quantization condition leads to... 

Fig. 9.6 Quasi-Landau spectrum observed by laser excitation and field ionization of even parity, m = —2 states of Na in a magnetic field of 4.2 T. The arrows indicate the quasi-Landau levels, the highest energy magnetic states of each principal quantum number. The intermediate peaks are due to other levels. The numbers between the arrows give the level separation in units of fuoc. A WKB analysis predicts a spacing of 1.5 at W = 0, increasing with binding energy in agreement with the data. Relative intensities are not reliable due to...

Figure 1 Energy spectrum of the low-lying states of four electrons confined in a quasi-one-dimensional Gaussian potential with (D, a>z,a>xy) = (4.0, 0.1, 20.0) for different-size basis sets. Energy levels of different spin multiplicities are indicated by different colors (See the caption to Figure 2). The number in the round brackets specifies the total number of basis functions and the parameter v p specifies the extended polyad quantum number (See the text for details). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this book.)...

The energy spectrum of two electrons confined in a quasi-fwo-dimensional Gaussian potential has also been studied for the same set of the strengths of confinement as the corresponding quasi-one-dimensional cases, and are compared to them. The energy spectrum of the quasi-two-dimensional quantum dot is qualitatively different from that of the quasi-one-dimensional quantum dot in the small confinement regime. The origin of the differences is due to the difference in the structure of the internal space. 

It has been argued that, while the HOMO-LUMO energy difference suffers from systematic errors, a more reliable estimate of G can be obtained from the quasi-particle spectrum of the ionized system. For example, in NiO, the presence of an excess hole leads to the formation of a narrow band of unoccupied states in the VB region [249] (Fig. 11). It has been stressed [250] that the gap between this band and the CB edge approximates the optical/conductivity band gap. In Li NiO [251] and bulk NiO [249], this method yields a value of 4 eV, in agreement with optical absorption measurements [252]. It was also used to estimate G in an NiO(lOO) monolayer [85]. 

The absorption bands of these ions combine to form a quasi-continuous spectrum. Via a complex cascade, energy absorbed by the various ions is eventually transferred to the Sly lasing level of Ho3+. 

The density of electronic states in a 2-D solid is therefore remarkably different from the 3-D case. The spacing between the allowed energy levels in the bands increases, because fewer levels are now present Consequently, as soon as one dimension is reduced to nanometer size, dramatic changes due to quantum confinement occur, as for example the non-negligible zero-point energy. In 2-D materials the energy spectrum remains quasi-continuous, but the density of states now is a step function [17,19]. 

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