Longitudinal vibrations vibration coupling

The smaller value of i found experimentally suggests that the coupling constant g is larger than we assumed. In our model of DNA we considered hole self-trapping due to interaction with longitudinal vibrations only. As discussed in Sect. 2.1, other degrees of freedom may also contribute to the coupling constant. 

Appendix II. Effect of Coupling Between Longitudinal and Rotational Vibrations of HB Molecules Appendix III. Applicability of Classical Theory for Harmonic Longitudinal Vibration... 

Below, unlike the work by Tseitlin, Gaiduk, Nikitov, 2005, denoted TGN, we shall not take into account a coupling of two harmonic motions longitudinal vibration and reorientation. This coupling is considered in the second part of the review. 

Figure 9 The partial absorption coefficients stipulated by harmonic reorientation (a) and longitudinal vibration (b) of HB molecules. Calculation for water H20 at the temperature 20.2°C with account of coupling of these vibration modes (solid lines) and with neglect of such coupling (open circles).

Ueha proposed a two-vibration-mode coupled type (Fig. 4.1.38), that is, a torsional Langevin vibrator was combined with three multilayer actuators to generate larger longitudinal and transverse surface displacements of the stator, as well as to control their phase difference [62]. The phase change can change the rotation direction. 

A well-known concept to introduce collective vibrations of atoms is based on the dynamics of a linear chain of atoms, which are coupled via harmonic springs to each other. Let us consider the longitudinal vibrations for such an infinite chain where we consider the atomic displacements u around the atomic equilibrium positions, according to Figure 8.2.1a. The force F acting on atom n is the sum... 

For the particular case of longitudinal optical modes, we found in Eq. (9-27) the electrostatic electron-phonon interaction, which turns out to be the dominant interaction with these modes in polar crystals. Interaction with transverse optical modes is much weaker. There is also an electrostatic interaction with acoustic modes -both longitudinal and transverse which may be calculated in terms of the polarization generated through the piezoelectric effect. (The piezoelectric electron phonon interaction was first treated by Meijer and Polder, 1953, and subsequently, it was treated more completely by Harrison, 1956). Clearly this interaction potential is proportional to the strain that is due to the vibration, and it also contains a factor of l/k obtained by using the Poisson equation to go from polarizations to potentials. The piezoelectric contribution to the coupling tends to be dominated by other contributions to the electron -phonon interaction in semiconductors at ordinary temperatures but, as we shall see, these other contribu-... 

In the solid state, the polar phonons (those that are IR active) split into two components, the transverse optical mode (TO) and the longitudinal optical mode (LO). This TO/LO splitting occurs because the electric field associated with the transverse wave = 0 while that associated with the longitudinal wave is 0. The coupling of these modes with the electric fields associated with the vibration gives rise to Vlo > Vto- This factor is relevant in relation to the shape and interpretation of the IR spectra of solid materials and will be further considered below. 

---