By John Fortier

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15); and local vibrations with bounded area for the changes of the angle (region (LMl)) in Fig. 15). 52) while ler and 10 can be obtained from the equations: h(J ) er = _ eler A(10) = 2 ' o. 73) 42 2. 14: The set of phase trajectories z (J, I) of the system for 10 (E) > 4cD. The solid curve (separatrix line) 1=10 separates the regions of local (LMI) and local (LM2) modes, while I = Ie separates local modes (LM2) from normal antisymmetric (NMA) ones. Normal symmetric modes (NMs) in the present case are absent.

The described changes of phase portraits of the system with the changes in its energy lead to the conclusion on the instability of symmetric normal vibrations with respect to energy fluctuations. Really, due to the inequality e « 1 the threshold for the disappearance of the region (NMs) of symmetric vibrations E = 4eD (1 - e) is a small quantity itself. Thus, even a small increase in energy destroys the symmetric normal mode. As the volume of region (NMs) is of the order of 4eD « 1, there are no quantum states, corresponding to a symmetric normal mode in the case of strong anharmonicity (not too large D).

15); and local vibrations with bounded area for the changes of the angle (region (LMl)) in Fig. 15). 52) while ler and 10 can be obtained from the equations: h(J ) er = _ eler A(10) = 2 ' o. 73) 42 2. 14: The set of phase trajectories z (J, I) of the system for 10 (E) > 4cD. The solid curve (separatrix line) 1=10 separates the regions of local (LMI) and local (LM2) modes, while I = Ie separates local modes (LM2) from normal antisymmetric (NMA) ones. Normal symmetric modes (NMs) in the present case are absent.

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