The author establishes the principal contradiction between the requirements for increasing the energy lifetime of a signal and attaining wide frequency bandwidth of a resonator. This can be resolved on the basis of stochastic mechanics principles. The ideas which lie at the basis of this problem are connected with the fundamental concepts of stochastic dynamics of material particles such as local instability and mixing. Under a local instability it is understood that there is an exponential divergence of the particle motion trajectories.
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