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Local Classical and Quantum Criticality due to Electron-Vibration Interaction

We study the local classical and quantum critical properties of electron-vibration interaction, represented by the Yu-Anderson model. It exhibits an instability, similar to the Wentzel-Bardeen singularity, whose nature resembles to weakly first order quantum phase transitions at low temperatures, and crosses over to Gaussian behaviour with increasing temperature. We determine the dominant energy scale separating the quantum from classical criticality, study the effect of dissipation and analyze its impact on correlation functions. Similar phenomenon should be observable in carbon nanotubes around local defects.