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The quantum version of Kramers turnover theory is generalized beyond the parabolic barrier approximation. The result is a uniform instanton-based quantum Kramers turnover theory that does not display any divergence at what is known as the crossover temperature. The theory is analyzed using a model of a particle trapped in a cubic potential. As the temperature is lowered, the maximum in the Kramers turnover curve moves to lower friction values. When the temperature is sufficiently low, the quantum rate at low friction becomes almost independent of the friction strength.
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Eli Pollak (2024) studied this question.
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