Effective Landau theory for crossover from thermal hopping to quantum tunnelling

Abstract

In this paper the decay rate is obtained accurately near the crossover temperature. Because of the strong fluctuations near the crossover temperature a method called the effective Landau theory beyond the Gaussian semiclassical approximation is developed. We find that in the crossover region the transition rate of the first-order transition changes much more sharply than that of the second-order one. For both cases there is no discontinuity of transition rate for any of the order derivatives.