By using numerical and semiclassical methods, we evaluate the quantum
breaking, or Ehrenfest time for a wave packet localized around classical
equilibrium points of autonomous one-dimensional systems with polynomial
potentials. We find that the Ehrenfest time diverges logarithmically with the
inverse of the Planck constant whenever the equilibrium point is exponentially
unstable. For stable equilibrium points, we have a power law divergence with
exponent determined by the degree of the potential near the equilibrium point.Comment: 4 pages, 5 figure
