A quartic trial action in the path-integral approach to an asymmetrical double-well potential

An improved variational path-integral method including partial fourth-order fluctuational modes is proposed, where three variational parameters are introduced and determined by minimizing the effective classical potential. It is shown that the effective classical potential and the free energy calculated by the present approach are better than that of the second-order variational one, indeed, our method can appearance rich quantum saddle behavior of an asymmetrical double-well potential and avoid dangerous modes.