2-DIMENSIONAL TUNNELING IN A POTENTIAL WITH 2 TRANSITION-STATES

Two-dimensional tunneling is studied for a model potential V(Q,X) = V0(Q) + 1/2-lambda(Q2-Q0(2))X2 + 1/4-alpha-X4. V0(Q) is a symmetric double-well potential which has two transition states placed symmetrically in the dividing line. Extremal trajectories are shown to be of three types replacing each other at bifurcation values of the parameters Q0 and beta = 1/k(B)T: The doubly degenerate path near the saddle points (i) occurs in the Arrhenius region (beta < beta(c)(Q0)) and is replaced by the two-dimensional instanton (ii) at the cross-over temperature beta(c)(Q0). At Q0 less than the critical value, the one-dimensional instanton (iii) arises as the temperature drops. As Q0 decreases, the region of existence of the two-dimensional instanton vanishes.