Two-dimensional tunneling in a potential with two transition states

✍ Scribed by V.A. Benderskii; V.I. Goldanskii; D.E. Makarov

• Publisher: Elsevier Science
• Year: 1991
• Tongue: English
• Weight: 391 KB
• Volume: 186
• Category: Article
• ISSN: 0009-2614
• DOI: 10.1016/0009-2614(91)90461-h

✦ Synopsis

Two-dimensional tunneling is studied for a model potential V( Q, X) = V,(Q) t tl(Q'-Qa)X*+ @X4. Vo(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 p= 1 /k&F The doubly degenerate path near the saddle points (i) occurs in the Arrhenius region (b< /?,( QO)) and is replaced by the two-dimensional instanton (ii) at the cross-over temperature a( Q,,). At & less than the critical value, the one-dimensional instanton (iii) arises as the temperature drops. As Q, decreases, the region of existence of the two-dimensional instanton vanishes.