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We present a path - integral approach to treat a 2D model of a quantumbifurcation. The model potential has two equivalent minima separated by one ortwo saddle points, depending on the value of a continuous parameter. Tunnelingis therefore realized either along one trajectory or along two equivalentpaths. Zero point fluctuations smear out the sharp transition between these tworegimes and lead to a certain crossover behavior. When the two saddle pointsare inequivalent one can also have a first order transition related to the factthat one of the two trajectories becomes unstable. We illustrate these resultsby numerical investigations. Even though a specific model is investigated here,the approach is quite general and has potential applicability for varioussystems in physics and chemistry exhibiting multi-stability and tunnelingphenomena.Comment: 11 pages, 8 eps figures, Revtex-

Competing tunneling trajectories in a two-dimensional potential with variable topology as a model for quantum bifurcations