  Two-particle tunneling in synchronous and asynchronous regimes is studied in
the framework of dissipative quantum tunneling. We show that the use of the
proposed model is justified by a comparison with realistic potential energy
surfaces of porphyrin and experimental dependence of the reaction rate on
temperature. The critical temperature T_c corresponding to a bifurcation of the
underbarrier trajectory is determined. The effect of a heat bath local mode on
the probability of two-dimensional tunneling transfer is also investigated. At
certain values of the parameters, the degeneracy of antiparallel tunneling
trajectories is important. Thus, four, six, twelve, etc., pairs of the
trajectories should be taken into account (a cascade of bifurcations). For the
parallel particle tunneling the bifurcation resembles phase transition of a
first kind, while for the antiparallel transfer it behaves as second order
phase transition. The proposed theory allows for the explanation of
experimental data on quantum fluctuations in two-proton tunneling in porphyrins
near the critical temperature.
