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Tunneling of two particles in synchronous and asynchronous regimes is studied in the framework of dissipative quantum tunneling. 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.Comment: RevTeX4, twocolumn, 12 pages, 11 figures (17 eps-files). Revised version, to appear in Phys. Rev.

Tunneling of two particles interacting with each other is considered. The semiclassical (instant on) action is calculated taking into account the interaction with an oscillator bath. It is shown that for repulsive interaction between particles, there are two regions of tunneling depending on the value of the interaction constant a. For values larger than a critical value a c , simultaneous transition occurs. For a fixed interaction constant, there is a critical temperature at which a change of tunneling regime takes place (from single particle to cooperative tunneling). The same analysis has also been applied to a model including the interaction with phonons. The transition to the cooperative tunneling regime of two particles moving in opposite direction should be observable in optical absorption spectra.

We observe a series of sharp resonant features in the tunnelling differential conductance of InAs quantum dots. We found that dissipative quantum tunnelling has a strong influence on the operation of nano-devices. Because of such tunnelling the current-voltage characteristics of tunnel contact created between atomic force microscope tip and a surface of InAs/GaAs quantum dots display many interesting peaks. We found that the number, position, and heights of these peaks are associated with the phonon modes involved. To describe the found effect we use a quasi-classical approximation. There the tunnelling current is related to a creation of a dilute instanton-anti-instanton gas. Our experimental data are well described with exactly solvable model where one charged particle is weakly interacting with two promoting phonon modes associated with external medium. We conclude that the characteristics of the tunnel nanoelectronic devices can thus be controlled by a proper choice of phonons existing in materials, which are involved.

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