Abstract
The influence of an electric field on 1D and 2D tunneling in a quantum molecule located in dielectric and metamaterial (with effective negative permittivity) matrices at a finite temperature has been theoretically investigated within the one-instanton approximation. It is shown that the stable mode of 2D bifurcations in a metamaterial matrix can be implemented in a much narrower range of parameters in comparison with conventional dielectric matrices. The dependence of the probability of 1D dissipative tunneling on the strength of an external electric field is qualitatively compared with the experimental tunnel I-V characteristic of semiconductor (InAs/GaAs) quantum dots.