2D-tunnel bifurcations for interacting quantum molecules in the matrices of metamaterials

The problem of controllability for 2D-tunnel bifurcations in systems with quantum molecules in a dielectric matrix of a metamaterial in the external electric field at finite temperature has been investigated. Usage of the theory of quantum tunneling with dissipation to study the interaction of quantum molecules (QM) with contact medium is productive, because, in spite of usage of the instanton approach, it is possible to get the main results in an analytical form with account of the environment effects on the tunneling process, which it is not possible in other often used approaches. A theoretical study of the electric field influence on the 2D-quantum tunneling for quantum molecules in the matrix of a metama-terial (with negative effective permittivity) at finite temperature has been fulfilled in the instanton approximation. It is shown that a stable regime of 2D-bifurcations in such matrix can take place in a narrower range of parameters than in the case of usual dielectric matrix. An important problem in this case is to identify the range of experimentally realizable values of the relative dielectric permittivity (including negative values) for the matrix environment that allows realization of the 2D-bifurcations regime. A range of the control parameters (electric field, temperature, and the relative permittivity of the meta-material matrix), in which the regime of stable 2D-bifurcations in the system of quantum molecules, as well as in the system “AFM/STM cantilever - quantum dot or quantum molecule”, can take place, has been theoretically investigated. The “phase diagram” for the stable 2D-bifurcations regime for tunnel current in the matrix of a metamaterial in dependence on controllable parameters (the inverse temperature, electric field intensity and values of the negative relative permittivity for the heat bath environmental matrix), has been presented. It is shown that in contrast to usual dielectric matrices, in the case of the metamaterial matrix the region of stable 2D-bifurcation is significantly narrowed, which is probably due to inversion of the sign of the tunneling particles interaction.