Ivanov N. The dinamical laws of quantum systems with resonance levels.

The object of research is the wave packet tunneling through open quantum systems. Subject of investigation is, firstly, the packet and system parameters that affect tunneling, and secondly, parameter values for packets that leave a system. The purpose of research is to apply the formalized approach (based on the modified saddle point method and the scattering matrix formalism) to study dynamic characteristics of quantum systems. The study used methods of analytical and numerical calculations. Research methods include basic quantum scattering theory, the modified saddle point method and Maple computational package. Theoretical results: for the first time, a general analytical solution of the problem is obatained. This solution can be used to study the processes and all their features. Practical results: based on the results it is possible to select parameter values of a system and a signal that will lead to minimum observed time delay. This should increase efficiency of nanoelectronic devices. Novelty: for the first time a general solution is obtained, along with all parameters of a system and a packet that affect tunneling process. The area of application for the obtained results includes quantum electronics and engineering.