A.L. Sanin, A.T. Bagmanov

Dynamical tunneling in quantum systems with two wells and barrier between them is the evolution process of the quantum wave packet transitions from one well into another and backward when packet energy is less than the barrier height. Investigation of this process represents not only abstract academic interest but has the fundamental significance for different applications in radio-electronics including elaboration of quantum computers. In scientific literature the polynomial model of double-well is wide-ly used, it represents the function superposition of fourth and second degrees in coordinate. Here, with increasing of coordinate the potential infinitely increases. In this paper it is offered the non-polynomial model of double-well potential which has horizontal asymptotics and finite depth of wells. By changing the parameters offered potential can be symmetric as well as non-symmetric, the well structure and barrier height can be varied. The model consists of exponential function, the power of its contents two terms which are inversely proportional to the coordinate modulus, it is smooth. The model behaves as coulomb if the coordinate is increased. But, if the coordinate is decreased, potential tends to a finite value. In context of this model, the calculations of energy spectrum and eigenfunctions were carried out. The ground and first exciting states play the essential role in dynamics of tunneling. The energy difference of these states determines the transition frequency of quantum wave packet from one well into other and back. Using numerical solutions for eigenfunctions of lowest states, the analytic approximation was used as the initial wave function in dynamical problem. Another initial condition was postulated as Gaussian packet located in one chosen well. The numerical integration of the non-stationary Shrödinger equations was performed under different initial conditions and varied distance between minima of symmetric potential. They demonstrate the basic temporal scale caused by the dynamical tunneling from one well into other. The temporal scales related with dynamical tunneling represent the periods of regular oscillations. By increasing distance between wells and growing of barrier height, the periods are also increased and corresponding them the frequencies are decreased. Separate calculations with non-symmetric potential demonstrate the similar properties. To emphasize these results it is necessarily to carried out the calculations the map of probability density on plane "coordinate-time", the phase trajectories on plane «mean coordinate - mean velocity» and the frequent Fourier analysis of temporal dependence for mean coordinate. All those calculations were performed and showed the consistency of temporal scales and frequencies including the transition frequency between corresponding stationary states of quantum system. Quantum wave packet can be transported from one well into other under action of external force. If the force is sufficiently large, the packet can be injected and extracted from well. In paper, it is explored the action of external pulse force on wave packet and extraction of probable fluid from well in external domain.