arXiv subjects
Publications and source records attributed to Dmytro Babyuk.
Process of dynamical tunneling in two-dimensional coupled potentials is considered within Bohmian approach to quantum mechanics. Quantum trajectories tend to go along the paths where potential energy increases and then decreases. It leads to a suggestion that dynamical and barrier tunneling are the same processes but the former is hidden due to specific potential surface.
A behavior of quantum states (superposition of two lowest eigenstates, Gaussian wave packet) in phase space is studied for one and two dimensional double well potential. Two dimensional potential is constructed from double well potential coupled linearly and quadratically to harmonic potential. Quantum trajectories are compared with classical ones. Preferable tunneling path in phase space is found. An influence of energy of initial Gaussian wave packet and trajectory initial condition on tunneling process is analyzed.. Coupling effect on trajectories and preferable tunneling path for two dimensional potential is studied.
A combined method for analyzing quantum dynamical equations which uses the Bohmian mechanics and the quantum phase space representation is proposed. It is based on a presentation of the wave function in phase space in a polar form. The combined method is very effective for comparison of classical and quantum dynamics for polynomial potentials of order no higher than second. Application for the harmonic oscillator and quartic double well potential is performed. Quantum fluxes and particle energy are derived by means of the proposed method.