Quantum‐classical transition of the dissipative wave packet dynamics for barrier scattering

Abstract

AbstractA nonlinear equation based on the Schrödinger–Langevin equation is employed to analyze the quantum‐classical transition of dissipative systems for wave packet barrier scattering. The transition equation is obtained by subtracting a modified quantum potential term depending on a degree of quantumness in the Schrödinger–Langevin equation, and it provides a continuous description for the transition process of dissipative systems from purely quantum to purely classical regimes. Important properties possessed by the equation are derived. The energy dissipation rate of the dissipative system does not depend on the degree of quantumness. It is shown that the equations of motion for the expectation values of the position and momentum operators for dissipative systems hold for all the degree of quantumness. This feature establishes the correspondence between classical and quantum dissipative systems. Computational results for the transition process of dissipative wave packet dynamics and transition trajectories are presented and analyzed for model systems involving the propagation of a free Gaussian wave packet and the wave packet scattering from an Eckart barrier. Computational results demonstrate that the agreement between the classical‐limit transition trajectories and classical trajectories is excellent, except in some regions. The single‐valued transition wave function implies that transition trajectories cannot pass through the same configuration space point at the same time.